leqciaTa kursi saganSileqciaTa kursi saganSi · PDF file4 leqciaTa kursi xelovnur inteleqtSi leqciaTa kursi xelovnur inteleqtSi is gamoiyenebs ra mTel Tavis gamocdilebas, rac mas gaaCnia

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leqciaTa kursi saganSileqciaTa kursi saganSileqciaTa kursi saganSileqciaTa kursi saganSi

xelovnuri inteleqtixelovnuri inteleqtixelovnuri inteleqtixelovnuri inteleqti

asocirebuli profesori z. qoClaZeasocirebuli profesori z. qoClaZeasocirebuli profesori z. qoClaZeasocirebuli profesori z. qoClaZe

leqcia #1. leqcia #1. leqcia #1. leqcia #1.

xelovnuri inteleqtis warmoSoba da ganviTareba xelovnuri inteleqtis warmoSoba da ganviTareba xelovnuri inteleqtis warmoSoba da ganviTareba xelovnuri inteleqtis warmoSoba da ganviTareba

1.1. ras Seiswavlis xelovnuri inteleqti. 1.1. ras Seiswavlis xelovnuri inteleqti. 1.1. ras Seiswavlis xelovnuri inteleqti. 1.1. ras Seiswavlis xelovnuri inteleqti. adamianebi imiT gamoirCevian sxva cocxali

arsebebisagan, rom maT gaaCniaT azrovnebis unari. ukve mravali saukunea adamiani cdilobs

Cawvdes am fenomens, gaigos Tu rogor axerxebs is gare samyaros Secnobas grZnobaTa

organoebis saSualebiT, ukve erTxel Sexvedrili situaciebis damaxsovrebas, swavlas maT

safuZvelze, Tavisi codnis ganzogadebas, swori gadawyvetilebebis miRebas logikuri

msjelobis safuZvelze da Tavisi moTxovnilebebis dasakmayofileblad gare samyaros

marTvasa da Secvlas. swored aseT qmedebaTa erToblioba qmnis adamianis iseT qcevas,

romelsac Cven vuwodebT inteleqtualurs.

xelovnuri inteleqtixelovnuri inteleqtixelovnuri inteleqtixelovnuri inteleqti aris mecnierebis dargi, romelic cdilobs ara marto Seicnos

inteleqtis buneba, aramed Seqmnas kidec (zogjer swored esaa ufro mTavari)

inteleqtualuri qcevis mqone xelovnuri sistemebi, anu rogorc maT uwodeben xelovnuri

inteleqtualuri sistemebi.

xelovnuri inteleqti mecnierebis erTerTi yvelaze axalgazrda dargia. pirveli

Sromebi am mimarTulebiT gaCnda meore msoflio omis Semdeg, xolo termini – xelovnuri

inteleqti pirvelad gamoiyenes 1956 wels. misi warmoSobac da ganviTarebac mWidrodaa

dakavSirebuli kompiuterul teqnikasTan da es ra Tqma unda SemTxveviTi araa. yvela is

zemoTCamoTvlili qmedebebi, romlebic gansazRvraven inteleqts, rogorc fenomens, Tavisi

arsiT warmoadgenen informaciul procesebs, anu yvela am qmedebis dros xdeba

informaciis miReba, damuSaveba, Senaxva da gadacema. kompiuteruli teqnikis warmoSobamde

aseTi unari gaaCndaT mxolod cocxal organizmebs (sxvadasxva doneze). kompiuterebma

saSualeba mogvces mogvexdina am procesebis meqanizacia teqnikur sistemebSi, rac gaxda

xelovnuri inteleqtualuri sistemebis ganviTarebis safuZveli.

Aswored amitomac kompiuterebis warmoSobasTan erTad gaCnda kiTxva – SeiZleba Tu

ara kompiuters gaaCndes inteleqtualuri qceva? ufro mZafrad ki es kiTxva JRerda ase:

SeuZlia Tu ara manqanas iazrovnos? am or kiTxvas Soris arsebiTi gansxvavebaa.

moviyvanoT aseTi magaliTi, SeuZlia Tu ara manqanas frena? ra Tqma unda SeuZlia, ityvis

nebismieri adamiani, TviTmfrinavi xom swored amisTvisaa Seqmnili. magram aq arsebiTia Tu

ra igulisxmeba cneba “frenis” qveS. Tu Cven frenis qveS vigulisxmebT mxolod CitiviT

frenas, maSin manqanas ukve aRar SeuZlia frena, mas SeuZlia mxolod haerSi gadaadgileba.

magram Tu frena swored gadaadgilebaa haerSi, maSin manqanasac SeuZlia frena. zustad

aseve, Tu azrovneba esaa mxolod da mxolod cocxali sistemebis prerogativa, Tu is

damaxasiaTebelia mxolod Tavis tvinSi mimdinare procesebisaTvis, maSin cxadia manqana

verasodes SeZlebs iazrovnos da is mxolod Seasrulebs raRac garkveul qmedebebs,

romlebic Sesrulebuli adamianis mier aRiqmeba rogorc azrovnebis procesi. magram Tu

azrovneba swored aseTi qmedebebis Sesrulebis unaria, maSin cxadia manqanac SeZlebs

azrovnebas. ra qmedebebzea laparaki da rogori qcevis SemTxvevaSi SeiZleba CaiTvalos,

rom kompiuteri azrovnebs? Yyvela im parametris CamoTvla, romlebsac unda

akmayofilebdes xelovnuri inteleqtualuri sistema, raTa misi qceva Sefasdes rogorc

leqcia #1. xelovnuri inteleqtis warmoSoba da ganviTarebaleqcia #1. xelovnuri inteleqtis warmoSoba da ganviTarebaleqcia #1. xelovnuri inteleqtis warmoSoba da ganviTarebaleqcia #1. xelovnuri inteleqtis warmoSoba da ganviTareba 3

azrovneba, albaT Zalian Znelia. 1948 wels ingliselma mecnierma a. tiuringma, romelic

TviTon idga kompiuterebis Seqmnis saTaveebTan, statiaSi “inteleqtualuri manqanebi” (A.

Turing A Intelligent Machinery ), SemogvTavaza “martivi” testi kompiuteris inteleqtualurobis

Sesamowmeblad. testi mdgomareobs SemdegSi: movaTavsoT erT oTaxSi adamiani, meoreSi

manqana da mesameSi gamomcdeli. maT Soris vizualuri kavSiri ar arsebobs da

gamomcdelma ar icis, romel oTaxSi zis adamiani da romel oTaxSi dgasMmanqana. isini

dakavSirebulni arian erTmaneTTan ise, rom gamomcdels SeuZlia gacvalos informacia

adamianTan da manqanasTan mxolod werilobiT. Tu gamomcdeli Tavis mier dasmul

SekiTxvebze miRebuli pasuxebis mixedviT ver SeZlebs gaarCios romel oTaxSi zis

adamiani, xolo romelSi manqana, maSin manqana SeiZleba CaiTvalos inteleqtualur

sistemad, winaaRmdeg SemTxvevaSi ki ara. cxadia, rom manqanas, romelic miiRebs

monawileobas aseT gamocdaSi unda gaaCndes minimum Semdegi SesaZleblobebi:

• USeeZlos teqstebis damuSavebateqstebis damuSavebateqstebis damuSavebateqstebis damuSaveba bunebriv enaze, rac miscems mas saSualebas

esaubros gamomcdels romelime bunebriv enaze;

• gaaCndes codnis warmodgeniscodnis warmodgeniscodnis warmodgeniscodnis warmodgenis saSualebebi, raTa SeZlos gaigos ras ekiTxeba

gamomcdeli;

• hqondes logikuri daskvnebislogikuri daskvnebislogikuri daskvnebislogikuri daskvnebis gamotanis unari, raTa SeZlos mis mexsierebaSi

Senaxuli codnisa da miRebuli informaciis safuZvelze gamoitanos daskvna da

upasuxos dasmul SekiTxvas;

• flobdes manqanuri daswavlismanqanuri daswavlismanqanuri daswavlismanqanuri daswavlis saSualebebs, rom SeZlos aRmoaCinos ukve

nacnobi situaciebi, gaerkves axal situaciebSi da moaxdinos maTze reagireba.

esaa tiuringis arasruli testi. sruli testis SemTxvevaSi gamomcdels gaaCnia

agreTve videokavSiri, romlis saSualebiTac mas SeuZlia Seamowmos obieqtis mier (ise,

rom ver xedavdes TviT obieqts) gare samyaros aRqmisa da masSi moqmedebis unari.

AaseT SemTxvevaSi manqanas damatebiT unda SeeZlos obieqtebis aRqma, anu unda hqondes

mxedvelobamxedvelobamxedvelobamxedveloba da gaaCndes robototeqnikurirobototeqnikurirobototeqnikurirobototeqnikuri saSualebebi, raTa SeeZlos sivrceSi

gadaadgileba da obieqtebiT manipulireba.

gasagebia rom aseTi universaluri programa dReisaTvis jer ar arsebobs, magram

yovelwliurad tardeba im programebis konkursi, romlebic yvelaze ukeTesad

daakmayofileben tiuringis tests da gamarjvebuls eniWeba lebneris prizi.

zemoTCamoTvlili eqvsi SesaZlebloba, romelsac unda flobdes programa, raTa

daakmayofilos tiuringis testi, faqtobrivad warmoadgens xelovnuri inteleqtis im eqvs

ZiriTad mimarTulebas, romlebic gansazRvraven dRes xelovnuri inteleqtis ganviTarebis

gzebs.

da mainc, davubrundeT mTavar kiTxvas da ganvmartoT ras niSnavs, rom manqana

azrovnebs? ganvixiloT martivi magaliTi, kvadratuli gantolebis amoxsna. TiTqmis

yvelasaTvis cnobilia am gantolebis amoxsnis algoriTmi. davsvaT aseTi kiTxva –

azrovnebs Tu ara adamiani kvadratuli gantolebis amoxsnis dros? pasuxi albaT Zalian

martivia. Tu man icis amoxsnis algoriTmi, is meqanikurad Casvavs ricxvebs formulaSi da

gamoiangariSebs pasuxs, magram Tu mas daaviwyda es formula, an arc arasdros uswavlia,

leqciaTa kursi xelovnur inteleqtSileqciaTa kursi xelovnur inteleqtSileqciaTa kursi xelovnur inteleqtSileqciaTa kursi xelovnur inteleqtSi 4

is gamoiyenebs ra mTel Tavis gamocdilebas, rac mas gaaCnia saerTod, Seecdeba raime

saSualebebiT miagnos am amoxsnas. moqmedebas pirvel SemTxvevaSi Znelad Tu vuwodebT

azrovnebis process, maSin, rodesac meore SemTxveva namdvilad warmoadgens azrovnebis

process imis da miuxedavad miagnebs Tu ara adamiani amoxsnas. A

imisaTvis, rom movaxdinoT azrovnebis procesis modelireba, pirvel rigSi Cven unda

vicodeT rogor azrovnebs adamiani. am sakiTxSi gasarkvevad arsebobs ori gza: pirveli

esaa introspeqciaintrospeqciaintrospeqciaintrospeqcia (mivyveT Cveni sakuTari azrovnebis process da gadmovceT igi sityvebis

saSualebiT), rac xSir SemTxvevaSi SeuZlebelia, radganac adamiani iSviaTad Tu SeZlebs

gadmosces zustad Tavisi azrovnebis procesi sityvebiT. meore gzaa SeviswavloT

azrovnebis procesi fsiqologiuri eqsperimentebis saSualebiT da CamovayaliboT

azrovnebis metnaklebad zusti Teoria, warmovadginoT is programis saxiT da Tu aseTi

programis Sesasvleli da gamosasvleli monacemebi da programis mier Sesrulebuli

qmedebebis droSi ganawileba zustad Seesabameba adamianis qcevas, es iqneba imis dasturi,

rom am programis zogierTi meqanizmi marTlac aRweris adamianis Tavis tvinSi mimdinare

informaciul procesebs.

Aam gziT wavidnen amerikeli mecnierebi a. niueli da g. saimoni, romlebmac 1956

wels warmoadgines pirveli programa xelovnur inteleqtSi – logikos Teoretikosilogikos Teoretikosilogikos Teoretikosilogikos Teoretikosi ( ( ( (LG) ....

am programis Seqmnis procesSi maT Caatares uamravi eqsperimenti, romelic mdgomareobda

imaSi, rom eqsperimentSi monawile pirebs (romlebsac ar hqondaT Seswavlili

maTematikuri logika) unda daemtkicebinaT maTematikuri logikis Teoremebi da amasTan

unda efiqraT “xmamaRla”, anu dawvrilebiT aReweraT ratom asrulebdnen ama Tu im

qmedebas. eqsperimentis Sedegebis damuSavebis Semdeg maT Camoayalibes TeoremaTa

damtkicebis procesSi adamianis qmedebis garkveuli wesebi da Seqmnes programa, romelic

xSir SemTxvevaSi moqmedebda ise, rogorc albaT imoqmedebda igive situaciaSi adamiani da

met-naklebi warmatebiT amtkicebda logikur Teoremebs..

DdRes am mimarTulebas ewodeba kognitologiakognitologiakognitologiakognitologia da warmoadgens disciplinaTSoris

mimarTulebas. fsiqologiuri eqsperimentebis safuZvelze iqmneba Tavis tvinSi mimdinare

procesebis garkveuli modeli, romelic meordeba kompiuterSi programis saxiT. Tu

Sedegebi damakmayofilebelia, anu Tu programis moqmedeba emTxveva adamianis moqmedebas,

maSin es modeli marTlac Seesabameba Tavis tvinSi momdinare procesebs.

Cven rodesac ganvixileT TviTmfrinavis magaliTi, aRvniSneT, miuxedavad imisa, rom

frinvelebi da TviTmfrinavebi sxvadasxva principebis da meqanizmebis safuZvelze

dafrinaven, orive SemTxvevaSi Sedegi erTi da igivea, isini gadaadgildebian haerSi. am

principidan gamomdinare albaT SesaZlebeli unda iyos, rom kompiuteri raime amocanis

gadaWris dros moqmedebdes ara aucileblad adamianis “azrovnebis kanonebis” Sesabamisad,

aramed sxva principebis, magaliTad logikuri kanonebis gamoyenebiT. Aam dros CvenTvis

mTavaria ara is, emTxveva Tu ara kompiuteris qceva adamianis qcevas, aramed is, aRwevs Tu

ara kompiuteri mis winaSe dasmuli amocanis amoxsnas, moqmedebs Tu ara am dros

racionalurad, anu mocemul situaciaSi irCevs Tu ara yvelaze saukeTeso qmedebas,

SeuZlia Tu ara ganazogados Tavisi codna da ase Semdeg.

imis mixedviT, am problemebidan ra Dufro mniSvnelovania mecnieris, Tu mecnierTa


jgufisaTvis gvaqvs xelovnuri inteleqtis sxvadasxva ganmarteba, romlebic ar

ewinaaRmdegebian erTmaneTs da romlebSic xelovnuri inteleqtis sxvadasxva aspeqtebia win

wamoweuli. moviyvanoT aseT ganmartebaTa ramdenime magaliTi:

“axali, saintereso mimarTuleba iseTi kompiuterebis Sesaqmnelad, romelTac

SeuZliaT iazrovnon”.

“im qmedebaTa avtomatizacia, romlebsac Cven vaigivebT adamianis azrovnebasTan, anu

iseTi qmedebebis, rogoricaa gadawyvetilebis miReba, amocanaTa amoxsna, daswavla da a.S.”.

“azrovnebis procesis Seswavla gamoTvliTi modelebis saSualebiT”.

“iseTi gamoTvlebis Seswavla, romlebic saSualebas gvaZleven vigrZnoT, vimsjeloT

da vimoqmedoT”.

“manqanebis Seqmnis xelovneba, romlebic asruleben funqciebs, romelTa Sesruleba

adamianis mier moiTxovs inteleqts”.

“mecniereba imis Sesaxeb, rogor vaswavloT kompiuters is, raSic mas adamianebi exla

jobnian”.

“gamoTvliTi inteleqti esaa mecniereba inteleqtualuri agentebis proeqtirebis

Sesaxeb”.

“xelovnuri inteleqti – esaa mecniereba, romelic Seiswavlis artefaqtebis

inteleqtualur qcevas” (artefaqti laTinuri sityvaa da niSnavs xelovnur obieqts).

1.2. xelovnuri inteleqtis ganviTarebis mokle istoria.1.2. xelovnuri inteleqtis ganviTarebis mokle istoria.1.2. xelovnuri inteleqtis ganviTarebis mokle istoria.1.2. xelovnuri inteleqtis ganviTarebis mokle istoria. rogorc ukve aRvniSneT, 1956 wels

a. niuelma da g. saimonma warmoadgines programa logikos Teoretikosi (LG), romelic

gansxvavebiT manamade arsebuli yvela programisagan, moqmedebda ara ricxvebze, aramed

simboloebze da misi qceva avtorebis mtkicebiT Zalian waagavda adamianis qcevas msgavs

situaciebSi. LG amtkicebda Teoremebs winadadebaTa aRricxvidan, romelSic mocemulia

cvladebi p,q,r,…,A,B,C,… da kavSirebi ¬¬¬¬ (uaryofa), ∨∨∨∨ (an) da →→→→ (implikacia). kombinaciebs,

Sedgenils cvladebisa da kavSirebisagan ewodebaT gamosaxulebebi. xuTi maTgani

miRebulia rogorc aqsiomebi:

)]()[()(

)]([)]([

)()(

)(

)(

qrprqp

rpqrqp

pqqp

pqp

ppp

∨→∨→→∨→→∨∨

∨→∨∨→→∨

gvaqvs gamoyvanis sami wesi: Casmis, SecvlisCasmis, SecvlisCasmis, SecvlisCasmis, Secvlis da gamoyofisgamoyofisgamoyofisgamoyofis.... Casmis wesis Tanaxmad,

nebismieri cvladi SeiZleba Seicvalos nebismieri gamosaxulebiT, Tuki es Secvla

xorcieldeba yvelgan mTel gamosaxulebaSi. Secvlis wesi saSualebas gvaZlevs SecvaloT

kavSiri misi ganmartebiT da piriqiT yvelgan da yovelTvis. Tanaxmad gamoyofis wesisa, Tu

A Teoremaa da BA → Teoremaa, maSin B ----c Teoremaa. Teoremad iTvleba gamosaxuleba,

romelic SeiZleba gamoviyvanoT romelime zemoT moyvanili xuTi aqsiomidan an ukve

damtkicebuli Teoremidan, gamoyvanis am sami wesis saSualebiT.

aSkaraa, rom gamosaxulebebi SeiZleba iyos Zalian bevri da isini SeiZleba adgendnen


mimdevrobaTa jaWvs, rodesac erTi gamosaxulebidan gamodis meore da a.S.. Teoremis

damtkiceba mocemuli gamosaxulebisaTvis daiyvaneba im mimdevrobis povnaze, romelic

gamomdinareobs aqsiomebidan (an ukve damtkicebuli Teoremebidan) da mTavrdeba

dasamtkicebeli gamosaxulebiT. Sesabamisad, algoriTmi, romelic sruli garantiiT

mogvcems saSualebas (aseTi algoriTmi cnobilia britaneTis muzeumis algoriTmis

saxeliT) vipovoT Teoremis damtkiceba (Tuki es damtkiceba arsebobs), muSaobs Semdegi

principiT: sawyisi aqsiomebidan da ukve damtkicebuli Teoremebidan aagebs yvela SesaZlo

mimdevrobebs sami wesis gamoyenebiT. Yyovel nabijze Seamowmebs, xom ar miiRo ukve

dasamtkicebeli gamosaxuleba. aseve yovel nabijze moiSorebs dublikatebs, anu iseT

gamosaxulebebs, romlebic ukve aigo am an romelime sxva mimdevrobaSi. adre Tu gvian

algoriTmi aucileblad ipovis sasurveli Teoremis damtkicebas, ra Tqma unda, Tuki is

arsebobs. algoriTmi iZleva damtkicebis povnis srul garantias, magram misi efeqtianoba

seriozul eWvs iwvevs. rogorc ukve aRvniSneT, a.niulema da g. saimonma Caatares Semdegi

saxis eqsperimentebi. maT SearCies studentebi, romlebmac ar icodnen maTematikuri

logika, Camoayalibes amocana da sTxoves studentebs “efiqraT xmamaRla”, anu aexsnaT Tu

ratom Rebulobdnen ama Tu im gadawyvetilebebs. eqsperimentis mizani iyo aRmoeCinaT is

meqanizmebi, romlebic ganapirobeben adamianis inteleqtualur qcevas ucnob garemoSi

(amitom iyo SerCeuli studentTa jgufebi, romlebsac ar hqondaT Seswavlili

maTematikuri logika). Catarebuli eqsperimentebis safuZvelze a. niuelma da g. saimonma

daadgines, rom gansxvavebiT britaneTis muzeumis algoriTmisagan adamiani yovelTvis

cdilobs daiwyos mimdevrobis ageba dasamtkicebeli gamosaxulebidan cnobili

Teoremebisa da aqsiomebisaken da am mimdevrobebis agebisas ZiriTadad xelmZRvanelobs

Semdegi oTxi wesiT: Casmis meTodi,Casmis meTodi,Casmis meTodi,Casmis meTodi, gamoyofis meTodi, pirdapiri jaWvwarmoqmnis meTodigamoyofis meTodi, pirdapiri jaWvwarmoqmnis meTodigamoyofis meTodi, pirdapiri jaWvwarmoqmnis meTodigamoyofis meTodi, pirdapiri jaWvwarmoqmnis meTodi

da uku jaWvwarmoqmnisuku jaWvwarmoqmnisuku jaWvwarmoqmnisuku jaWvwarmoqmnis meTomeTomeTomeTodidididi.

Casmis meTodi eZebs Teoremis damtkicebas cnobil Teoremebsa da aqsiomebSi

cvladebisa da kavSirebis Secvlis gziT. gamoyofis meTodi gamoiyenebs ra gamoyofis

wess, cvlis amocanas qveamocaniT. magaliTad, Tu B gamosaxulebaa, romelic unda

davamtkicoT, meTodi eZebs gamosaxulebas BA → (romelic ukve Teoremaa) da maSin axali

qveamocana xdeba AAAA A -s damtkiceba. pirdapiri da uku jaWvwarmoqmnis meTodebi ki BA →

gamosaxulebis dasamtkiceblad eZeben aqsiomas an Teoremas BC → (Sesabamisad CB → )

da Tu ipovnian, maSin axal qveamocanad iqceva )( ACCA →→ gamosaxulebis damtkiceba.

gansxvavebiT adamianisagan, LG am wesebs iyenebs mkacrad gansazRvruli mimdevrobiT, rac

cxadia amcirebs mis efeqtianobas.

ganvixiloT konkretuli magaliTi. DdavuSvaT, mocemulia gamosaxuleba

pqp ¬→→¬ )( . LG –Tvis garda xuTi aqsiomisa cnobilia agreTve ori Teorema:

1. )( BAA ∨→ (1)

2. )()( ABBA ¬→¬→→ (2)

LG am Teoremas amtkicebs Semdegnairad: pirvel TeoremaSi A –s magivrad Casvavs p -s,

xolo B –s magivrad _ q -s. miiRebs gamosaxulebas


)( qpp ∨→ (3)

Semdeg (2) –Si Casvavs A – s magivrad p - s da B –s magivrad )( qp ∨ ––––s. miiRebs

gamosaxulebas

])([)]([ pqpqpp ¬→→¬→∨→

gamoiyenebs ra gamoyofis wess, miiRebs, rom gamosaxuleba

pqp ¬→→¬ )( Teoremaa.

marto es meTodebi ar iqneboda sakmarisi LG–s warmatebuli muSaobisaTvis, mas rom

ar gaaCndes msgavsebaze Sedarebisa da gamocdis procedurebi. msgavsebaze Sedarebis

proceduris mizania aRmoaCinos is Teoremebi Tu aqsiomebi, romlebic yvelaze efeqturad

SeiZleba gamoviyenoT mocemuli Teoremis dasamtkiceblad. es procedura mdgomareobs

SemdegSi: Tu mocemulia gamosaxuleba

)( pqp →→

LG adarebs mas aqsiomas

)( pqp ∨→

da swrafad aRmoaCens, rom aqsiomaSi unda Seicvalos kavSiri ∨ kavSirze → . . . . moaxdens ra

am Secvlas, miiRebs

)( pqp →¬→ .

Semdeg q¬ Secvlis q –Ti da miiRebs gamosaxulebas )( pqp →→ .

Sedarebis procedura saSualebas gvaZlevs mniSvnelovnad SevamciroT qveamocanebis

Zebnis procesi. am proceduris efeqtianoba aixsneba imiT, rom Sedareba xdeba

komponentebis mixedviT da ukukavSiris saSualebiT Sedegebi maSinve SeiZleba

gamoyenebuli iqnas Semdegi bijis samarTavad. Sedarebis procedura gamoiyeneba yvela

meTodSi, magram misi efeqtianobisaTvis saWiroa jer vipovoT swori Teorema an aqsioma,

romelsac SevadarebT gamosaxulebas. Aam miznisaTvis LG –s gaaCnia msgavsebaze gamocdis

procedura, romlis Tanaxmadac, LG or logikur gamosaxulebas Tvlis msgavsad, Tu

marcxena da marjvena nawilebSi Tanabaria:

1. doneTa maqsimaluri raodenoba mTavari kavSiridan nebismier cvladamde;

2. gansxvavebul cvladTa raodenoba;

3. gamosaxulebaSi cvladebis saerTo raodenoba.

LG -s yvela oTxive meTodis samarTavad gaaCnia mmarTveli programa, romelic Tavisi

arsiT aris algoriTmuli, da mdgomareobs SemdegSi: meTodebis gamoyeneba xdeba mkacrad

gansazRvruli mimdevrobiT. jer gamoiyeneba Casmis meTodi, Semdeg gamoyofis meTodi,

pirdapiri jaWvwarmoqmnis meTodi da bolos uku jaWvwarmoqmnis meTodi. am gziT LG

cdilobs gamoimuSaos axali qveamocana, romelsac daamtkicebs Casmis meTodiT. Tu es

SeuZlebelia, qveamocana Seitaneba qveamocanaTa siaSi. Tu damtkicdeba Tundac erTi

qveamocana Casmis meTodiT, cxadia amiT damtkicebuli iqneba sawyisi Teoremac. Tu ver

moxerxda sawyisi Teoremis damtkiceba vercerTi meTodis gamoyenebiT, maSin amoirCeva

axali qveamocana qveamocanaTa siidan da misTvis yvelaferi meordeba axlidan. procesi

damTavrdeba roca napovni iqneba damtkiceba, an rodesac kompiuters aRar eyofa dro an


mexsiereba.

amgvarad, Teoremis damtkicebisas LG warmoqmnis qveamocanaTa garkveul xes, romlis

saSualebiTac is cdilobs dasamtkicebeli gamosaxulebidan miaRwios aqsiomebs da ukve

damtkicebul Teoremebs. miuxedavad imisa, rom im qveamocanaTa simravle, romelsac

gamoimuSavebs LG gacilebiT mcirea, vidre is simravle, romelsac aagebda britaneTis

muzeumis algoriTmi, arseboben amocanebi, romelTa gadawyvetac LG ar SeuZlia. es imitom

xdeba, rom mmarTveli programa aris algoriTmuli saxis, romelc iZleva imis garantias,

rom Tuki raime qveamocana SeiZleba miRebuli iqnas gamoyofis da jaWvwarmoqmnis

meTodebiT, is aucileblad iqneba agebuli (Tundac ar arsebobdes misi saWiroeba). garda

amisa, yvela es qveamocana ganixileba im TanmimdevrobiT, romliTac isini warmoiSvnen, rac

agreTve did gavlenas axdens damtkicebis processze. aseTi mmarTveli programis gamo da

imis gamo rom meTodebi didi raodenobiT gamoimuSaveben qveamocanebs, yovel bijze

qveamocanaTa xe izrdeba eqsponencialurad. es ki iwvevs imas, rom Tu damtkiceba Seicavs

ramdenime bijs (sami, oTxi an meti) LG efeqturoba Zalian mcirea. ase magaliTad, man

SesZlo daemtkicebina mxolod erTi oTxbijiani Teorema.

am programis gamoqveynebam didi interesi gamoiwvia mecnierebs Soris da sul male

gaCnda kidev sxva programebi, romlebic cdilobdnen amoexsnaT sxvadasxva amocanebi

analogiuri midgomiT. KkerZod, Seiqmna programa, romelic xsnida geometriul amocanebs

saskolo kursidan; programa, romelic simbolur doneze xsnida integralur gantolebebs;

programa, romelic axdenda amwyobi konveiris muSaobis balansirebas da sxva. yvela am

programisaTvis damaxasiaTebeli iyo iseTi procedurebis gamoyeneba, romlebsac uwodebnen

evristikebsevristikebsevristikebsevristikebs da romlebic gamomdinareoben ara amocanis pirobebidan, aramed efuZnebian aramed efuZnebian aramed efuZnebian aramed efuZnebian

bunebrivi intelbunebrivi intelbunebrivi intelbunebrivi inteleqtis zogad mosazrebebs an /da gamocdilebas aseTi amocanebis amoxsniseqtis zogad mosazrebebs an /da gamocdilebas aseTi amocanebis amoxsniseqtis zogad mosazrebebs an /da gamocdilebas aseTi amocanebis amoxsniseqtis zogad mosazrebebs an /da gamocdilebas aseTi amocanebis amoxsnis

drosdrosdrosdros. Aamitom xelovnuri inteleqtis am mimarTulebas ewoda evristikuli programireba.

evristikuli programirebis ZiriTadi principia problemis (amocanis) warmodgena

Zebnis procesis saxiT da Semdeg am procesis gamartiveba evristikebis saSualebiT

evristikuli programebis mravalferovnebam dagvanaxa, rom es programebi xSir SemTxvevaSi

ar warmoadgendnen adamianis azrovnebis models. marTlac, yvela es programa Seqmnili

iyo igive principiT, ra principiTac LG, anu emyarebodnen eqsperimenetebs da hqondaT

pretenzia, rom warmoadgendnen adamianis azrovnebis models informaciuli procesebis

doneze. magram es programebi absoluturad gansxvavdebodnen erTmaneTisagan da erT

programas ar SeeZlo meore programis amocanebis gadaWra. amgvarad, gamodioda, rom

praqtikulad maTgan arc erTi ar warmoadgenda azrovnebis models, radganac cxadia, rom

azrovnebis procesi ar SeiZleba icvlebodes imis da mixedviT, Tu ra amocanas davusvavT

mas. aman gamoiwvia evristikuli programirebis gayofa or mimarTulebad. warmoqmnili

winaaRmdegobis gadasalaxavad da imisaTvis, rom eCvenebinaT, rom maT mier Sedgenili

programa namdvilad aris azrovnebis procesis modeli informaciuli procesebis doneze,

a. niuelma da g. saimonma daiwyes muSaoba axal programaze, romelsac uwodes problemaTa

zogadi amomxsneli (GPS – General Problem Solvers). am programas ukve SeeZlo amoexsna

sxavdasxva klasis amocanebi, magram iyo naklebad efeqturi da ukve saSualo zomis

amocanebis amoxsnis dros aRar yofnida dro da mexsiereba. avtorebi amas xsnidnen


imdroindeli kompiuterebis sisustiT da fiqrobdnen, rom momavalSi, rodesac

gaizrdeboda kompiuterebis siswrafe da mexsiereba, SesaZlebeli iqneboda nebismieri

zomis amocanebis amoxsna. evristikuli programirebis meore mimarTuleba cdilobda

Seeqmna amocanaTa amoxsnis efeqturi algoriTmebi, romelTa gamoyenebac SesaZlebeli

iqneboda praqtikuli amocanebis gadasaWrelad da ar fiqrobda, warmoadgendnen es

programebi azrovnebis models Tu ara. Tu SevadarebT Cvens magaliTs Citebisa da

TviTmfrinavis Sesaxeb, SeiZleba iTqvas, rom pirveli mimarTuleba cdilobda xelovnuri

Citis Seqmnas, xolo meore ki sxadasxva saxis TviTmfrinavebis agebas konkretuli

miznebisaTvis da TviTmfrinavTmSeneblobis Teoriis Seqmnas.

evristikuli programirebis aseTi aRmavloba grZeldeboda gasuli saukunis

samocdaaTian wlebamde. Aam droisaTvis TandaTanobiT aSkara gaxda, rom is dapirebebi,

romlebsac uxvad iZleodnen mecnierebi, Seusrulebeli iyo. pirvel rigSi am programaTa

udides nawils ar hqondaT (an hqondaT Zalian mcire) codna im sakiTxebze, romelTa

gadaWrasac isini cdilobdnen. am mxriv tipuri magaliTia is samuSaoebi, romlebsac uxvad

afinansebda aSS nacionaluri samecniero – kvleviTi sabWo. saqme exeboda samecniero

teqstebis manqanur Targmnas rusuli enidan inglisurze. iTvleboda, rom winadadebis

zusti azris SesanarCuneblad sakmarisi iyo CaetarebinaT sintaqsuri gardaqmna,

damyarebuli rusuli da inglisuri enebis gramatikebze da SeecvalaT sityvebi

eleqtronuli leqsikonis gamoyenebiT. Mmagram saqme imaSia, rom araerTmniSvnelovnebis

mosaspobad da winadadebis azris gasarkvevad saWiroa sistema flobdes codnas

mecnierebis im dargSi, romelsac exeba statia. ai rogori Sedegi miiRes inglisuri

frazis “The spirit is willing but the fiesh is weak” (suli savsea survilebiT, magram xorci

sustia), jer rusul da Semdeg kvlav inglisur enaze: “The vodka is good but the meat is rotten”

(arayi kargia, magram xorci gafuWebulia).

arsebiTi gavlena xelovnuri inteleqtis ganviTarebis Seferxebaze moaxdina imanac,

rom yvela am programebSi problemebis gadaWras cdilobdnen gadarCevis gziT, anu

SesaZlo nabijebis sxvadasxva kombinaciebis Semowmebis gziT, romelic grZeldeboda sanam

ar iqneboda napovni amoxsna. patara amocanebis amoxsnis dros es strategia amarTlebda,

amitom miaCndaT, rom ufro didi amocanebis amosaxsnelad sakmarisia ufro swrafi

kompiuterebi mexsierebis didi moculobiT. magram gamoTvliTi sirTulis Teoriis Seqmnis

Semdeg aSkara gaxda, rom es ase ar aris da eqsponencialuri algoriTmebis Sesruleba

realur droSi yvelTvis araa SesaZlebeli.MmagaliTad, is optimizmi, romelic mohyva

rezoluciis principis aRmoCenas, Zalin male gaqra, rodesac ver SesZles daemtkicebinaT

am principiT Teoremebi, romlebic Seicavdnen ramdenime aTeul faqts. AaRmoCnda, rom is is is is

faqti, rom programas principulad SeuZlia ipovos amoxsna, sulac arfaqti, rom programas principulad SeuZlia ipovos amoxsna, sulac arfaqti, rom programas principulad SeuZlia ipovos amoxsna, sulac arfaqti, rom programas principulad SeuZlia ipovos amoxsna, sulac ar niSnavs rom is niSnavs rom is niSnavs rom is niSnavs rom is

marTlac Seicavs yvela meqanzms, romelic saSualebas mogvcems vipovoT amoxsna marTlac Seicavs yvela meqanzms, romelic saSualebas mogvcems vipovoT amoxsna marTlac Seicavs yvela meqanzms, romelic saSualebas mogvcems vipovoT amoxsna marTlac Seicavs yvela meqanzms, romelic saSualebas mogvcems vipovoT amoxsna

praqtikulad.praqtikulad.praqtikulad.praqtikulad.

1.3. neironuli qselebis Teoria.1.3. neironuli qselebis Teoria.1.3. neironuli qselebis Teoria.1.3. neironuli qselebis Teoria. a. niuelisa da g. saimonis LLLLgamoCenamde didi xniT adre,

jer kidev ormocian wlebSi, u. mak-kalokma da u. pitsma gamoaqveynes statia ““““logical calculus

of the ideas immanent in nervous activity”””” (neironisaTvis damaxasiaTebel aqtiurobis ideaze


dafuZnebuli logikuri gamoTvlebi). am statiaSi maT SemogvTavazes adamianis nervuli

sistemis ZiriTadi elementis – nervuli ujredis – neironis modeli. im informaciis

safuZvelze, rac mecnierebas gaaCnia neironis agebulebis da funqcionirebis Sesaxeb, maT

daaskvnes, rom neironi es aris elementi mravali SesasvleliTa da erTi gamosasvleliT.

Sesasvlelebi SeiZleba iyvnen or mdgomareobaSi, aRgznebul an mosvenebul mdgomareobaSi.

imisda mixedviT ramdeni Sesasvlelia agznebuli da rogoria neironis agznebis zRurbli,

neironis gamosasvlelze an gveqneba signali (neironi aRigzneba) an ara. u. mak-kalokma da

u. pitsma Seqmnes aseTi elementis teqnikuri modeli, romelsac uwodes xelovnuri neironi.

magaliTad, orSesasvleliani xelovnuri neironis saSualebiT Zalian martivad

SesaZlebelia ∨ da ∧ kavSirebis modelireba (ix. nax. # 1.1) u. mak-kalokma da u. pitsma aCvenes, romYaseTi xelovnuri neironebisagan SeiZleba Seiqmnas qseli, romelSic neironebi

imyofebian “CarTul” an “gamorTul” mdgomareobaSi. gadasvla “CarTul” mdgomareobaSi

xdeba mezobeli neironebis stimulaciis Sedegad da aseTi neironuli qselebis

saSualebiT SeiZleba gamovTvaloT nebismieri gamoTvladi funqcia da amasTanave martivi

logikuri qseliT movaxdinoT nebismieri logikuri kavSiris (“ara”, “an”, “da” da ase

Semdeg) realizacia. garda amisa, maT gamoTqves mosazreba, rom aseT logikur qselebs

aqvT daswavlis unari.

a) operacia ∧ b) operacia ∨

nax. # 1.1. logikuri funqciebis ganxorcieleba xelovnuri neironebis saSualebiT;

1957 wels f. rozenblatma gamoaqveyna aseTi neironuli qselebis saSualebiT Seqmnili

perceptronis (aRmqmeli mowyobiloba) aRwera, romelsac SeuZlia Seasrulos ufro meti,

vidre esaa logikuri gamoTvlebi, kerZod perceptrons SeeZlo gamoecno organzomilebiani

figurebi da gaaCnda daswavlis unaridaswavlis unaridaswavlis unaridaswavlis unari. amasTan procesebi, romlebic mimdinareoben

perceptronSi emyareba ara marto logikas, aramed statistikasac.

f. rozenblatis umartivesi samSriani perceptroni Sedgeba gamosaxulebis aRmqmeli

neironebis pirveli )(S Srisagan, romelzec xdeba gamosaxulebis proecireba. Tu

neironze moxvdeba gamosaxuleba, neironi aRigzneba da gamosasvleze gveqneba signali (1),

Tu ara, neironi mosvenebul mdgomareobaSia da gamosasvlelze signali ara gvaqvs (0).

gamosaxulebis aRmqmeli Sre dakavSirebulia asociaciur neironebis )(A SresTan

nebismierad (magaliTad yvela yvelasTan). am Sris neironebs gaaCniaT garkveuli zRurbli

da Tu mosuli signalebis jami gadaaWarbebs am zRurbls, gamosasvlelze gveqneba

signali, romelic )( ir -uri regulatorebis saSualebiT SeiZleba gavaZlieroT, an

SevasustoT. mesame Sre Sedgeba erTi neironisagan, romelic warmoadgens sumators

neironis zRurbli =2

neironis zRurbli =1

1x

2x

1x

2x

21 xx ∧ 21 xx ∨


garkveuli zRurbliT da erTi gamosasvleliT, romelzedac SeiZleba gvqondes signali (1),

A

nax. # 1.2. f. rozenblatis samSriani perceptroni

an ar gvqondes signali (0). aseT perceptrons SeuZlia ganasxvavos erTmaneTisagan

obieqtebis ori klasi. Cven unda mivaRwioT imas, rom erTi klasis obieqtebis

proecirebisas perceptronis gamosasvlelze vRebulobdeT erT signals (magaliTad 1) da

meore klasis obieqtebze meore signals (0), anu unda davaswavloT perceptrons obieqtebis

erTmaneTisagan garCeva. es mizani miiRweva )( ir regulatorebis saSualebiT. faqtobrivad

perceptronis Tavdapirveli stoqasturi sqema daswavlis procesSi Rebulobs garkveul

struqturas, romelic Seesabameba im obieqtebs, romelTa proecirebac xdeba perceptronis

Sesasvlelze. f. rozenblatma daamtkica Teorema aseTi perceptronis krebadobis Sesaxeb,

romelic adasturebs, rom mis mier SemoTavazebul algoriTms SeuZlia perceptronSi

gaerTianebuli xelovnuri neironebs Soris kavSirebis raodenobebis koreqtireba

nebismieri Sesasvleli monacemebis Sesabamisad, im pirobiT, rom aseTi Sesabamisoba

arsebobs.

1969 wels m. minskma da s. peipertma gamoaqveynes Sroma, romelSic aCvenes, rom

perceptrons, romelic warmoadgens neironuli qselis martiv formas, marTlac SeuZlia

Seiswavlos yvelaferi, rac SeiZleba warmodgenili iqnas misi saSualebiT, magram

problema imaSi mdgomareobs, rom maTi saSualebiT SeuZlebelia warmovadginoT

yvelanairi obieqtebi. magaliTad, perceptroni mxolod ori Sesasvleli neironiT

verasodes daiswavlis iseTi situaciebis garCevas, rodesac mis Sesasvlelebze modis

sxvadasxva signali.

R

S

1

0


1.4. codnis warmodgena inteleqtualur sistemebSi.1.4. codnis warmodgena inteleqtualur sistemebSi.1.4. codnis warmodgena inteleqtualur sistemebSi.1.4. codnis warmodgena inteleqtualur sistemebSi.AaSkara gaxda, rom specifikuri codnis

gareSe, mxolod Zebnis zogadi principebis gamoyenebiT, rTuli amocanebis amoxsna

SeuZlebelia. erTerTi pirveli programa, romelSic amocanis gadasaWrelad gamoiyeneboda

codna, iyo programa Dendral----i. Pprograma Seqmnili iyo qimiuri nivTierebebis struqturis

dasadgenad. programis Sesasvleli monacemebi iyo SenaerTis qimiuri formula da masaTa

speqtri, programas ki unda daedgina molekulis sivrciTi struqtura.Yprogramis pirveli,

primitiuli versia cdilobda gamoemuSavebina mocemuli formulis Sesabamisi yvela

SesaZlo struqtura da Semdeg daedgina rogori masaTa speqtri unda Seesabamebodes

mocemul struqturas. Ddidi zomis molekulebisaTvis aseTi amocanis amoxsna SeuZlebeli

aRmoCnda, amitom, qimikos-analitikosebTan konsultaciebis Semdeg, programis avtorebi

mividnen im daskvnamde, rom saWiroa piriqiT, masaTa speqtrSi arsebuli pikebis saSualebiT

moeZebnaT is cnobili qvestruqturebi, romlebic iZlevian am pikebs. magaliTad, ketonuri

qvejgufebis dasadgenad (C=O) atomuri masiT 28, maT gamoiyenes Semdegi wesi:

TuTuTuTu arsebobs ori wertili 1x da 2x , iseTi ,rom:

a) =+ 21 xx 28+M (sadac M aris mTeli molekulis masa);

b) wertilSi 281 −x - maRalia pikia;

g) wertilSi 282 −x –––– maRali pikia;

d) erTerT wertilSi mainc 1x an 2x - maRali pikia,

maSinmaSinmaSinmaSin arsebobs ketonuri jgufi.

Aprograma Dendral aRmoCnda Zalian Zlieri da efeqturi programa, rac ganpirobebuli

iyo imiT, rom yvela is Teoriuli codna, romelic saWiroa aseTi amocanis amosaxsnelad

Camoyalibebuli iqna zusti receptebis saxiT. Ees iyo pirveli eqspertuli sistema,

romelic amocanis amoxsnis dros iyenebda ara marto Zebnis zogad meTodebs, aramed

codnasac. ase gaCnda xelovnur inteleqtSi codnis warmodgenis problemacodnis warmodgenis problemacodnis warmodgenis problemacodnis warmodgenis problema.

1.5. xelovnuri inteleqtis Camoyali1.5. xelovnuri inteleqtis Camoyali1.5. xelovnuri inteleqtis Camoyali1.5. xelovnuri inteleqtis Camoyalibeba mecnierebad.beba mecnierebad.beba mecnierebad.beba mecnierebad. gasuli saukunis oTxmociani

wlebidan xelovnuri inteleqti TandaTanobiT Camoyalibda rogorc mecniereba, romelsac

gaaCnia Tavisi kvlevis sagani, meTodologia da sakmaod farTo praqtikuli gamoyeneba.

pirvel rigSi ZiriTadi aqcenti gadatanili iqna imaze, rom xelovnuri inteleqtis

Teoriebi unda iyos dafuZnebuli maTematikis principebze. amas xeli Seuwyo imanac, rom

TviTon maTematikam ganicada seriozuli cvlilebebi xelovnuri inteleqtis gavleniT,

mxedvelobaSi gvaqvs aramkafio simravleTa Teoriis ganviTareba da misi sul ufro farTo

gamoyeneba gadawyvetilebis miRebisa da marTvis Teoriis problemebSi. aqedan gamomdinare,

SesaZlebeli gaxda maTematikaSi miRebuli Sedegebis farTod gamoyeneba xelovnuri

inteleqtis problemebis gadwyvetis dros (pirvel rigSi unda aRiniSnos miRwevebi saxeTa

gamocnobis dargSi).

erTianma Teoriulma midgomam SesaZlebeli gaxada kvlav wina planze wamoweuliyo

“erTiani agentis” problemis Seqmnis sakiTxic, rac saSualebas mogvcems davakavSiroT

erTmaneTTan xelovnuri inteleqtis sxvadasxva mimarTulebebSi miRebuli Sedegebi.


ssssakontrolo kiTxvebi:akontrolo kiTxvebi:akontrolo kiTxvebi:akontrolo kiTxvebi:

1. ras Seiswavlis xelovnuri inteleqti?

2. ratomaa xelovnuri inteleqtis warmoSoba dakavSirebuli kompiuteruli teqnikis

warmoSobasTan?

3. raSi mdgomareobs a. tiuringis testi?

4. ra ZiriTad mimarTulebebs moicavs xelovnuri inteleqti?

5. romel wels Seiqmna pirveli evristikuli programa da riT gansxvavdeboda is

manamde arsebuli programebisagan?

6. ras efuZneba is evristikebi, romlebic gamoiyeneba LG -Si?

7. ratom ver xerxdeba evristikuli programirebis meTodebiT rTuli amocanebis

amoxsna?

8. ras warmoadgens xelovnuri neironi da ra tipis funqciebi SeiZleba aRiweros

neironuli qselebis saSualebiT?

9. ra principi udevs safuZvlad f. rozenblatis mier Seqmnil perceptrons?

10. ra mimarTulebiT ganviTarda xelovnuri inteleqti gasuli saukunis oTxmociani

wlebidan?

savarjiSoebi:savarjiSoebi:savarjiSoebi:savarjiSoebi:

1. arsebobs problemaTa klasi, romelTa gadaWra kompiuretebisaTvis Zalian Znelia.

arsebobs agreTve klasi gadauWreli amocanebisa. rogor fiqrobT, niSnavs es imas,

rom xelovnuri ineteleqtis Seqmna SeuZlebelia?

2. Tqveni azriT, ratom SeiZleba aRmoCndes araswori rasac gadmoscems adamiani imis

Sesaxeb Tu ras fiqrobs is amocanis amoxsnis dros?

3. “cxadia, rom kompiuterebi ar SeiZleba iyos inteleqtualuri, isini

xom asruleben mxolod imas, rasac karnaxobT maT programa”. rogor

fiqrobT, sworia Tu ara am winadadebis meore nawili da

gamomdinareobs Tu ara aqedan misi pirveli nawili?

lllleqcia #2.eqcia #2.eqcia #2.eqcia #2.

inteleqtualur agentTa Teoria. inteleqtualur agentTa Teoria. inteleqtualur agentTa Teoria. inteleqtualur agentTa Teoria.

2.1. inteleqtualuri agentis cneba.2.1. inteleqtualuri agentis cneba.2.1. inteleqtualuri agentis cneba.2.1. inteleqtualuri agentis cneba. Aagenagenagenagentadtadtadtad SeiZleba CaiTvalos yvelaferi, rac moqmedebs

(sityva agenti laTinuri sityvaa da niSnavs agereagereagereagere - imoqmede), magram igulisxmeba, rom

imteleqtualuri agentebi Cveulebrivi “programebisagan” gansxvavebiT floben damatebiT

kidev sxva Tvisebebs. ase magaliTad, maT SeuZliaT funqcionireba avtonomiurad, aqvT

garemos aRqmis unari, arseboben xangrZlivi drois ganmavlobaSi, adapturebi arian

cvlilebebis mimarT da rac yvelaze ufro mTavaria SeuZliaT Tavis Tavze aiRon sxvebis

sur. # 2.1. agentis urTierTqmedeba garemosTan

mier dasmuli miznis miRweva. aseTi tipis sistemebisaTvis Zalian mniSvnelovanis

racionalurracionalurracionalurracionalurobisobisobisobis cneba. racionaluria agenti, Tu mas SeuZlia miaRwios saukeTeso

Sedegebs determinirebul garemoSi, an Tu garemo araa determinirebuli – saukeTeso

mosalodnel Sedegebs. racionalurobis koncefcia SegviZlia gamoviyenoT nebismieri

agentis mimarT, romelic moqmedebs nebismier garemoSi, romlis warmodgenac Cven

SegviZlia. Tavis mxriv agenti SeiZleba iyos nebismieri sistema, romelic aRiqvams garemos

gadamwodebisgadamwodebisgadamwodebisgadamwodebis saSualebiT da zemoqmedebs am garemoze Semsrulebeli meqanizmebisSemsrulebeli meqanizmebisSemsrulebeli meqanizmebisSemsrulebeli meqanizmebis

saSualebiT. Tu ganvixilavT adamians agentis rolSi, mas gaaCnia gadamwodebi – Tvalebi,

yurebi da grZnobis sxva organoebi, romelTa saSualebiTac is aRiqvams garemos da

zemoqmedebs am garemoze xelebiT, fexebiT da sxeulis sxva nawilebiT, romlebic

warmoadgenen mis Semsrulebel meqanizmebs. robots, romelic asrulebs agentis rols,

gadamwodebad SeiZleba hqondes videokamera, infrawiTeli manZilmzomi da sxva. mis

Semsrulebel meqanizmebs ki warmoadgenen motorebi, meqanikuri xeli da sxva. programuli

uzrunvelyofac SeiZleba warmoviginoT inteleqtualuri agentis rolSi. am SemTxvevaSi

gadamwodis rols asrulebs klaviatura da informaciis Seyvanis sxvadasxva saSualebebi,

xolo garemoze zemoqmedeba gamoixateba monacemebis gamoyvaniT ekranze, failze CaweriT

da ase Semdeg.

2.2.2.2.2.2.2.2. aRqma, funqcia, programa.aRqma, funqcia, programa.aRqma, funqcia, programa.aRqma, funqcia, programa. termins aRqmaaRqmaaRqmaaRqma viyenebT imisaTvis, rom aRvniSnoT

sensoruli informaciis miReba drois nebismier konkretul momentSi. aRqmaTa aqtebis aRqmaTa aqtebis aRqmaTa aqtebis aRqmaTa aqtebis

agentiagentiagentiagenti gadamwodebigadamwodebigadamwodebigadamwodebi Semsrulebeli meqanizmebiSemsrulebeli meqanizmebiSemsrulebeli meqanizmebiSemsrulebeli meqanizmebi

?

garemo garemo garemo garemo

lllleqcia #eqcia #eqcia #eqcia #2. inteleqtualur agentTa Teoria2. inteleqtualur agentTa Teoria2. inteleqtualur agentTa Teoria2. inteleqtualur agentTa Teoria 15

mimdevrobamimdevrobamimdevrobamimdevroba ewodeba imis srul istorias, rac saerTod rodesme aRiqva agentma. zogadad

agentis mier drois nebismier momentSi arCeuli qmedeba SeiZleba damokidebuli iyos agentis mier drois nebismier momentSi arCeuli qmedeba SeiZleba damokidebuli iyos agentis mier drois nebismier momentSi arCeuli qmedeba SeiZleba damokidebuli iyos agentis mier drois nebismier momentSi arCeuli qmedeba SeiZleba damokidebuli iyos

aRqmaTa aqtebis mTelaRqmaTa aqtebis mTelaRqmaTa aqtebis mTelaRqmaTa aqtebis mTel mimdevrobaze dasawyisidan am momentamdemimdevrobaze dasawyisidan am momentamdemimdevrobaze dasawyisidan am momentamdemimdevrobaze dasawyisidan am momentamde. Tu SesaZlebelia

davadginoT romel qmedebas airCevs agenti nebismier SesaZlo aRqmaTa aqtebis

mimdevrobaze, maSin SesaZlebelia agentis met-naklebad zusti gansazRvra. maTematikurad

es niSnavs, rom romeliRac agentis qceva SeiZleba aRiweros agentis funqciisagentis funqciisagentis funqciisagentis funqciis saSualebiT,

romelic aRqmis aqtebis nebismier konkretul mimdevrobas asaxavs romelime qmedebaze.

Aagentis funqciis dasadgenad SesaZlebelia SevadginoT cxrili, romelic aRwers am

funqcias, magram es cxrili iqneba praqtikulad usasrulo, Tu ar davadgenT aRqmaTa

aqtebis mimdevrobis maqsimalur zomas. TavisTavad aseTi cxrilis dadgena araa cudi,

magram es iqneba agentis garegnuli aRwera. Sinagani aRwera mdgomareobs imis

gansazRvraSi, Tu agentis ra funqcia xorcieldeba agentis programisagentis programisagentis programisagentis programis saSualebiT. agentis

funqciisagan gansxvavebiT, romelic warmoadgens agentis abstraqtul, maTematikur

aRweras, agentis programa aris konkretuli realizacia, romelic moqmedebs agentis

arqiteqturul CarCoSi.

ganvixiloT Zalian martivi magaliTi:UdavuSvaT gare samyaro Sedgeba mxolod ori (A

da B) oTaxisagan, romlebSic dgas oTxkuTxa da samkuTxa piramidebi. am garemoSi SeiZleba

imyofebodes agenti, romelsac SeuZlia aRiqvas romel oTaxSi imyofeba TviTon, dgas Tu

ara am oTaxSi piramidebi da gaarCios erTmaneTisagan oTxkuTxa da samkuTxa piramidebi.

Semsrulebeli meqanizmebis saSualebiT agents SeuZlia imoZraos garemoSi, aiRos da

gadaitanos erTi adgilidan meoreze piramidebi. agentis mizania A oTaxSi Seagrovos

mxolod oTxkuTxa da B oTaxSi mxolod samkuTxa piramidebi. EaseTi agentis erTerTi

umartivesi funqcia SeiZleba mdgomareobdes SemdegSi: Tu aris A oTaxSi samkuTxa

sur. # .2.2. garemo, romelSic moqmedebs agenti

piramida, gadaitanos is B oTaxSi, Tu ar aris A oTaxSi samkuTxa piramida, gadavides B

oTaxSi da Caataros igive procedura oTxkuTxa piramidebisaTvis. rogorc am cxrilidan

Cans, SesaZlebelia misi sxvadasxvanairad Sevseba, rac TavisTavad gamoiwvevs agentis

sxadasxva qcevas. MmaSin cxadia dgeba kiTxva Tu rogor unda SevavsoT cxrili, rom

agentis qceva iyos inteleqtualuri?

2.32.32.32.3. racionaluri agenti.. racionaluri agenti.. racionaluri agenti.. racionaluri agenti. Aswored aq gvWirdeba zemoT ganmartebuli racionalurobis

cneba. racionaluriracionaluriracionaluriracionaluriaaaa agenti agenti agenti agenti,,,, romelic asrulebs swor qmedebebs, anu mis funqciaTa

cxrilSi yoveli Canaweri aris swori.


cxrili 2.1.

aRqmaTa aqtebis mimdevroba qmedeba

[A, ar aris samkuTxa piramida] gadadi B oTaxSi

[A, aris samkuTxa piramida] gadaitane is B oTaxSi

[B, ar aris oTxkuTxa piramida] gadadi A oTaxSi

[B, aris oTxkuTxa piramida] gadaitane A oTaxSi

[A, ar aris samkuTxa piramida],[A,ar aris samkuTxa piramida] gadadi B oTaxSi

……………………………………………………………………………………………………

[A, aris samkuTxa piramida],[A, ar aris samkuTxa piramida] , . . . , [A, ar aris samkuTxa

piramida] gadadi B oTaxSi

… …………………………………………………………………………………………………….

cxadia rom swori qmedebebis Sesruleba unda sjobdes araswori qmedebebis

Sesrulebas, magram romelia swori da romeli araswori qmedeba? am problemidan Tavis

dasaRwevad Semogvaqvs kidev erTi araformaruli cneba – agentis warmatebuliwarmatebuliwarmatebuliwarmatebuli

funqcionirebis cneba. imisaTvis ki, rom SevafasoT, warmatebulia Tu ara agentis

funqcionireba, saWiroa raime formaluri kriteriumebi, Torem yvela es ganmatebebi iqneba

carieli wylis nayva.

maSasadame, SeiZleba vTqaT, rom garemos, gadamwodebis, Semsrulebeli meqanizmebisa da garemos, gadamwodebis, Semsrulebeli meqanizmebisa da garemos, gadamwodebis, Semsrulebeli meqanizmebisa da garemos, gadamwodebis, Semsrulebeli meqanizmebisa da

warmatebis kriteriumebis aRwera wawarmatebis kriteriumebis aRwera wawarmatebis kriteriumebis aRwera wawarmatebis kriteriumebis aRwera warmoadgens im amocanis srul specifikacias,rmoadgens im amocanis srul specifikacias,rmoadgens im amocanis srul specifikacias,rmoadgens im amocanis srul specifikacias, romlisromlisromlisromlis

gadaWrac uxdeba agentsgadaWrac uxdeba agentsgadaWrac uxdeba agentsgadaWrac uxdeba agents. rodesac Cven gveqneba yvela es komponenti, SevZlebT ufro

zustad ganvmartoT ra igulisxmeba racionalurobis qveS.

2.4. muSaobis maxsiaTeblebi2.4. muSaobis maxsiaTeblebi2.4. muSaobis maxsiaTeblebi2.4. muSaobis maxsiaTeblebi.Aagentis warmatebuli qcevis Sefasebis kriteriumebs

warmodgenen misi muSaobis maxasiaTeblebimuSaobis maxasiaTeblebimuSaobis maxasiaTeblebimuSaobis maxasiaTeblebi. mas Semdeg, rac agents movaTavsebT garemoSi, is

gamoimuSavebs qmedebaTa mimdevrobax miRebul aRqmaTa Sesabamisad. qmedebaTa es mimdevroba

aiZulebs garemos gaiaros raRac mdgomareobebi. Tu es mimdevroba Seesabameba sasurvels,

maSin cxadia agenti muSaobs kargad. Seesabameba Tu ara miRebuli Sedegi sasurvels? amis

Sesaxeb SeiZleboda gvekiTxa TviT agentisaTvis, magram zogierTi agenti saerTod ver

SesZlebs am kiTxvaze pasuxis gacemas, xolo zogierTma maTganma SeiZleba an Tavi

moityuos an Cven mogvatyuos rom swored am miznis miRweva surda. (gavixsenoT meliis da

yurZnis araki). aqedan gamomdinare gansakuTrebiT mniSvnelovania Tu ra kriteriumebiT

SevafasebT agentis mier Sesrulebul samuSaos. davuSvaT, Cveni magaliTis SemTxvevaSi

kriteriumad aviReT gadatanili piramidebis raodenoba, romelsac agenti gadaitans erTi

oTaxidan meoreSi rva saaTiani samuSao dRis ganmavlobaSi. maSin Cveni agenti SeiZleba ase

moiqces: gadaitanos samkuTxa piramidebi A oTaxidan B oTaxSi da oTxkuTxa piramidebi B-

dan A-Si, Semdeg kvlav gadmoitans B-dan A-Si samkuTxa piramidebi da ase Semdeg. Cveni

kriteriumis mixedvT is iqneba warmatebuli agenti da unda miiRos Sesabamisi anazRaureba.

am magaliTidan kargad Cans, rom aseT martiv SemTxvevaSic ki aucilebelia agentis

qmedebis Sefasebis kriteriumebis sworad SerCeva, Tu gvinda rom miviRoT marTlac

racionaluri qmedeba dasaxuli miznis misaRwevad.

A


agentis qmedebis racionalurobas drois nebismier momentSi gansazRvravs Semdegi

oTxi faqtori:

• muSaobis maxasmuSaobis maxasmuSaobis maxasmuSaobis maxasiaTeblebiiaTeblebiiaTeblebiiaTeblebi, romlebic gansazRvraven warmatebis kriteriumebs;

• agentis codnacodnacodnacodna garemos Sesaxeb, romelic man miiRo adre;

• qmedebebiqmedebebiqmedebebiqmedebebi, romelTa Sesrulebac SeuZlia agents;

• agentis mier aRqmuli aqtebis mimdevrobaaRqmuli aqtebis mimdevrobaaRqmuli aqtebis mimdevrobaaRqmuli aqtebis mimdevroba drois mocemul momentamde.

yvela am faqtoris gaTvaliswinebiT SegviZlia CamovayaliboT racionaluri agentis

ganmarteba. aRqmis aqtebis yvela SesaZlo mimdevrobebisaTvis agentma unda amoirCios is aRqmis aqtebis yvela SesaZlo mimdevrobebisaTvis agentma unda amoirCios is aRqmis aqtebis yvela SesaZlo mimdevrobebisaTvis agentma unda amoirCios is aRqmis aqtebis yvela SesaZlo mimdevrobebisaTvis agentma unda amoirCios is

qmedeba, romelic, rogorc mosalodnelia, moaxdens misi muSaobis maxasiaTeblebis qmedeba, romelic, rogorc mosalodnelia, moaxdens misi muSaobis maxasiaTeblebis qmedeba, romelic, rogorc mosalodnelia, moaxdens misi muSaobis maxasiaTeblebis qmedeba, romelic, rogorc mosalodnelia, moaxdens misi muSaobis maxasiaTeblebis

maqsimizacias mocemuli aqtebis mimdevrmaqsimizacias mocemuli aqtebis mimdevrmaqsimizacias mocemuli aqtebis mimdevrmaqsimizacias mocemuli aqtebis mimdevrobiT miRebuli faqtebisa da agentSi obiT miRebuli faqtebisa da agentSi obiT miRebuli faqtebisa da agentSi obiT miRebuli faqtebisa da agentSi

CamontaJebuli mTeli codnis gaTvaliswinebiT.CamontaJebuli mTeli codnis gaTvaliswinebiT.CamontaJebuli mTeli codnis gaTvaliswinebiT.CamontaJebuli mTeli codnis gaTvaliswinebiT.

2.5.2.5.2.5.2.5. racionalurobis sazRvrebiracionalurobis sazRvrebiracionalurobis sazRvrebiracionalurobis sazRvrebi. Zalian mniSvnelovania ganvasxvavoT erTmaneTisagan

racionaluroba da yvelafris codna. yvelafris mcodne agentma faqtobrivad icis Tavisi

qmedebis Sedegi (rac zogierT garemoSi SeuZlebelia) da SeuZlia imoqmedos Sesabamisad.

ganvixiloT magaliTi. davuSvaT, agentma seirnobis dros gadawyvita gadavides quCis meore

mxares. is xedavs rom quCaSi ar moZraobs arcerTi avtomobili da rogorc racionalurma

agentma, daiwyo quCis gadakveTa. am momentamde cota xniT adre ki 10 000 metris simaRleze

TviTmfrinavs moswyda karebi, romelic daeca Cvens agents. iyo Tu ara agentis qmedeba

racionaluri? albaT arcerTi adamiani quCaze gadasvlis dros ar ixedeba maRla da ar

eZebs saSiSroebas zevidan. es magaliTi gviCvenebs Tu ra gansxvavebaa racionalur

qmedebasa da yvelafris codnas Soris.

Mmeore SemTxvevaSi, Tuki agenti ise gadadis quCaze, rom winaswar ar gaixedavs

marcxniv da marjvniv, mis mier aqamde aRqmuli aqtebis mimdevroba ver ukarnaxebs mas, rom

gadasasvlels didi siswrafiT uaxlovdeba satvirTo manqana. racionalur agents unda

SeeZlos iseT qmedebaTa Sesruleba, romelic saSualebas miscems mas SesaZleblobis

farglebSi winaswar gansazRvros mosalodneli Sedegi. anu mas unda SeeZlos SeagSeagSeagSeagrovosrovosrovosrovos

informaciainformaciainformaciainformacia garemos Sesaxeb da agreTve gamoikvlios ucnobi situaciebi.ucnobi situaciebi.ucnobi situaciebi.ucnobi situaciebi.

2.6.2.6.2.6.2.6. problemuri garemoproblemuri garemoproblemuri garemoproblemuri garemo,,,, romelSic moqmedebs agentiromelSic moqmedebs agentiromelSic moqmedebs agentiromelSic moqmedebs agenti. racionaluri agentis ganmarteba

agreTve gulisxmobs, rom agenti ara marto unda agrovebdes informacias garemos Sesaxeb,

aramed swavlswavlswavlswavlobdesobdesobdesobdes kidec. swavlis qveS igulisxmeba rom agentis sawyisi konfiguracia

SeiZleba Seicavdes raime winaswar codnas garemos Sesaxeb, magram TandaTanobiT, agentis

gamocdilebasTan erTad es codna icvleba da ganicdis modificirebas. arsebobs

gansakuTrebuli SemTxvevebi, rodesac garemo mTlianad cnobilia. aseT SemTxvevaSi agents

aRar sWirdeba arc informaciis Segroveba da arc daswavla, magram aseTi agenti iqneba

Zalian ususuri. sakmarisia sul patara cvlileba garemoSi, rom agentis qmedebebi ukve

aRar iqneba racionaluri.

rodesac Cven vixilavdiT agents, romelsac piramidebi gadahqonda erTi oTaxidan

meoreSi, saWiro gaxda misi muSaobis maxasiaTeblebis, garemos, gadamwodebisa da

Semsrulebeli meqanizmebis gansazRvra. gavaerTianoT am faqtorebis aRwera problemuriproblemuriproblemuriproblemuri

garemosgaremosgaremosgaremos cnebaSi. ganvixiloT axali magaliTi – taqsis avtomatizebuli mZRolis Seqmnis

problema. manqanis tarebis problemis sruli gadaWra Zalian rTuli amocanaa, radganac


usazRvroa im yvelanair situaciaTa raodenoba, romlebic SeiZleba warmoiSvas manqanis

tarebis Ddros da amitom SeuZlebelia avtomatizebuli mZRolis Seqmnis dros yvelaferi

winaswar gaviTvaliswinoT.

pirvel rigSi davadginoT muSaobis maxasiaTeblebi, romlebic gansazRvraven taqsis

avtomatizebuli mZRolis moqmedebas mTlianobaSi: sasurvelia warmatebiT miaRwios

daniSnulebis adgils; moaxdinos sawvavis, avtomanqanis detalebis cveTis, mgzavrobis

xangrZlivobis da/an mgzavrobis Rirebulebis minimizacia; imoZraos ise, rom ar daarRvios

moZraobis wesebi da ar Seuqmnas problemebi sxva mZRolebs; Seuqmnas maqsimaluri

usafrTxoeba da komforti mgzavrebs; miaRwios maqsimalur mogebas. cxadia, rom am

miznebidan zogierTi araa mkafiod Camoyalibebuli da agreTve zogierTi maTgani modis

winaaRmdegobaSi sxvebTan, amitom saWiroa raRac kompromisis gamonaxva.

ganvixiloT, risgan Sedgeba garemo, romelSic moZraobs manqana. pirvel rigSi esaa

gzebi dawyebuli avtobanebidan damTavrebuli soflis orRobeebiT. am gzebze mZRols

SeiZleba Sexvdes sxva satransporto saSualebebi, fexiT mosiaruleni, cxovelebi, muSebi,

romlebic awarmoeben saremonto samuSaoebs, sapatrulo policia. taqsis mZRols saqme aqvs

potenciur an realur mgzavrebTan. man unda gaiTvaliswinos agreTve meteorologiuri

pirobebi. avtomatizebul mZRols dasWirdeba Semsrulebeli meqanizmebi, romelTa

saSualebiTac is SesZlebs marTos manqana da iqonios urTierToba rogorc mgzavrebTan,

aseve moZraobis sxva monawileebTan. am miznebis misaRwevad mas dasWirdeba gadamwodebi.

maT Soris erTi an ramdenime videokamera, spidometri, odometri, aqselometri da yvela is

sistemebi, romlebic Seatyobineben manqanis teqnikur gamarTulobas. garda amisa mas

dasWirdeba agreTve garemos eleqtronuli ruka da navigaciis globaluri Tanamgzavruli

sistema Tavisi adgilmdebareobis gansasazRvravad. ai aseTi SeiZleba iyos avtomatizebuli

mZRolis problemuri garemo. saerTod cxadia, rom rac ufro rTulia amocana, romelic

dgas agentis winaSe, miT ufro rTulia problemuri garemoc. SevecadoT movaxdinoT

problemuri garemos klasificireba.

1.1.1.1. mTlianad dakvirvebadi an nawilobriv dakvirvebadimTlianad dakvirvebadi an nawilobriv dakvirvebadimTlianad dakvirvebadi an nawilobriv dakvirvebadimTlianad dakvirvebadi an nawilobriv dakvirvebadi.MTuki gadamwodebi agents awvdian

srul informacias garemos Sesaxeb drois nebismier momentSi, aseTi garemo iqneba

mTlianad dakvirvebadi. sruli informaciis qveS vgulisxmobT im informacias, romelic

agents sWirdeba gadawyvetilebis misaRebad. aseTi garemo mosaxerxebelia imiT, rom agents

ar sWirdeba Seinaxos Tavis mexsierebaSi garemos mdgomareoba. garemo SeiZleba iyos

nawilobriv dakvirvebadi im SemTxvevaSi, rodesac warmoiSveba xmauri an rodesac

gadamwodebi ver awvdian zust informacias agents. nawilobriv dakvirvebadi iqneba garemo

maSinac, rodesac agents ar gaaCnia informacia garemos romelime maxasiaTebelze.

magaliTad, Cvens mier ganxilul agents, romelsac gadaaqvs piramidebi erTi oTaxidan

meoreSi, gaaCnia mxolod lokaluri gadamwodi, da amitom ar SeuZlia gansazRvros aris

Tu ara samkuTxa piramida meore oTaxSi, xolo avtomatizebul mZRols ar gaaCnia

informacia ra manevris Sesrulebas apireben moZraobis sxva monawileni.

2222. determinirebuli an stoqasturideterminirebuli an stoqasturideterminirebuli an stoqasturideterminirebuli an stoqasturi. Tu garemos Semdegi mdgomareoba mTlianad

gansazRvrulia mimdinare mdgomareobiT da agentis qmedebiT, maSin garemo

determinirebulia, winaaRmdeg SemTxvevaSi ki stoqasturi. mTlianad dakvirvebad garemoSi


agents ar uxdeba imoqmedos ganuzRvrelobis pirobebSi, magram Tu garemo nawilobriv

dakvirvebadia, maSin iqmneba STabeWdileba, rom garemo stoqasturia, radgan agents ar

SeuZlia daakvirdes mis yvela maxasiaTebels. amitom zogjer ufro mosaxerxebelia vTqvaT,

rom garemo determinirebulia an stoqasturia agentis TvalsazrisiT. aSkaraa, rom aseTi

ganmartebis SemTxvevaSi agent – taqsistis garemo stoqasturia, radgan mas ar SeuZlia

zustad gansazRvros sxva monawileTa qceva, an SeiZleba mis avtomobils moulodnelad

raime gaufuWdes.

3333. epizoduri an mimdevrobiTiepizoduri an mimdevrobiTiepizoduri an mimdevrobiTiepizoduri an mimdevrobiTi. epizodur problemur garemoSi agenti aRiqvams

konkretul epizods, Rebulobs Sesabamis gadawyvetilebas da moqmedebs am gadawyvetilebis

safuZvelze. am SemTxvevaSi arsebiTia, rom miRebuli gadawyvetileba aranair gavlenas ar

axdens Semdeg epizodze. magaliTad, davuSvaT agenti axdens detalebis gadarCevas

konveirze. agenti akvirdeba detals romelic mis winaSea da Tu mas gaaCnia defeqti,

gadadebs mas konveiridan. es gadawyvetileba veranairad ver gansazRvravs imas, iqneba Tu

ara Semdegi detalic defeqtiT.AaseT garemoSi agents uadvildeba moqmedeba, radgan araa

saWiro gaiTvaliswinos ra gavlenas moaxdens misi gadawyvetileba problemur garemoze.

gansxvavebiT aseTi garemosgan, mimdevrobiT garemoSi yoveli gadawyvetileba moqmedebs

problemuri garemos SesaZlo mdgomareobaze da agents uxdeba amis gaTvaliswineba. aseTi

garemos magaliTia Wadrakis TamaSi.

4444.... statikuri an dinamiuristatikuri an dinamiuristatikuri an dinamiuristatikuri an dinamiuri. Tu problemuri garemo SeiZleba Seicvalos im periodSi,

rodesac agenti irCevs Tavis qmedebas, aseT garemos ewodeba am agentisaTvis dinamiuri

garemo, winaaRmdeg SemTxvevaSi problemuri garemo statikuria. statikur garemoSi

moqmedeba ufro martivia, radgan agents ar sWirdeba gadawyvetilebis miRebis momentSi

akvirdebodes garemos da agreTve araa SezRuduli droSi. Tu droTa ganmavlobaSi garemo

ar icvleba, magram icvleba agentis muSaobis maxasiaTeblebi, maSin aseT garemos uwodeben

naxevrad dinamiur garemos.

5555. diskretuli an uwyvetidiskretuli an uwyvetidiskretuli an uwyvetidiskretuli an uwyveti. gansxvaveba diskretul da uwyvet garemos Soris SeiZleba

exebodes garemos mdgomareobebs, drois aRricxvis meTodebs da agreTve agentis mier

garemos aRqmasa da qmedebebs. magaliTad, Wadrakis TamaSis garemo diskretulia rogorc

garemos mdgomareobebiT, agreTve aRqmisa da qmedebebis mixedviT, gansxvavebiT taqsis

tarebis garemosgan, romelSic garemos mdgomareobebi, dro, aRqma da qmedebebic uwyvetia.

6666. erTagentiani da multiagentianierTagentiani da multiagentianierTagentiani da multiagentianierTagentiani da multiagentiani. gansxvaveba erTagentian da multiagentian

garemoebebs Soris erTi SexedviT Zalian martivia. magaliTad, krosvordis amoxsnis

garemo erTagentiani garemoa, xolo Wadrakis TamaSis garemo ki oragentiani, Tumca aqac

arsebobs garkveuli niuansebi. Cven aRvwereT ra niSnebis safuZvelze esa Tu is arsi

SeiZlebaSeiZlebaSeiZlebaSeiZleba CavTvaloT agentad, magram ar migviTiTebia romeli arsi undaundaundaunda ganvixiloT

rogorc agenti. unda CaTvalos Tu ara taqsis mZRolma sxva satransporto saSualebebis

mZRolebi agentebad, Tu moeqces maT rogorc ubralod stoqasturad moZrav obieqtebs?

arsebiTi gansxvaveba mdgomareobs imaSi, CaiTvalos Tu ara obieqtis qceva iseT faqtorad,

romelic gavlenas axdens agentis muSaobis maxasiaTeblebze. Wadrakis TamaSSi

mowinaaRmdege cdilobs ra moaxdinos Tavisi muSaobis maxasiaTeblebis maqsimizacia,


avtomaturad iwvevs agentis muSaobis maxasiaTeblebis minimizacias. amitom Wadrakis TamaSi

aris konkurentulikonkurentulikonkurentulikonkurentuli multiagenturi garemo. taqsis tarebis garemoSi ki dajaxebaTa

Tavidan acileba iwvevs yvela agentis muSaobis maxasiaTeblebis maqsimizirebas, amitom

aseTi garemo aris nawilobriv kooperaciulikooperaciulikooperaciulikooperaciuli garemo (nawilobriv imitom rom sxva

parametrebiT is SeiZleba iyos konkurentuli). @M

2.7.2.7.2.7.2.7. agentTa tipebi.agentTa tipebi.agentTa tipebi.agentTa tipebi. aqamde Cven agentebis Tvisebebs ganvixilavdiT mxolod maTi qcevis

analizis mixedviT. gadavideT maTi funqcionirebis aRweraze. xelovnuri inteleqtis

amocana mdgomareobs agentis programis SeqmnaSi, romelic axdens agentis funqciis

realizacias. igulisxmeba, rom es programa unda muSaobdes garkveul gamomTvlel

mowyobilobaSi fizikuri gadamwodebiT da Semsrulebeli meqanizmebiT. am komponentebs

mTlianobaSi uwodeben arqiteqturasarqiteqturasarqiteqturasarqiteqturas. agentis struqtura SeiZleba warmovadginoT Semdegi

saxiT:

agentis stagentis stagentis stagentis struqtrura = arqiteqtura + programaruqtrura = arqiteqtura + programaruqtrura = arqiteqtura + programaruqtrura = arqiteqtura + programa

cxadia, rom arCeuli programa unda Seesabamebodes agentis arqiteqturas. ase magaliTad,

Tu programa gamoimuSavebs iseT rekomendaciebs, rogoricaa “siaruli”, arqiteqturaSi

gaTvaliswinebuli unda iyos Sesabamisi meqanizmi. gansxvavebiT agentis funqciisagan,

romelic Tavis Sesasvlelze Rebulobs aRqmaTa aqtebis mTel mimdevrobas, agentis

programaSi SesaZlebelia mxolod mimdinare aRqmis an. swored am momentiT gansxvavdeba

erTmaneTisagan agenris funqcia da agentis programa. amitom Tu mas qmedebis

Sesasruleblad sWirdeba aRqmaTa aqtebis garkveuli mimdevroba, man TviTon unda

daimaxsovros es mimdevroba.

sur. # 2.3. refleqsuri agentis struqtura

2.8.2.8.2.8.2.8. martivi refleqsuri agentimartivi refleqsuri agentimartivi refleqsuri agentimartivi refleqsuri agenti. A aseTi agentebi irCeven qmedebas mxolod mimdinare

aRqmis aqtis safuZvelze da ar iTvaliswineben winaistorias. Cvens magaliTSi ganxiluli

agenti, romelsac erTi oTaxidan meoreSi gadaaqvs piramidebi warmoadgens swored aseT

agentiagentiagentiagenti gadamwodebi Semsrulebeli meqanizmebi

rogoria garemo

wesi “piroba -qmedeba”

garemo garemo garemo garemo exla romeli

qmedeba Sevasrulo


agents. mis programas aqvs Semdegi saxe:

refleqsuri agentis Ffunqcia [mdgomareoba,statusi] Seasrule qmedeba

Tu Tu Tu Tu mdgomareoba = A oTaxi

Tu Tu Tu Tu statusi = aris samkuTxa piramida maSin maSin maSin maSin Seasrule: gadaitane B –Si, TuTuTuTu ara

gadadi B oTaxSi

TuTuTuTu mdgomareoba = B oTaxi

TuTuTuTu statusi = aris oTxkuTxa piramida maSinmaSinmaSinmaSin Seasrule: gadaitane A –Si, Tu Tu Tu Tu ara

gadadi A oTaxSi

rogorc vxedavT, es programa gacilebiT pataraa im cxrilTan SedarebiT, romelic

aRwerda agentis funqcias. es Semcireba ganpirobebulia imiT, rom ugulvebelyofilia

aRqmaTa aqtebis istoria, ris gamoc yvela SesaZlo variantebis ricxvi davida oTxamde.

refleqsuri agentis qmedebis safuZvels warmoadgens principi: Tu sruldeba raime

piroba, Seasrule Sesabamisi qmedeba. SemoklebiT es SegviZlia aRvniSnoT rogorc wesi

“piroba “piroba “piroba “piroba –––– qmedeba”. qmedeba”. qmedeba”. qmedeba”. aseTi agentebi mravlad gvxvdeba rogorc teqnikur sistemebSi, aseve

cocxal organizmebSic. maTi funqcionireba Zalian martivia, magram maT gaaCniaT Zalian

SezRuduli inteleqti (Tu gaaCniaT saerTod). refleqsuri agentis gadawyvetilebebi

mxolod maSin iqneba swori, rodesac mxolod mimdinare aRqmis aqti sakmarisia swori

gadawyvetilebis misaRebad, anu Tu garemo aris mTlianad dakvirvebadi. sakmarisia garemo

gaxdes nawilobriv dakvirvebadi da agentis qmedebebi aRar iqneba situaciis Sesabamisi.

magaliTad, ganvixiloT taqsis tarebis problemuri garemo. Tu win mimavali manqana iwyebs

damuxruWebas da inTeba misi samuxruWe farebi, mZRolma es unda SeniSnos da TviTonac

daiwyos damuxruWeba. anu SeiZleba CamovayaliboT “piroba – qmedebis” Semdegi wesi:

TuTuTuTu avto win – amuxruWebs maSinmaSinmaSinmaSin daiwye damuxruWeba

davuSvaT, am pirobis aRqma xdeba mxolod mimdinare aRqmis aqtiT. radganac zogierT

Zveli markis avtomobils samuxruWe farebi SeTavsebuli aqvs sxva sasignalo farebTan,

mimdinare aRqmis faqtiT SeuZlebelia davadginoT, amuxruWebs Tu ara win mimavali manqana.

martivi refleqsuri agenti, romelic misdevs am manqanas, an daamuxruWebs maSin rodesac

amis aucilebloba ar iqneba, an rac kidev ufo savalaloiqneba, saerTod ar daamuxruWebs.

2.9. 2.9. 2.9. 2.9. modelze dafuZnebuli refleqsuri agentebimodelze dafuZnebuli refleqsuri agentebimodelze dafuZnebuli refleqsuri agentebimodelze dafuZnebuli refleqsuri agentebi. nawilobriv dakvirvebadi garemos

SemTxvevaSi kargi iqneba Tu agenti daakvirdeba agreTve mimdinare aRqmis aqtis istorias.

rac niSnavs, rom agents unda gaaCndes garkveuli SSSSinagani mdgomareobainagani mdgomareobainagani mdgomareobainagani mdgomareoba,,,, romelic

damokidebulia aRqmis aqtebis istoriaze da amitom asaxavs mimdinare momentSi zogierT

daukvirvebad aspeqts. zemoT ganxilul magaliTSi imisaTvis, rom agentma daadginos,

amuxruWebs Tu ara manqana, sakmarisia agentis Sinagani mdgomareoba inaxavdes mxolod wina

kadrs, rac miscems agents saSualebas aRmoaCinos damuxruWebis dawyebis momenti.

imisaTvis, rom uzrunvelvyoT am Sinagani informaciis ganaxleba, saWiroa agentis

programaSi SevitanoT ori saxis codna. pirveli, agentma unda icodes Tu rogor


Seicvleba garemo misi Carevis gareSe da meore, ra cvlilebebs gamoiwvevs misi

qmedebebi garemoSi. aseT codnas uwodeben garemos modelsgaremos modelsgaremos modelsgaremos models, xolo agents, romelSic

gamoiyeneba aseTi modeli, uwodeben modelze dafdafdafdafuuuuZnebul agentsZnebul agentsZnebul agentsZnebul agents.

sur. # 2.4. modelze dafuZnebuli refleqsuri agenti

2.10. mizanze da modelze dafuZnebuli agentebimizanze da modelze dafuZnebuli agentebimizanze da modelze dafuZnebuli agentebimizanze da modelze dafuZnebuli agentebi. garemos codna xSirad ar aris

sakmarisi imisaTvis rom agentma miiRos swori gadawyvetileba. magaliTad, Tu taqsi dgas

sur. # 2.5. mizanze da modelze dafuZnebuli agentis struqtura

gadamwodebi

agentiagentiagentiagenti Semsrulebeli meqanizmebi

mdgomareoba

garemogaremogaremogaremo

rogoria exla garemo

rogor viTardeba garemo

ra zegavlena eqneba Cems qmedebas

miznebi romeli qmedeba Sevasrulo

ra moxdeba Tu Sevasruleb A qmedebas

gadamwodebi


mdgomareoba


rogoria exla garemo



wesi “piroba-qmedeba” romeli qmedeba Sevasrulo


gzajvaredinze, swori gadawyvetilebis misaRebad aucilebelia agentma icodes Tu sad

unda mivides is. agents sWirdeba ara marto garemos mimdinare mdgomareobis codna, aramed

informacia miznis miznis miznis miznis Sesaxeb, romelic aRwers problemuri garemos sasurvel situaciebs.

agentis programas SeuZlia am informaciisa da SesaZlo qmedebaTa Sedegebis kombinireba

iseTi qmedebis asarCevad, romelic SesaZleblobas misces miaRwios mizans. zogjer miznis

miRweva Zalian advilia, radgan mis misaRwevad sakmarisia erTi qmedeba. ufro rTul da

realur SemTxvevebSi, es ase ar aris. maSin agentis programaSi gaTvaliswinebuli unda

iyos iseTi procedurebi, romlebic moaxdenen miznis ZebnasZebnasZebnasZebnas da qmedebaTa mimdevrobis

dagegmvasdagegmvasdagegmvasdagegmvas am miznis misaRwevad.

AaseTi agentis gadawyvetilebis miRebis procedura arsebiTad gansxvavdeba refleqsuri

agentis gadawyvetilebis miRebis procedurisagan, radganac agents uxdeba upasuxos or

kiTxvas: “ra moxdeba Tu me miviReb am gadawyvetilebas?” da “mivaRwev Tu ara am qmedebis

Sedegad mizans?”. refleqsur agentSi aseTi informacia araa warmodgenili, radganac masSi

CamontaJebuli wesebi amyareben pirdapir kavSirs garemos aRqmasa da qmedebas Soris.

mizanze dafuZnebuli agenti ufro moqnilia, radganac codna, romelic mas gaaCnia

saSualebas aZlevs garemos cvlilebebis dros Secvalos Tavisi qmedeba. magaliTad, Tu

daiwyeba wvima, taqsis avtomatizebuli mZRoli Sesabamisad moZebnis Tavis codnaSi, Tu

rogor Seicvala damuxruWebis manZili da amis Sesabamisad Seitans cvlilebebs Tavis

qmedebebSi. refleqsuri agentis SemTxvevaSi ki mogviwevda Segvecvala “piroba – qmedebis”

wesebi.

sur. #2.6. sargeblianobaze dafuZnebuli agentis struqtura

gadamwodebi


mdgomareoba


rogoria exla garemo



sargebeli

romeli qmedeba Sevasrulo

ra moxdeba Tu Sevasruleb A qmedebas

ra sargebels momitans es qmedeba


2.11. sargeblia2.11. sargeblia2.11. sargeblia2.11. sargeblianobaze dafuZnebuli agentebinobaze dafuZnebuli agentebinobaze dafuZnebuli agentebinobaze dafuZnebuli agentebi. xSir SemTxvevaSi kargi gadawyvetilebis

misaRebad sakmarisi ar aris mxolod miznis miRweva. igive taqsis marTvis SemTxvevaSi

daniSnulebis adgils SeiZleba mivaRwioT sxvadasxva gziT, romelTagan zogi gza iqneba

ufro grZeli, ukeTesi xarisxis da SeiZleba dagvexarjos ufro meti dro (da SeiZleba

sawvavic), magram manqanis cveTa iqneba minimaluri, zogi ki ufro mokle, ufro cudi

xarisxis da SesaZlebelia droisa da sawvavis dazogva, magram SeiZleba davazianoT

manqana. mizani gvaZlevs saSualebas movaxdinoT mxolod xisti garCeva “mizani

dakmayofilebulia”, an mizani “ar aris dakmayofilebuli”, magram am SemTxvevaSi es ar

aris sakmarisi, radganac mizani orive SemTxvevaSi dakmayofildeba. aseT SemTxvevaSi

SesaZlebelia gamoviyenoT sargeblisargeblisargeblisargeblianobis anobis anobis anobis cneba. sargeblianobis funqcia sargeblianobis funqcia sargeblianobis funqcia sargeblianobis funqcia asaxavs

mdgomareobas, an mdgomarebaTa mimdevrobas namdvil ricxvTa R simravleSi agentis

prioritetebis gaTvaliswinebiT. aqedan gamomdinare, agenti airCevs im qmedebas (an

qmedebaTa mimdevrobas), romelic ukeT daakmayofilebs agentis muSaobis maxasiaTeblebis

kriteriumebs. sargeblianobis funqcia gansakuTrebiT mosaxerxebelia, rodesac gvaqvs

konfliqturi miznebi magaliTad, siCqare da moZraobis usafrTxoeba. aseT SemTxvevaSi

sargeblianobis funqcia saSualebas gvaZlevs vipovoT misaRebi kompromisi. aseve

aucilebelia sargeblianobis funqcia, rodesac gvaqvs ramdenime mizani, romlebiskenac

miiswrafis agenti, magram zustad arcerTi miznis miRweva ar xerxdeba.aseT SemTxvevaSi

sargeblianobis funqcia saSualebas gvaZlevs miznebis prioritetebis gaTvaliswinebiT

SevafasoT romelime miznis miRwevis albaToba. A

2.122.122.122.12. dadadadaswavladi agentebiswavladi agentebiswavladi agentebiswavladi agentebi. aqamde Cven vixilavdiT agentebis programebs, romlebSic

gamoiyeneba gadawyvetilebis miRebis sxvadsaxva meTodebi, magram araferi ar gviTqvams, Tu

rogor unda Seiqmnas aseTi programebi. jer kidev a. tiuringma gaanaliza aseTi

mwarmoeblobis standartimwarmoeblobis standartimwarmoeblobis standartimwarmoeblobis standarti

sur. N# 2.7. daswavladi agentebis zogadi sqema.

gadamwodebi ukukavSiri cvlilebebi swavlis miznebi


kritikosi

daswavladi komponenti

problemaTa generatori

mawarmoebeli komponenti



programebis Seqmnis problema da mivida im daskvnamde, rom saWiroa raime produqciuli

meTodi, romelic gaaadvilebs programebis Seqmnas. manve aseT meTodad miiCnia daswavladi

manqanis Seqmna da Semdeg maTi swavleba. dRes swored aseTi midgoma dominirebs xelovnur

inteleqtSi.

rogorc naCvenebia sur. # 2.7. daswavladi agentis struqturadaswavladi agentis struqturadaswavladi agentis struqturadaswavladi agentis struqtura Sedgeba oTxi

konceptualuri komponentisagan. yvelaze mniSvnelovania gansxvaveba daswavladdaswavladdaswavladdaswavlad

komponentsakomponentsakomponentsakomponentsa da muSa komponentsmuSa komponentsmuSa komponentsmuSa komponents Soris. daswavladi komponenti pasuxismgebelia agentis

muSaobis gaumjobesebaze, xolo muSa komponenti uzrunvelyofs qmedebis Sesrulebas.

faqtobrivad, muSa komponenti aris is, rasac aqamde ganvixilavdiT rogorc agents: is

Rebulobs aRqmiT informacias da iRebs gadawyvetilebas ra qmedeba unda ganxorcieldes.

daswavladi komponenti iyenebs ra informacias, romelsac is iRebs kritikosisagankritikosisagankritikosisagankritikosisagan

ukukavSiris saSualebiT, romelic Seicavs agentis muSaobis Sefasebas, gansazRvravs Tu

rogor unda Seicvalos muSa komponenti raTa misi muSaoba gaumjobesdes.

daswavladi agentis meoTxe ZiriTad komponents warmoadgens problemaTa generatoriproblemaTa generatoriproblemaTa generatoriproblemaTa generatori,

romlis amocanas warmoadgens iseTi eqsperimentebis SeTavazeba muSa komponentisaTvis,

romelTa safuZvelzec SesaZlebeli iqneba axali, ufro ukeTesi qmedebebis aRmoCena.

sakontrolo kiTxvebisakontrolo kiTxvebisakontrolo kiTxvebisakontrolo kiTxvebi:

1. ras ewodeba inteleqtualuri agenti?

2. rogor agents ewodeba racionaluri agenti?

3. aRwereT inteleqtualuri agentis struqtura da moiyvaneTYmagaliTebi.

4. ra faqtorebi gansazRvraven agentis racionalurobas?

5. ra aris agentis funqcia da agentis programa da ra gansxvavebaa maT Soris?

6. garda informaciis Segrovebisa, ra unda SeeZlos racionalur agents?

7. ras warmoadgens problemuri garemo?

8. ramden da ra ZiriTad tipebad SeiZleba daiyos garemo

9. risgan Sedgeba agentis struqtura

10. aRwereT yvela tipis agentebis struqturebi.

sasasasavarjiSoebi:varjiSoebi:varjiSoebi:varjiSoebi:

1. CamoayalibeT piramidebis gadamtani agentis racionalurobis pirobebi. aris Tu ara

leqciaSi moyvanili funqcia racionaluri?

2. aRwereT problemuri garemo Semdegi agentebisaTvis: roboti – fexburTeli;

avtonomiuri yvelganmavali marsze.

3. SeadgineT refleqsuri agentis proeqti, romelsac gaaCnia Sinagani mdgomareobebi.

leqleqleqleqcicicicia #a #a #a #3333

agentebi, romlebic problemebs wyveten Zebnis saSualebiT agentebi, romlebic problemebs wyveten Zebnis saSualebiT agentebi, romlebic problemebs wyveten Zebnis saSualebiT agentebi, romlebic problemebs wyveten Zebnis saSualebiT

3.1. problemebis (amocanebis) warmodgena mdgomareobaTa sivrceSi.3.1. problemebis (amocanebis) warmodgena mdgomareobaTa sivrceSi.3.1. problemebis (amocanebis) warmodgena mdgomareobaTa sivrceSi.3.1. problemebis (amocanebis) warmodgena mdgomareobaTa sivrceSi. wina leqciaze Cven

ganvixileT mizanze damyarebuli agentebis klasi, romlebsac SeuZliaT Tavisi muSaobis

maxasiaTeblebis maqsimizacia da aRvniSneT, rom Tu mizani ar aris advilad miRwevadi,

maSin agentis programaSi gaTvaliswinebuli unda iyos iseTi procedurebi, romlebic

uzrunvelyofen miznis Zebnasmiznis Zebnasmiznis Zebnasmiznis Zebnas.. ganvixiloT ra procedurebis saSualebiT SeiZleba am

Zebnis ganxorcieleba. . . . am SemTxvevaSi Cven ar ganvixilavT, Tu rogor xdeba miznis

formireba. igulisxmeba, rom agenti winaswar axdens miznis formirebas, an sxva usvams mas

mizans. ubralod, mizani CvenTvis aris garemos mdgomdgomdgomdgomareobaTa raime simravlemareobaTa raime simravlemareobaTa raime simravlemareobaTa raime simravle. agentis

(aseTi tipis agentebs uwodeben amocanaTa amomxsnel agentebsamocanaTa amomxsnel agentebsamocanaTa amomxsnel agentebsamocanaTa amomxsnel agentebs) amocanaa gansazRvros

qmedebaTa qmedebaTa qmedebaTa qmedebaTa ra mimdevroba miiyvans mas miznis mdgomareobamde. magram sanam is daiwyebs am

qmedebaTa ganxilvas, saWiroa jer dazustdes, Tu ra donis qmedebebi iqneba mocemuli

amocanisaTvis misaRebi. am problemis ukeT gasagebad ganvixiloT aseTi magaliTi,

davuSvaT, agenti imyofeba baTumSi da misi mizania moxvdes TbilisSi. Tu is daiwyebs

qmedebebis ganxilvas im doneze, rom “saWiroa gadavdga marcxena fexi 50 santimetrze,

Semdeg marjvena 60 santimetrze da ase Semdeg”, an Tu agenti mogzaurobs avtomobiliT -

“movatrialo saWe ori gradusiT”, maSin cxadia is realurad ver SesZlebs amocanis

gadawyvetas. amocanis warmodgenidan detalebis mocilebas ewodeba abstragiabstragiabstragiabstragireba.reba.reba.reba.

mdgomareobaTa abstragirebasTan erTad, saWiroa qmedebaTa abstragirebac. magaliTad Tu

Cveni agenti mogzaurobs avtomobiliT, sulac ar aris saWiro iseTi qmedebebis ganxilva,

romlebic dakavSirebulia manqanis marTvis problemebTan, an agentis sxva qmedebebTan.

Zebnis sxvadasxva algoriTmebis gamoyenebis SemTxvevaSi SesaZlebelia gamoviyenoT

abstragirebis sxvadasxva done.E

3.2. amocanis formulireba 3.2. amocanis formulireba 3.2. amocanis formulireba 3.2. amocanis formulireba mdgomareobs swored abstragirebis donis SerCevaSi, anu im

qmedebebisa da mdgomareobaTa simravleebis gansazRvraSi, romlebic saSualebas mogvcemen

yvelaze optimalurad mivaRwioT garkveul mizans. Cveni magaliTis SemTxvevaSi, Tu

davuSvebT, rom agenti mogzaurobs avtomobiliT, albaT yvelaze swori iqneba Tu is

qmedebebad ganixilavs avtomobiliT gadaadgilebas erTi qalaqidan meoreSi. maSin

agentisaTvis mdgomareobebi iqneba misi yofna sxvadasxva konkretul qalaqebSi, qmedebebi

ki gadasvla erTi qalaqidan meoreSi.

davuSvaT, agenti ar icnobs saqarTvelos geografias, baTumidan ki gamodis ramdenime

gza, romlebsac mivyavarT sxvadasxva qalaqebSi. maSin, Tu agents ar eqneba damatebiTi

informacia, is alalbedze airCevs romelime gzas da Tu es arCevani ar iqneba swori, is

Tbilisis magivrad SeiZleba moxvdes erzrumSi. exla davuSvaT, mivawodeT agents

damatebiTi informacia saqarTvelos rukis saxiT. aseT SemTxvevaSi agents SeuZlia

ganixilos yvela gadasvla baTumidan sxva qalaqebSi, Semdeg am qalaqebidan Semdeg

qalaqebSi da aRmoaCinos im qmedebaTa mimdevroba, romelic Caiyvans mas baTumidan

TbilisSi.

rogor problemur garemoSi uxdeba muSaoba amocanaTa amomxsnel agents? cxadia, rom

leqcia #leqcia #leqcia #leqcia #3333. agentebi, romlebic problemebs wyveten Zebnis saSualebiT. agentebi, romlebic problemebs wyveten Zebnis saSualebiT. agentebi, romlebic problemebs wyveten Zebnis saSualebiT. agentebi, romlebic problemebs wyveten Zebnis saSualebiT 27

garemo aris statikuri, radganac amocanis amoxsnis procesSi ar aris gaTvaliswinebuli

misi cvlileba (magaliTad, rom SeiZleba xidi Caingres, an gza gadaiketos, an romelime

qalaqi gaqres mTlianad). cnobilia agreTve agentis sawyisi mdgomareobac (saidan unda

daviwyoT qmedebebi), ese igi garemo mTlianad dakvirvebadia. radganc garemos aRweraSi

Sedian mxolod qalaqebi da maT Soris damakavSirebeli gzebi da Cven vgulisxmobT, rom

gadasvla erTi qalaqidan meoreSi xdeba myisierad, cxadia, rom garemo aris diskretuli....

aseT garemoSi amocanaTa amonaxsnebi warmoadgenen qmedebaTa mimdevrobebs da maTSi ar

SeiZleba gaTvaliswinebuli iyos raime moulodneli SemTxvevebi. ufro metic, agenti

gadawyvetilebis miRebis dros ar iTvaliswinebs raime aRqmis Sedegebs, rac imas niSnavs,

rom garemo aris determinirebuli. yovelive zemoTTqmulidan gamodis, rom saqme gvaqvs

umartives garemosTan.

AmdgomareobaTa garemo aseT SemTxvevaSi warmoadgens grafsgrafsgrafsgrafs, romlis wveroebi

aRniSnaven mdgomareobebs, xolo rkalebi Seesabamebian im qmedebebs, romelTa

saSualebiTac SesaZlebelia gadasvla erTi mdgomarebidan meoreSi. Zebnis amocana aseT

SemTxvevaSi SeiZleba ganvsazRvroT Semdegi xuTi parametris saSualebiT:

))(},{},{},{},({ 0 TwTFSS , sadac }{ 0S aris sawyis mdgomasawyis mdgomasawyis mdgomasawyis mdgomareobaTa simravlereobaTa simravlereobaTa simravlereobaTa simravle, anu grafis im

wveroebis simravle, romelSic SeiZleba imyofebodes agenti amocanis amoxsnis dawyebisas

( SS ⊂0 ).

}{ F aris im qmedebaTa simravle, romelic xelewifeba agents. sxvanairad es aris

SvilobiSvilobiSvilobiSvilobil wveroTa ganmsazRvrel funqciaTal wveroTa ganmsazRvrel funqciaTal wveroTa ganmsazRvrel funqciaTal wveroTa ganmsazRvrel funqciaTa simravle, romelTa saSualebiTac erTi

mdgomareobidan SeiZleba miviRoT meore mdgomareoba lki SSf =)( . yoveli aseTi if

funqciis gansazRvris area SSk ⊂ simravle da mniSvnelobaTa simravlea SSl ⊂

simravle. am simravles xSirad uwodeben agreTve operatorTa simravlesoperatorTa simravlesoperatorTa simravlesoperatorTa simravles.

}{S aris mdgomareobmdgomareobmdgomareobmdgomareobaTaaTaaTaaTa sivrce sivrce sivrce sivrce, anu yvela im mdgomareobaTa simravle, romelic

SeiZleba Segvxvdes mocemul amocanaSi. es simravle aracxadad ganisazRvreba sawyisi

mdgomareobisa da operatorTa simravlis saSualebiT. gzagzagzagza mdgomareobaTa sivrceSi

ewodeba im mdgomareobaTa mimdevrobas, romelic iwyeba sawyisi mdgomareobiT da

erTmaneTTan dakavSirebulia dasaSveb operatorTa mimdevrobiT.

}{}{ ST ⊂ miznis mdgomareobebis simravlemiznis mdgomareobebis simravlemiznis mdgomareobebis simravlemiznis mdgomareobebis simravle – warmoadgens im mdgomareobebs,

romelTagan erTerTSi moxvedra Seesabameba problemis gadawyvetas, anu amocanis amoxsnas.

)(Tw aris funqcia, romelic yovel gzas sawyisi mdgomareobidan miznis

mdgomareobamde Seusabamebs raime ricxviT mniSvnelobas. mas uwodeben gzisgzisgzisgzis Rirebulebis Rirebulebis Rirebulebis Rirebulebis

funqciasfunqciasfunqciasfunqcias. agenti irCevs iseT funqcias, romelic Seesabameba misi muSaobis maxasiaTeblebs.

mniSvnelovania, rom amocanaTa amomxsnel agents unda gaaCndes miznis Semmiznis Semmiznis Semmiznis Semowmebisowmebisowmebisowmebis

proceduraproceduraproceduraprocedura, romelic mas miscems saSualebas gansazRvros aris Tu ara mocemuli

konkretuli mdgomareoba miznis mdgomareoba. zogjer miznis mdgomareobaTa simravle

moicema cxadi saxiT da es procedura daiyvaneba ubralo Semowmebaze, aris Tu ara

mocemuli mdgomareoba }{T simravlis elementi (rogorc Cvens mier zemoTganxilul


magaliTSi). SeiZleba mizani mocemuli iyos raime Tvisebebis aRweriT, rogorc gvaqvs

Wadrakis TamaSis SemTxvevaSi. aseT SemTxvevaSi unda Semowmdes, akmayofilebs Tu ara

mocemuli mdgomareoba am Tvisebebs.

3.3 magaliTebi. 3.3 magaliTebi. 3.3 magaliTebi. 3.3 magaliTebi. ai aseTi komponentebi gansazRvraven amocanas da saWiroa maTi gaerTianeba

monacemTa stuqturaSi, romelic miewodeba Sesasvlelze amocanaTa amomxsnel agents.

aseTi formulirebis dros amocanis amonaxsniamocanis amonaxsniamocanis amonaxsniamocanis amonaxsni ewodeba gzas sawyisi mdgomareobidan miznis

mdgomareobamde. amoxsnis xarisxi izomeba gzis Rirebulebis funqciiT, xolo optimaluri optimaluri optimaluri optimaluri

amonaxsniamonaxsniamonaxsniamonaxsni ewodeba im gzas, romelsac aqvs minimaluri Rirebuleba.

ganvixiloT aseTi amocanebis ramdenime magaliTi. pirvel rigSi aRvniSnoT, rom es

amocanebi SeiZleba iyos sxvadasxva Tavsatexebi, xelovnurad mofiqrebuli mcire zomis

amocanebi, romlebic Zalian kargia algoriTmebis gamosakvlevad. aseT amocanebs uwodeben

gamartivebul amocanebs. arseboben agreTve realuri amocanebi, romelTa amoxsna marTlac

sWirdeba adamians. aseT amocanebs, rogorc wesi ar gaaCniaT iseTive sayovelTaod

miRebuli erTiani aRwera, rogorc es gaaCniaT gamartivebul amocanebs.

gamartivebuli amocanebidan pirvel rigSi unda aRvniSnoT rvianisrvianisrvianisrvianis TamaSis amocanaTamaSis amocanaTamaSis amocanaTamaSis amocana. es

saTamaSo warmoadgens dafas cxra ujriT (3× 3) da rva fiSkiT, romlebic gadanomrilia erTidan rvamde. fiSka, romelic mdebareobs carieli ujris gverdiT, SeiZleba gadaweuli

iqnas am ujraze. TamaSis mizania mivaRwioT romelime konkretul miznis mdgomareobas

sawyisi mdgomareobidan (iseTs, rogoric magaliTad miTiTebulia sur. #4.1.). am amocanis

standartul formulirebas aqvs Semdegi saxe:

1. mdgomareobebi (mdgomareobaTa simravle). mdgomareobebi (mdgomareobaTa simravle). mdgomareobebi (mdgomareobaTa simravle). mdgomareobebi (mdgomareobaTa simravle). mdgomareobaTa aRwera gansazRvravs

TiToeuli fiSkis da carieli adgilis mdgomareobas mocemul cxra kvadratze. es

Zalian

a) b)

sur. # 4.1. rvianis TamaSis sawyisi a) da miznis b) mdgomareobebi.

advilia 3× 3 matricis saSualebiT, sadac TiToeuli elementi Rebulobs

mniSvnelobebs nolidan rvis CaTvliT, im pirobiT, rom cxrave elementi Rebulobs

gansxvavebul mnSvnelobebs,

=

333231

232221

131211

aaa

aaa

aaa

A

sadac Naa ijij ∈≤≤ ,80 , 3, Nji ∈ da klij aa = maSin da mxolod maSin, rodesac

2 8 3

1 6 4

7 5

1 2 3

8 4

7 6 5


., ljki ==

2. ssssawyisi mdgomareobaawyisi mdgomareobaawyisi mdgomareobaawyisi mdgomareoba.... sawyis mdgomareobad SeiZleba aviRoT nebismieri

mdgomareoba.

amasTan, unda aRvniSnoT, rom mocemuli mizani (miznis mdgomareoba) miiRweva

SesaZlo sawyisi mdgomareobebis zustad naxevridan.

3.3.3.3. Svilobili wveros ganmsazRvreli funqcia (operatorebis simravle). Svilobili wveros ganmsazRvreli funqcia (operatorebis simravle). Svilobili wveros ganmsazRvreli funqcia (operatorebis simravle). Svilobili wveros ganmsazRvreli funqcia (operatorebis simravle). es funqcia

axdens dasaSvebi mdgomareobebis formirebas, romlebic warmoadgenen mSobel

wveroze oTxi qmedebis (zeviT, qveviT, marjvniv da marcxniv) Sedegs.

4.4.4.4. miznis Semowmeba. miznis Semowmeba. miznis Semowmeba. miznis Semowmeba. miznis Semowmeba saSualebas gvaZlevs ganvsazRvroT, Seesabameba

Tu ara mocemuli mdgomareoba miznis mdgomareobas.

5.5.5.5. gzis fasi. gzis fasi. gzis fasi. gzis fasi. TiToeuli gadasvla erTi mdgomareobidan meoreSi moiTxovs erTi da

igive samuSaos Sesrulebas rogorc fizikurad (fiSkis gadaweva erTi ujridan

meoreSi), aseve kompiuteruli gamoTvlebis TvalsazrisiT. amitom gadasvlis fasi

ija ujridan romelime mezobel 1+ija -ur ujraSi ),( 1+ijij aaw SegviZlia CavTvaloT

erTis tolad, maSin gzis fasi )(Tw toli iqneba gadasvlebis raodenobisa sawyisi

mdgomareobidan miznis mdgomareobamde.

ganvixiloT kidev erTi magaliTi. rva lazieris amocanis rva lazieris amocanis rva lazieris amocanis rva lazieris amocanis mizania ganvalagoT

Wadrakis dafaze rva lazieri ise, rom arc erTi maTgani ar esxmodes Tavs arcerT sxva

laziers. miuxedavad imisa, rom arseboben specializirebuli algoriTmebi, romlebic

zogadad xsnian am amocans n cali lazierisaTvis, is mainc sainteresoa Zebnis

algoriTmebisaTvis.

SesaZlebelia am amocanis ori ZiriTadi formulireba. inkremeinkremeinkremeinkrementalurintalurintalurintaluri, romlis

drosac gamoiyeneba iseTi operatorebi, romlebic iwyeben ra carieli dafidan,

TandaTanobiT amateben lazierebs dafaze, amasTan, ar iTvaliswineben emuqreba Tu ara

romelime lazieri sxva laziers. srulsrulsrulsruli mdgomareobis mdgomareobis mdgomareobis mdgomareobis formulireba iwyeba dafaze rvave

lazieris dasmis Semdeg da iTvaliswinebs maT Semdgom gadaadgilebebs. aseTi

formulirebis SemTxvevaSi amocanis aRweras aqvs Semdegi saxe:

mdgomareobebi. mdgomareobebi. mdgomareobebi. mdgomareobebi. mdgomareobas warmoadgens dafaze lazierebis nebismieri ganlageba

nolidan rvamde.

sawyisi mdgomaresawyisi mdgomaresawyisi mdgomaresawyisi mdgomareoba. oba. oba. oba. dafaze ar dgas arc erTi lazieri.

Svilobilis ganmsazRvreli funqcia (operatorebi). Svilobilis ganmsazRvreli funqcia (operatorebi). Svilobilis ganmsazRvreli funqcia (operatorebi). Svilobilis ganmsazRvreli funqcia (operatorebi). lazieris dasma dafaze.

Mmiznis Semowmeba.Mmiznis Semowmeba.Mmiznis Semowmeba.Mmiznis Semowmeba. dafazea rva lazieri da arcerTi maTgani ar emuqreba sxva romelimes.

am SemTxvevaSi saWiroa Semowmdes 64 × 63 × 62 ×. . . × 57 = 3 ×10 14 SesaZlo mimdevroba.

Tu Cven gvinda gavaumjobesoT amocanis formulireba, rac gulisxmobs mdgomareobaTa

simravlis Semcirebas, unda avkrZaloT lazieris dasma im ujrebze, romlebic imyofebian

Setevis qveS, maSin miviRebT amocanis axal formulirebas.

mdgomareobebi. mdgomareobebi. mdgomareobebi. mdgomareobebi. Mmdgomareobas warmoadgens n cali lazieris ganlageba )80( ≤≤ n

dafaze, amasTan erTi lazieri dgas marcxnidan dawyebuli TiTo vertikalze ise, rom

arcerTi lazieri ar esxmis Tavs sxvas.


Svilobilis ganmsazRvreli funqcia. Svilobilis ganmsazRvreli funqcia. Svilobilis ganmsazRvreli funqcia. Svilobilis ganmsazRvreli funqcia. lazieris dasma marcxnidan pirvel Tavisufal

vertikalze ise, rom ar moxdes masze Tavdasxma.

AaseTi formulirebis SemTxvevaSi SesaZlebeli xdeba SevamciroT mdgomareobaTa

simravle 2057-mde, da amiT amocana seriozulad gaioldeba. magram, Tu Cven ganvixilavT

davuSvaT 100 lazieris amocanas, pirveli formulirebis SemTxvevaSi mdgomareobaTa

simravle iqneba 40010 , xolo meore SemTxvevaSi –

5210 . Ees ra Tqma unda kolosalurad

didi Semcirebaa, magram darCenili sivrcec Zalian didia imisaTvis, rom Cvenma

algoriTmebma SeZlon realur droSi aseTi amocanis amoxsna.

realuri amocanebidan aRvniSnoT marSrutis Zebnis amocana, marSrutis Zebnis amocana, marSrutis Zebnis amocana, marSrutis Zebnis amocana, cnobili komkomkomkomivoiaJeris ivoiaJeris ivoiaJeris ivoiaJeris

amocana, integraluri sqemebSi elementebis ganlagebis amocana, robotis gadaadgilebis amocana, integraluri sqemebSi elementebis ganlagebis amocana, robotis gadaadgilebis amocana, integraluri sqemebSi elementebis ganlagebis amocana, robotis gadaadgilebis amocana, integraluri sqemebSi elementebis ganlagebis amocana, robotis gadaadgilebis

marTvis amocana, konveiris marTvis amocana marTvis amocana, konveiris marTvis amocana marTvis amocana, konveiris marTvis amocana marTvis amocana, konveiris marTvis amocana da sxva.

3.4. Zebnis algoriTmebis Sefaseba.3.4. Zebnis algoriTmebis Sefaseba.3.4. Zebnis algoriTmebis Sefaseba.3.4. Zebnis algoriTmebis Sefaseba. mas Semdeg, rac movaxdenT amocanis formalizebas,

saWiroa vipovoT amoxsna. Cven ganvixilavT meTodebs, romlebic amocanas xsnian Zebnis Zebnis Zebnis Zebnis

saSualebiTsaSualebiTsaSualebiTsaSualebiT mdgomareobaTa sivrceSi. Aaq aucilebelia gavarCioT ori SemTxveva.

mdgomarebiTa sivrce SeiZleba iyos grafi an xe (xe aris grafis kerZo SemTxveva, rodesac

yovel wveros hyavs mxolod erTi mSobeli wvero). magaliTad, rva lazieris

amocanaSiD(rodesac yoveli Semdegi lazieri dgeba yvelaze marcxena cariel vertikalze),

mdgomareobaTa sivrce warmoadgens xes. amitomac mdgomareobaTa sivrce miiReba SedarebiT

patara da Zebna gaiolebulia. Tu ganvixilavT meore formulirebas, sadac nebismieri

dedofali SeiZleba davdgaT nebismier vertikalze, mdgomareobaTa sivrce iqneba grafi,

sadac erTi da igive mdgomareoba miiRweva !8 gansxvavebuli gziT, rac arTulebs Zebnas.

zogierT amocanebSi mdgomareobaTa sivrce aucileblad warmoadgens grafs (aseTia yvela

amocana, sadac arseboben operatorebi, romlebsac mdgomareoba gadayavT ukan, mSobel

mdgomareobaSi. rvianis TamaSi, marSrutis moZebnis amocana da sxva). aseT amocanebSi Zebnis

xe SeiZleba miviRoT usasrulo maSinac ki, rodesac mdgomareobaTa sivrece sasruloa.

garda amisa, grafze Zebnis dros algoriTmi SeiZleba Caiciklos da veRar ipovnos

amoxsna. imisaTvis, rom Tavidan aviciloT es momentebi, TiTqmis yvela qvemoT ganxilul

algoriTmebSi gamoiyeneba specialuri procedura romelic Tavidan agvacilebs Zebnas

grafze da grafs gadaaqcevs xed. amisaTvis algoriTmi imaxsovrebs yvela wveros romelic

warmoiSveba Zebnis procesSi. amasTan wveroebs, romelTa Svilobili wveroebi jer ar

augia, anu wvero jer ar gauxsnia, imaxsovrebs siaSi “RRRRiaa”iaa”iaa”iaa”,,,, xolo im wveroebs romelTa

Svilobili wveroebic ukve aago, siaSi “daxurulia”daxurulia”daxurulia”daxurulia”.... muSaobis procesSi,Ayoveli axali

wveros agebis Semdeg, algoriTmi adarebs am wveros im wveroebs, romlebic moTavsebulia

orive siaSi. Tu aseTi wvero ar aris arc erT siaSi, algoriTmi mas Seitans siaSi Riaa. Tu

algoriTmi aRmoaCens aseT wveros romelime siaSi, misi Semdegi qmedeba damokidebulia

algoriTmis moqmedebis principze da aucileblad winaswar unda iyos gansazRvruli

algoriTmSi. yvela SemTxvevaSi Sedegi iqneba is, rom Cven miviRebT Zebnis xes da ara

grafs. amocanaTa amoxsnis yvela algoriTms, romelic eZebs amonaxsns Zebnis saSualebiT,

Cven SevafasebT oTxi kriteriumis saSualebiT:

1. sisrule. sisrule. sisrule. sisrule. iZleva Tu ara algoriTmi amoxsnis povnis garantias, rodesac es


2. amoxsna arsebobs?

3. optimaluroba. optimaluroba. optimaluroba. optimaluroba. Uuzrunvelyofs Tu ara algoriTmi optimaluri amonaxsnis

moZebnas?

4. droiTi sirTule.droiTi sirTule.droiTi sirTule.droiTi sirTule. ra droSi SeuZlia algoriTms amonaxsnis moZebna?

5. sivrciTi sirTule. sivrciTi sirTule. sivrciTi sirTule. sivrciTi sirTule. ra moculobis mexsiereba sWirdeba algoriTms amonaxsnis

sapovnelad?

droiTi da sivrciTi sirTuleebi yovelTvis iangariSeba amocanis sirTulis

gaTvaliswinebiT. gansakuTrebiT unda aRvniSnoT, rom gansxvavebiT im meTodebisagan,

romlebic gamoiyeneba grafebze Zebnisas, sadac mdgomareobaTa grafi yovelTvis moicema

cxadi saxiT da sirTulis tipur kriteriums warmoadgens am grafis zoma, xelovnur

inteleqtSi grafi moicema aracxadi saxiT, sawyisi mdgomareobisa da operatorebis

saSualebiT da misi agebis procesi gaerTianebulia amonaxsnis Zebnis procesTan, amitom am

SemTxvevaSi is xSirad usasruloa, sirTule aRiwereba sami koeficientis saSualebiT: b –

ganStoebis koeficientiganStoebis koeficientiganStoebis koeficientiganStoebis koeficienti, anu nebismieri wveros Svilobil wveroTa maqsimaluri raodenoba;

d –yvelaze zemoT myofi miznis wveros siRrme da m – mdgomareobaTa sivrceSi nebismier

gzaTa Soris maqsimaluri sigrZe. droiTi sirTule xSirad izomeba drois erTeulSi

gamomuSavebul wveroTa raodenobiT, xolo sivrciTi sirTule – im wveroTa maqsimaluri

raodenobiT, romlebic unda daimaxsovros algoriTmma.

sakontrolo kiTxvebi:sakontrolo kiTxvebi:sakontrolo kiTxvebi:sakontrolo kiTxvebi:

1. ra mizans isaxavs amocanis formalizeba?

2. rogor problemur garemoSi uxdeba muSaoba amocanaTa amomxsnel agents?

3. ra komponentebiT aRiwereba amocana?

4. moiyvaneT erTi da igive amocanis sxvadasxva aRweris magaliTebi.

5. ra gansxvavebaa grafze da xeze Zebnas Soris?

6. ra parametrebiT fasdeba Zebnis algoriTmebi?


1. zogierT amocanebSi, gansxvavebiT rvianis TamaSisagan, SeuZlebelia Svilobili

wveros gaxsnis dros miviRoT misi warmomSobi wvero. moiyvaneT aseTi amocanebis

magaliTebi.

2. gvaqvs xuTlitriani doqi, romelic savsea wyliT da orlitriani carieli doqi.

Cveni mizania orlitrian doqSi gadmovasxaT zustad erTi litri wyali. wyali

SeiZleba gadavRvaroT, an gadavasxaT erTi doqidan meoreSi. aRwereT amocana

mdgomareobaTa sivrceSi da aageT amoxsnis xe.

3. mdinaris erT napirze imyofeba n misioneri da n kanibali. imave napirTan aris

oradgiliani navic. Cveni mizania gadaviyvanoT n misioneri da n kanibali

mdinaris meore napirze ise, rom arsad, arc romelime napirze da arc navSi,

kanibalebis raodenoba ar iyos meti misionerebis raodenobaze. aRwereT amocana

mdgomareobaTa sivrceSi.

leqcialeqcialeqcialeqcia #4. #4. #4. #4.

Zebnis arainformirebuli algoriTmebiZebnis arainformirebuli algoriTmebiZebnis arainformirebuli algoriTmebiZebnis arainformirebuli algoriTmebi

4.1. sruli gadarCevis algoriTmi.4.1. sruli gadarCevis algoriTmi.4.1. sruli gadarCevis algoriTmi.4.1. sruli gadarCevis algoriTmi. Zebnis algoriTmebis ganxilvas daviwyebT iseTi

algoriTmebidan, romlebic miznis Zebnis procesSi iyeneben mxolod informacias, romelic

Sedis amocanis formalur aRweraSi da ar gaaCniaT araviTari damatebiTi informacia

mdgomareobebis erTmaneTTan Sesadareblad.

sur. # 4.1. sruli, anu ganivi gadarCevis algoriTmis sqema.

aseT algoriTmebs uwodeben arainformirebul arainformirebul arainformirebul arainformirebul (zogjer brmad Zebnis brmad Zebnis brmad Zebnis brmad Zebnis) algoriTmebs.

rogorc ukve vnaxeT, Zebnis amocanebis mniSvnelovani parametrebia sawyisi mdgomareobidan

miznis mdgomareobamde gzis fasi,gzis fasi,gzis fasi,gzis fasi, romelic warmoadgens amocanis amoxsnis gzaze

mdgomi yvela mezobel wveroebs Soris gadasvlaTa fasebis jams da amonaxsnis siRrmeamonaxsnis siRrmeamonaxsnis siRrmeamonaxsnis siRrme,

gadasvlaTa raodenoba sawyisi mdgomareobidan miznis mdgomareobamde. daviwyoT yvelaze

martivi, ganiviganiviganiviganivi anu sruli gadarCevissruli gadarCevissruli gadarCevissruli gadarCevis algoriTmiT. amocanebis (problemebis) amomxsneli

agenti am algoriTms (iseve rogorc yvela danarCen algoriTmebs, romlebic aRwerili

iqneba am TavSi, iyenebs mas Semdeg, rac moaxdens amocanis formalizebas. algoriTmis

blok-sqema mocemulia sur. # 4.1. is Sedgeba rva bijisagan:

1. sawyisi mdgomareoba movaTavsoT siaSi “Riaa”;Riaa”;Riaa”;Riaa”;

2. SevamowmoT, carielia Tu ara sia “RiaaRiaaRiaaRiaa”, Tu carielia gadavideT mesame bijze,

sia “Riaa”

dasasruli amocanas amoxsana ara aqvs

aviRoT pirveli wvero, gadavitaoT is siaSi “daxurulia” da avagoT misi yvela Svilobili wvero

dasasruli amoxsna napovnia

Svilobili wveroebi SevadaroT wveroebs siaSi “Riaa” da “daxurulia”, Tu romelime wvero emTxveva am siebidan erTerTs, is amovagdoT. danarCeni wveroebi SevitanoT siis “Riaa” boloSi

0S

?

?

leqcia #leqcia #leqcia #leqcia #4444. . . . Zebnis Zebnis Zebnis Zebnis arainformirebuli algoriTmebiarainformirebuli algoriTmebiarainformirebuli algoriTmebiarainformirebuli algoriTmebi 33

Tu ara - meoTxe bijze;

3. davamTavroT muSaoba, amocanas amoxsna ara aqvs;

4. aviRoT pirveli wvero siidan “RiaaRiaaRiaaRiaa”, gadavitanoT is siaSi “daxuruliadaxuruliadaxuruliadaxurulia”,

Svilobilis ganmsazRvreli funqciebis (operatorebis) saSualebiT, avagoT yvela

Svilobili wveroebi;

5. SevadaroT axlad agebuli wveroebi miznis mdgomareobas, Tu romelime maTgani

emTxveva miznis mdgomareobas gadavideT meeqvse bijze, Tu ara – meSvide bijze;

6. davamTavroT muSaoba, amonaxsni napovnia;

7. SevadaroT axladagebuli wveroebi siebSi “RiaaRiaaRiaaRiaa” da “daxuruliadaxuruliadaxuruliadaxurulia” myof wveroebs.

Tu romelime axladagebuli wvero emTxveva romelime wveros erTerT siaSi,

gadavagdoT es wvero.

8. darCenili axladagebuli wveroebi SevitanoT siis “Riaa” “Riaa” “Riaa” “Riaa” boloSi.

0S

1S 2S 3S

sur. # 4.2. algoriTmis muSaobis pirveli etapi

rogor muSaobs es algoriTmi? ganvixiloT misi muSaoba rvianis TamaSis magaliTze.

pirvel nabijze, sawyisi mdgomareoba Seva siaSi “Riaa”. aqedan gamomdinare, radganac sia

“Riaa” ar aris carieli, dasaSvebi operatorebis saSualebiT miiReba sami Svilobili

wvero (ix. sur. # 4.2.), xolo sawyisi wvero gadaitaneba siaSi “daxurulia”.

axladagebuli wveroebidan arcerTi ar emTxveva miznis wveros da arc siaSi

“daxurulia” myof erTaderT wveros (sia “Riaa” carielia), amitom samive axladagebuli

wveroebi Seva siaSi “Riaa” im mimdevrobiT, ra mimdevrobiTac isini iyo agebuli (sur. #

4.2. marcxnidan marjvniv). ciklis meored gameorebisas siidan “Riaa” aiReba pirveli wvero

da aigeba misi Svilobili wveroebi (ix. nax. # 4.3). algoriTmi kvlav Seadarebs

axladagebul wveroebs miznis wveros da radganac arcerTi maTgani ar emTxveva miznis

wveros, algoriTmi gadava ra bolo bijze, Seadarebs am wveroebs wveroebTan siebidan

“Riaa” da “daxurulia”. aRmoaCens, rom erTerTi maTgani emTxveva siaSi “daxurulia” myof

0S wveros da gadaagdebs mas. meore ( 4S ) wveros ki Seitans siis “Riaa” boloSi, amitom

2 8 3

1 6 4

7 5

2 8 3 2 8 3 2 8 3

1 6 4 1 4 1 6 4

7 5 7 6 5 7 5


0S

1S 2S 3S

4S

sur. # 4.3. algoriTmis mier ciklis meored gameorebisas agebuli wveroebi

Semdeg etapze is gasaxsnelad aiRebs 2S wveros. ase gaagrZelebs muSaobas algoriTmi

manamdis, sanam erTerT etapze an sia “Riaa” ar iqneba carieli, rac imas niSnavs, rom

algoriTmma gadasinja yvela SesaZlo mdgomareobebi da amocanas amoxsna ara aqvs, an

romelime axladagebuli wvero ar daemTxveva miznis wveros, rac imas niSnavs, rom

algoriTmma ipova amoxsna, anu gza sawyisi wverodan miznis wveromde.

rogorc vxedavT, es algoriTmi Tanmimdevrulad agebs yvela SesaZlo gzebs sawyisi

wverodan ise, rom ar gamotovebs arc erT SesaZlo gzas. amasTan misTvis yvela wvero

informaciulad erTnairia. swored amitom uwodeben mas sruli, anu brma gadarCevis

algoriTms. Cveni magaliTisaTvis is Cava meeqvse doneze da gaxsnis 46 wveros sanam

ipovnis miznis wveros.

SevafasoT algoriTmi zemoT moyvanili kriteriumebiT. cxadia, rom es algoriTmi

aris sruli. marTlac, Tuki arsebobs amocanis amoxsna, is mas adre Tu gvian aucileblad

ipovnis. Tu yvelaze zeviT mdgomi miznis wveros siRrmea d , algoriTmi mas ipovnis 1−d

donis yvela wveros gaxsnis Semdeg. radganac am algoriTmisTvis yvela gadasvlas erTi

fasi aqvs, napovni amoxsna avtomaturad iqneba optimaluric. am ori parametriT algoriTmi

SesaniSnavia, magram katastrofulad sustia danarCeni ori parametris mixedviT. GdavuSvaT,

TiToeuli mdgomareobidan SesaZlebelia maqsimum b cali Svilobili wveros ageba. maSin

algoriTmi pirvel doneze sawyisi mdgomareobidan aagebs b axal mdgomareobas, meore

etapze 2b mdgomareobas, mesameze

3b da ase Semdeg. davuSvaT exla, rom miznis mdgomareoba

mdebareobs d doneze da is aigeba am donis wveroebidan yvelaze bolos, maSin

mdgomareobebis raodenoba romlebic unda aagos algoriTma, raTa ipovos amoxsna tolia

2 8 3

1 6 4

7 5

2 8 3 2 8 3 2 8 3

1 6 4

1 4

1 6 4

7 5 7 6 5 7 5

2 8 3 2 8 3

1 6 4 6 4

7 5 1 7 5


dbbbb ++++ ...32

rac gvaZlevs Sefasebas )( dbO . es imas niSnavs rom algoriTmi aris eqsponencialuri da

amocanis zomebisa da amonaxsenis donis zrdasTan erTad Zalian swrafad izrdeba agebul

wveroTa raodenoba. donis, agebul wveroTa raodenobis, daxarjuli droisa da

gamoyenebuli mexsierebis Tanafardoba moyvanilia cxrilSi N2. am cxrilSi b tolia 10-

is; wveroebis gaxsnis siCqarea - 10 000 wv/wamSi; mexsierebis moculoba – 1000 baiti/wveroze.

cxrili

done md.raodenoba dro mexsiereba

2 1100 0,11wm 1 megabaiti

4 111 100 11 wm 106 megabaiti

6 107 19 wT 10 gigabaiti

8 10 9 31 sT 1 terabaiti

10 1011 129 dRe 101 terabaiti

12 1013 35 weli 10 petabaiti

14 1015 3523 weli 1 eqsabaiti

rogorc am cxrilidan Cans, amocanis zomebis gazrdasTan erTad pirvel rigSi

katastrofulad izrdeba moTxovna mexsierebaze, xolo realuri amocanebisaTvis, rogorc

mexsiereba, aseve amonaxsnis Zebnis dro praqtikulad SeuZlebels xdis amocanis amoxsnas

am algoriTmis saSualebiT.

4.2.4.2.4.2.4.2. Zebna gzis fasis kriteriumiT.Zebna gzis fasis kriteriumiT.Zebna gzis fasis kriteriumiT.Zebna gzis fasis kriteriumiT. ganivi gadarCevis algoriTmi iyo optimaluri, Tu

yvela Svilobili wveros agebis fasi iyo toli. magram es yovelTvis ase ar aris.

davuSvaT, Cvens amocanaSi fiSkis zeviT awevaze ixarjeba ufro meti energia, vidre qveviT

Camowevaze, maSin gadasvlis fasi erTi wverodan meoreSi iqneba sxvadasxva. martivi

gardaqmniT ganivi gadarCevis algoriTmidan SeiZleba miviRoT axali algoriTmi, romelic

axorcielebs Zebnas gzisgzisgzisgzis fasis kritefasis kritefasis kritefasis kriteriumiTriumiTriumiTriumiT ise, rom ar SevcvaloT algoriTmis

struqtura. amisaTvis saWiroa ori cvlilebis Setana ganivi Zebnis algoriTmSi. pirveli

exeba gauxsneli wveroebis ganlagebas siaSi “Riaa”. SemovitanoT funqcia )(ng ,,,, romelic

waroadgens gzis fass sawyisi mdgomareobidan n wveromde da siaSi “Riaa” wveroebi

ganvalagoT ise, rom siis TavSi moeqcnen is wveroebi, romelTa fasic aris minimaluri.

meore Sesworeba exeba grafis xed gadaqcevis proceduras. Gganivi Zebnis algoriTmisagan

gansxvavebiT, Tu romelime axlad agebuli wvero daemTxveva wveros siaSi “Riaa” (rac

niSnavs rom arsebobs ori gansxvavebuli gza sawyisi wverodan am wveromde), algoriTmi

datovebs ara pirvelad agebul gzas, rogorc es xdeboda sruli gadarCevis algoriTmSi,

aramed gzas minimaluri SefasebiT. Tu axlad agebuli wvero daemTxveva romelime wveros

siaSi “daxurulia”, Catardeba igive procedura da Tu axlad agebuli gzis fasi naklebia

arsebul gzis fasze, wvero dabrunebuli iqneba siaSi “Riaa”. Tu gadasvlis fasi erTi


wverodan mezobel wveroSi ε≥+ ),( 1ii nnw , , , , sadac ε aris raime nulisagan gansxvavebuli dadebiTi ricxvi, maSin algoriTmi iqneba sruli. es piroba sakmarisia imisTvisac, rom

algoriTmi iyos optimaluric.

am algoriTmSi Zebna xdeba ara doneebis mixedviT, aramed gadasvlebis fasis mixedviT,

amitom misi sirTule advilad ver ganisazRvreba b da d terminebSi. SemoviRoT

parametrebi C - amoxsnis optimaluri fasi amoxsnis optimaluri fasi amoxsnis optimaluri fasi amoxsnis optimaluri fasi da ε ---- wverodan mezobel wveroSi gadasvlis minimaluri fasi, maSin am algoriTmis droiTi da sivrciTi sirTule yvelaze cud

SemTxvevaSi tolia )(1 ε

CbO

+, anu SeiZleba iyos meti vidre )( dbO .

5.3.5.3.5.3.5.3. Zebna siRrmeSiZebna siRrmeSiZebna siRrmeSiZebna siRrmeSi. aseve struqturis Seucvlelad SegviZlia ganivi Zebnis algoriTmi

gardavqmnaT siRrmeSi Zebnis algoriTmad. amisaTvis sakmarisia axlad agebuli wveroebi

SevitanoT ara siis “Riaa” boloSi, aramed TavSi. aseTi Zebnis dros algoriTms sWirdeba

mexsierebis Zalin mcire moculoba, radganac is imaxsovrebs mxolod erT gzas sawyisi

wverodan damamTavrebel wveromdedamamTavrebel wveromdedamamTavrebel wveromdedamamTavrebel wveromde (damaTavrebelia wvero, Tu mas ar gaaCnia Svilobili

wveroebi), im mezobel wveroebTan erTad, romlebic jer ar gauxsnia algoriTms. Mmas

Semdeg, rac gaixsneba wvero, is SeiZleba waSlili iqnas mexsierebidan. Tu erTi wverodan

SeiZleba maqsimum b wveros miReba da Zebnis siRrmea d , , , , algoriTmi imaxsovrebs mxolod

1+⋅ db wveros, amitomac Tuki amonaxseni mdebareobs 12=d siRrmeze, mas sWirdeba

mxolod 118 kilobaiti mexsiereba gansxvavebiT ganivi gadarCevis algoriTmisagan,

romelsac sWirdeba 10 petabaiti mexsiereba. am algoriTmis erTerT variantSi, romelsac

ewodeba siRrmeSi Zebnis algoriTmi ukan dabrunebiTsiRrmeSi Zebnis algoriTmi ukan dabrunebiTsiRrmeSi Zebnis algoriTmi ukan dabrunebiTsiRrmeSi Zebnis algoriTmi ukan dabrunebiT, saWiroa kidev ufro mcire

mexsiereba. es algoriTmi yovel nabijze xsnis mxolod erT Svilobil wveros da

imaxsovrebs romeli Svilobili unda gaxsnas Semdeg, ukan dabrunebis SemTxvevaSi. maSin

algoriTms sWirdeba )(dO mexsiereba nacvlad )(bdO ....

ganvixiloT am algoriTmis muSaoba isev zemoTmoyvanil magaliTze. siRrmeSi Zebnis

algoriTmisa da sruli gadarCevis algoriTmis muSaoba pirvel da meore etapze

faqtobrivad erTnairia mcire gamonaklisis garda, romelic mdgomareobs SemdegSi: meore

etapze miRebuli erTaderTi wvero (meore wvero ukve gvxvdeba siaSi “daxurulia” da

amitom mas arc erTi algoriTmi aRar ganixilavs), sruli gadarCevis algoriTmSi Seva

siaSi “Riaa” sul bolo, meoTxe adgilze, maSin rodesac siRrmeSi Zebnis algoriTmSi es

wvero siaSi “Riaa” iqneba pirvel adgilze, amitom mesame etapidan am algoriTmebis

muSaoba iqneba gansxvavebuli. kerZod, siRrmeSi Zebnis algoriTmisaTvis mesame etapi

gamoiyureba Semdegnairad (ix. sur. # 4.4.).

siRrmeSi Zebnis algoriTms gaaCnia Tavisi naklovanebebi. pirvel rigSi is ukve aRar

aris sruli, radganac algoriTmi SeiZleba gayves qveviT Zalian grZel gzas, an saerTod

usasrulos da ver ipovos amonaxsni, maSin rodesac meore gziT ipovida amonaxsns,

romelic mdebareobs sawyisi wverodan Zalian axlos. amave mizeziT is ar iZleva

optimaluri amonaxsnis povnis garantias. usasrulo mdgomareobaTa sivrcis SemTxvevaSi ki

am algoriTmis gamoyeneba praqtikulad SeuZlebelia.

am problemis Tavidan acileba SesaZlebelia siRrmis winaswari SezRudviT. davuSvaT,


SemoviRoT parametri L da algoriTmSi mesame da meoTxe bijebs Soris CavamatoT erTi

1S

M

sur. # 4.4. siRrmeSi Zebnis algoriTmis mesame etapi

biji: sanam algoriTmi gaxsnis axal wveros, Seamowmos xom ar emTxveva am wveros siRrme

L -is mniSvnelobas. Tu emTxveva, aseTi wvero aRar gaxsnas da gadavides meore bijze. maSin

mdgomareobaTa sivrce miiReba sasruli da algoriTmi SeZlebs ipovos amonaxseni, Tu es

amonaxseni ar mdebareobs L doneze qveviT. advili misaxvedria, rom algoriTmi isevac ar

iqneba sruli da optimaluri. L parametris aReba SeiZleba nebismierad, an SeiZleba

gamoviyenoT eqspertTa codna Tu ra siRrmeze SeiZleba mdebareobdes am amocanis amoxsna.

4.4. 4.4. 4.4. 4.4. ormxrivmimarTuli Zebna.ormxrivmimarTuli Zebna.ormxrivmimarTuli Zebna.ormxrivmimarTuli Zebna. sainteresoa ormxrivi Zebnis idea. warmovidginoT ori

erTnairi algoriTmi (davuSvaT siganeSi gadarCevis), romlebic xsnian erTsa da imave

amocanas, oRond erTis sawyisi mdgomareoba meoresTvis warmoadgens miznis mdgomareobas.

es algoriTmebi dakavSirebulni arian erTmaneTTan da yoveli wveros gaxsnis win

amowmeben xom ar emTxveva es wvero meore algoriTmis romelime wveros. damTxvevis

SemTxvevaSi amocanis amoxsna ukve napovnia. aseTi algoriTmis rogorc droiTi, aseve

sivrciTi sirTule iqneba )( 2d

bO O, O, O, O, amave dros is iqneba sruli da optimaluri (Tu

gamoiyeneba sruli da optimaluri algoriTmebi). problema mdgomareobs imaSi, rom yvela

amocanisaTvis advili ar aris movaxerxoT Zebna miznis mdgomareobidan sawyisi

mdgomareobisaken, radganac realur amocanebSi xSirad CvenTvis cnobilia miznis

mdgomareobaTa simravlis aRwera, magram ucnobia am simravlis konkretuli elementebi

(magaliTad Wadrakis TamaSisaTvis es SeuZlebelia).


1. ratom ewodebaT am algoriTmebs Zebnis arainformirebuli algoriTmebi?

2. aRwereT sruli gadarCevis algoriTmi, rogoria misi Sefaseba?

3. ra gansxvavebaa srul da gzis fasis kriteriumiT Zebnis algoriTmebs Soris?

4. ra upiratesoba aqvs siRrmeSi gadarCevis algoriTms sruli gadarCevis

algoriTmTan SedarebiT?

2 8 3

6 4

1 7 5

8 3 2 8 3 2 8 3

2 6 4 6 4 1 6 4

1 7 5

1 7 5

7 5


5. ra principiT xdeba ormxrivi Zebna da ratom ar SeiZleba misi gamoyeneba nebismieri

amocanisaTvis?


1. komivoiaJeris amocana. komivoiaJeri imyofeba A qalaqSi. man unda moiaros B,C,D,E

qalaqebi da kvlav dabrundes A qalaqSi. manZilebi am qalaqebs Soris tolia:

.6,9,5,10,10,7,13,10,6,7 ========== DECECDBEBDBCAEADACAB

aRwereT amocana mdgomareobaTa sivrceSi da amoxseniT is sruli gadarCevis

algoriTmis gamoyenebiT, moZebneT jer umoklesi, xolo Semdeg udidesi gza.

2. amoxseniT igive amocana gzis fasis kriteriumis algoriTmiT da SeadareT es

amonaxsnebi erTmaneTs.

3. amoxseniT amocana siRrmeSi gadarCevis algoriTmiT, rodesac siRrme SezRudulia.

leqcia #leqcia #leqcia #leqcia #5555. . . .

Zebnis informirebuli algoriTmebi.Zebnis informirebuli algoriTmebi.Zebnis informirebuli algoriTmebi.Zebnis informirebuli algoriTmebi.

5555.1. evristikuli informacia.1. evristikuli informacia.1. evristikuli informacia.1. evristikuli informacia. Zebnis es yvela arainformirebuli algoriTmebi, romlebic

Cven ganvixileT, moqmedeben erTi principiT. isini raRac TanmimdevrobiT gamoimuSaveben

mdgomareobebs da Semdeg adareben mas miznis mdgomareobas, an mis aRweras. maT ar

SeuZliaT raime niSniT ganasxvaon es mdgomareobebi erTmaneTisagan da amoarCion is

mdgomareobebi, romlebic ufro swrafad migviyvanen miznis mdgomareobasTan, radgan ar

gaaCniaT informacia, romelic saSualebas miscemT, moaxdinon mdgomareobebis

diferencireba. magaliTad, cnobilia, rom Wadrakis TamaSis dros pirvel svlas aravin

akeTebs 42 aa − , Tumca TamaSis wesebiT es svla araa akrZaluli da radganac Zebnis

arainformirebuli algoriTmebi iyeneben mxolod informacias, romelic mocemulia

amocanis pirobebSi, maTTvis Wadrakis ocive sawyisi svla absoluturad erTnairia, maSin,

rodesac imisTvis, vinc kargad TamaSobs Wadraks, es ase ar aris.

imisaTvis, rom SevZloT SevafasoT mdgomareoba, unda gagvaCndes damatebiTi

informacia im klasis amocanebis Sesaxeb, romelsac vxsniT. es informacia ar gamodis

amocanis pirobebidan da ZiriTadad emyareba an logikur msjelobas, an Cvens

gamocdilebas da codnas, romelic dagvigrovda am tipis amocanebis amoxsnis dros. aseT

informacias uwodeben evristevristevristevristikul informaciasikul informaciasikul informaciasikul informacias, xolo Zebnis algoriTmebs, romlebic

iyeneben aseT informacias – evristikuli Zebnis algoriTmebsevristikuli Zebnis algoriTmebsevristikuli Zebnis algoriTmebsevristikuli Zebnis algoriTmebs.

sityva evristika, berZnulad eurisco, niSnavs gamokvlevas da mdgomareobaTa sivrceSi

Zebnisas ganisazRvreba rogorc iseTi wesebis erToblioba wveroebisa da gzebis

amosarCevad, romlebic yvelaze didi albaTobiT migviyvanen amocanis amonaxsnTan. aseTi

tipis Zebna gamoiyeneba or ZiriTad SemTxvevaSi:

1. ar arsebobs dasmuli amocanis amoxsnis algoriTmi imis gamo, rom SeuZlebelia

amocanis mkacri formalizeba, an/da araa sakmarisi sawyisi monacemebi.

2. amocanas gaaCnia amoxsnis algoriTmi, magram mdgomareobaTa sivrce imdenad

swrafad izrdeba, rom am algoriTmis gamoyeneba praqtikulad SeuZlebelia.

ganvixiloT aseTi funqciis Sedgenis procesi rvianis TamaSis magaliTze. rogorc

gvaxsovs, am TamaSSi mdgomareoba warmoadgens cxra kvadrats masze ganlagebuli rva

fiSkiT. yovel konkretul mdgomareobaSi raRac nawili fiSkebisa aris Tavis adgilze (anu

im poziciaSi, romelSic unda iyos miznis mdgomareobaSi) da nawili ki – ara.

mdgomareobis Sesafaseblad daviTvaloT ramdeni fiSka dgas Tavis adgilze. albaT

bunebrivi iqneba Tu CavTvliT, rom rac ufro meti fiSka dgas Tavis adgilas, miT ufro

pozicia “axlos” aris miznis mdgomareobasTan, Tumca, es albaT yovelTvis ase ar aris.

aRvniSnoT es funqcia )(nh -T. es iqneba evristikuli funqcia. aseTi Sefaseba ar

gamomdinareobs TamaSis wesebidan, amitom Cven ver SevZlebT mkacrad davamtkicoT, rom

aseTi Sefaseba yovelTvis sworia, ufro metic, gamomdinare iqidan, rom am TamaSSi

arseboben poziciebi, romlebidanac miznis mdgomareoba miuRwevadia, aSkaraa, rom aseTma

Semfasebelma funqciam SeiZleba verc gvapovninos amoxsna, magram Tu misi gamoyeneba

Seamcirebs gadarCevas da gaaiolebs amocanis amoxsnas, Cveni mizani miRweuli iqneba.


5.2.5.2.5.2.5.2. “xarbi” algoriTmebi. “xarbi” algoriTmebi. “xarbi” algoriTmebi. “xarbi” algoriTmebi. algoriTmebs, romlebic ZebnisaTvis gamoiyeneben mxolod

evristikul informacias, uwodeben “xarb”“xarb”“xarb”“xarb” algoriTmebs. erTerT aseT algoriTms

warmoadgens pikisken aRmavalipikisken aRmavalipikisken aRmavalipikisken aRmavali Zebnis algoriTmi. ganvixiloT es algoriTmi rvianis

TamaSis magaliTze. Tu Cven viyenebT Cvens mier zemoT aRweril evristikul funqcias, maSin

sur. # 5.1. lokaluri otpimumis Zebnis grafiki

cxadia, rom am funqcis mniSvneloba miznis mdgomareobaSi iqneba maqsimaluri. maSin

algoriTmi warmoadgens Cveulebriv cikls, romelSic mudmivad xdeba gadanacvleba )(nh

funqciis zrdisken (ix. sur. # 5.1.), anu xdeba asvla pikze manam, sanam algoriTmi ar

miaRwevs mdgomareobas, romelSic miznis funqcias aqvs yvelaze didi mniSvneloba mezobel

mdgomareobebTan SedarebiT. es algoriTmi gamoiyenebs ra mxolod evristikul funqcias

)(nh -s, mocemuli mdgomareobebidan amoarCevs saukeTesos da SemdegSi ganixilavs mxolod

am wveros, danarCenebs ki ar imaxsovrebs. magaliTad, Tu gamoviyenebT am algoriTms

zemoTganxiluli magaliTisaTvis, Zebnis xes eqneba Semdegi saxe (ix. sur. # 5.2.). sawyisi

0S mdgomareobidan algoriTmi aagebs Svilobil wveroebs, gamoTvlis maTTvis )(nh

funqciis mniSvnelobebs da amis mixedviT amoarCevs 2S wveros, danarCen wveroebs ki

gadaagdebs. meore etapze gaxsnis 2S wveros, gamoTvlis am wveros Svilobilebs )(nh

funqciis mniSvnelobebs, amoarCevs maT Soris saukeTesos da ase gaagrZelebs, sanam ar

miaRwevs piks.

rogorc mosalodneli iyo, es algoriTmi ver akmayofilebs Sefasebis pirvel da meore

kriteriumebs, magram radganac es algoriTmi ar imaxsovrebs arcerT mdgomareobas, garda

mocemulisa, mas ar sWirdeba didi mexsiereba amocanis amoxsnisaTvis, rac warmoadgens mis

Zalian did upiratesobas adre ganxilul Zebnis algoriTmebTan SedarebiT, Tumca mas

gaaCnia seriozuli naklic. Tu davukvirdebiT sur. # 5.2. mocemul situacias, am

situaciaSi algoriTmi wyvets muSaobas imis gamo, rom arcerTi Semdegi Svilobili wvero

aRar aumjobesebs )(nh funqcias, anu algoriTmma ipova lokaluri maqsimumi da gaCerda.

imisaTvis, rom SevZloT algoriTmis gamoyvana lokaluri maqsimumis wertilidan, saWiroa

“xarb” algoriTmSi gaviTvaliswinoT Sesabamisi procedura, rac SeuZlebeli iqneba,

Tu kvlav ar gamoviyenebT siebs “Riaa’ da “daxurulia”, rac saSualebas aZlevs algoriTms

)(nh

n

leqcia #leqcia #leqcia #leqcia #5555. . . . Zebnis informirebuli algoriTmebiZebnis informirebuli algoriTmebiZebnis informirebuli algoriTmebiZebnis informirebuli algoriTmebi 41

4)( 0 =Sh

3)( 1 =Sh 5)( 2 =Sh 3)( 3 =Sh

5)( 4 =Sh 5)( 5 =Sh 4)( 6 =Sh

sur. # 5.2. pikisaken aRmavali Zebnis algoriTmis muSaoba

gamovides lokaluri maqsimumis mdgomareobidan da gadavides sxva wveroebze. rogorc

advili misaxvedria, aseTi algoriTmi kargavs im upiratesobas, romelic gaaCnia pikisaken

aRmaval algoriTms da romelic mdgomareobs im mexsierebis moculobaSi, romelic

saWiroa amocanis amosaxsnelad, amasTan, pirveli ori kriteriumiT aseTi algoriTmi kvlav

rCeba sust algoriTmad, radganac is ver xdeba dasaSvebi da optomaluri.

5.3.5.3.5.3.5.3. mowesrigebuli Zebnis algoriTmi.mowesrigebuli Zebnis algoriTmi.mowesrigebuli Zebnis algoriTmi.mowesrigebuli Zebnis algoriTmi. ganvixiloT exla e.w. A tipis informirebuli

algoriTmi, romelic amonaxsnis Zebnis procesSi iyenebs TiTqmis igive )(nh evristikul

funqcias, magram Zebnis sxvanairi organizaciis xarjze SesaZlebeli xdeba

davakmayofiloT Sefasebis pirveli da meore kriteriumebi. davuSvaT, Cven romelime

algoriTmis (magaliTad sruli gadarCevis) saSualebiT ukve amovxseniT amocana da

vipoveT optimaluri amonaxsni. maSin am optimaluri amonaxsnis fasi )( /nf ∗, romelic

gadis romelime konkretul /n wveroze, SegviZlia gavyoT or nawilad:

),()()( /// nhngnf ∗∗∗ += sadac )( /ng∗ aris optimaluri gzis fasi sawyisi wverodan

/n

wveromde, xolo )( /nh∗ aris aseve optimaluri gzis fasi

/n wverodan miznis wveromde.

es funqcia gansazRvruli iqneba mxolod im wveroebisTvis, romlebic mdebareoben amoxsnis

optimalur gzaze da amitom SeuZlebelia gamoviyenoT yvela im wveros Sesafaseblad,

romlebsac algoriTmi warmoqmnis amocanis amoxsnis procesSi (miT umetes, rom amocanis

amoxsnamde )( /nh∗ mniSvneloba CvenTvis ucnobia). amitom A tipis algoriTmebSi

gamoiyeneba )()()( nhngnf += Semfasebeli funqcia, romelsac gaaCnia zustad igive

2 8 3

1 6 4

7 5

2 8 3 2 8 3 2 8 3

1 6 4 1 4 1 6 4

7 5 7 6 5 7 5

2 3 2 8 3 2 8 3

1 8 4 1 4 1 4

7 6 5 7 6 5 7 6 5


struqtura, magram gansxvavebuli Sinaarsi. aq )(ng kvlavac gzis fasia (ara aucileblad

optimaluri) sawyisi wverodan n wveromde, xolo )(nh evristikuli informacia, romelic

gamoiyeneba gzis fasis Sesafaseblad mocemuli wverodan miznis wveromde. imisaTvis, rom

ganivi gadarCevis algoriTmidan miviRoT A tipis (xSirad mas uwodeben mowesrigebuli

Zebnis) algoriTmi, saWiroa masSi SevitanoT mcireodeni cvlilebebi. kerZod, pirvel

rigSi, rogor movZebnoT optimaluri )( /ng∗ romelime konkretuli

/n wverosaTvis. Tu

romelime wveros gaxsnis Semdeg kvlav Segvxdeba /n wvero, romelic ukve aris siaSi

“Riaa” an “daxurulia”, saWiroa xelaxla gamovTvaloT )( /ng funqciis mniSvneloba da

SevadaroT is ukve arsebuls da Tu axladmiRebuli funqciis mniSvneloba ufro pataraa,

SevcvaloT arsebuli Sefaseba axliT da Tu /n wvero iyo siaSi “daxurulia”,

gadmovitanoT is siaSi “Riaa”. meore, sanam algoriTmi merve bijze axladagebul wveroebs

Seitans siaSi “Riaa”, is gamoiTvlis am wveroebis Sefasebas da amis Semedeg sias “Riaa”

moawesrigebs ise, rom pirvel adgilze idgnen wveroebi, romelTa Sefaseba yvelaze

pataraa. imisaTvis rom miviRoT aseTi Semfasebeli funqcia Cveni magaliTisaTvis, )(nh -iT

aRvniSnoT ara im fiSkebis raodenoba, romlebic dganan Tavis adgilze, aramed im fiSkebis

raodenoba, romlebic ar dganan Tavis adgilze.

ganvixiloT exla am algoriTmis muSaoba kvlav igive sawyisi da miznis

mdgomareobebisaTvis. algoriTmi kvlav daiwyebs muSaobas imiT, rom moaTavsebs sawyis 0S

wveros siaSi “Riaa”. Semdeg aiRebs pirvel wveros am siidan (es iqneba 0S wvero) da

gaxsnis ra mas, miiRebs sam axal wveros (ix. sur. # 5.3.). Semowmebis Semdeg aRmoCndeba,

rom arcerTi wvero ar emTxveva miznis wveros, amitom algoriTmi daiwyebs Semfasebeli

funqciis mniSvnelobebis gamoTvlas am wveroebisaTvis. miiReba: ;651)( 1 =+=Sf

431)( 2 =+=Sf ; .651)( 3 =+=Sf amitom siaSi “Riaa”, es wveroebi ganlagdeba Semdegi

TanmimdevrobiT: 2S , 1S da 3S . aqedan gamomdinare meore etapze algoriTmi aiRebs 2S

wveros da gaxsnis mas. miiReba sami axali wvero, romelTagan arcerTi ar emTxveva

miznis wveros da romelTa Sefasebebia Sesabamisad: 6)( 4 =Sf , 5)( 5 =Sf da 5)( 6 =Sf .

meore etapis Semdeg siSi “Riaa” gauxsneli wveroebi ganlagdeba Semdegi TanmimdevrobiT:

.,,,, 43165 SSSSS . . Semdeg etapze aiReba 5S wvero, romlisaganac miiReba ori axali wvero

7S da 8S . rogorc vxedavT, mowesrigebul algoriTms dasWirda mxolod aTi wveros

gaxsna gansxvavebiT sruli gadarCevis algoriTmisagan, romelic igive amocanis

amosaxsnelad xsnis ormocdaeqvs wveros. aseve gansxvavdeba es algoriTmi pikisaken

aRmavali algoriTmisagan, romelic ubralod Cerdeba da veRar agrZelebs Zebnas,

miuxedavad imisa, rom iyenebs igive evristikul funqcias.

5.4.5.4.5.4.5.4. ∗A algoriTmi da misi Sefasebebi.algoriTmi da misi Sefasebebi.algoriTmi da misi Sefasebebi.algoriTmi da misi Sefasebebi. SevafasoT algoriTmi zemoTmoyvanili oTxi

kriteriumis saSualebiT. daviwyoT sisruliT, cxadia, rom zogadad algoriTmis sisrule


0S

6)( 1 =Sf 4)( 2 =Sf 6)( 3 =Sf

5)( 4 =Sf 5)( 5 =Sf 6)( 6 =Sf

5)( 7 =Sf 7)( 8 =Sf

5)( 9 =Sf

sur. # 5.3. mowesrigebuli algoriTmis mier agebuli amoxsnis xe.

damokidebulia )(nh funqciis saxeze. magaliTad, Tu Cven aviRebT am funqcias iseTs,

romelic pirdapir krZalavs zogierTi wveroebis gaxsnas, maSin TavisTavad cxadia

algoriTmi ver iqneba sruli. A klasis algorTmebidan gamoyofen ∗A klasis

algoriTmebs, romlebisTvisac nebismieri n -Tvis sruldeba piroba, rom )()( nhnh ∗≤ . aseT

SemTxvevaSi SesaZlebelia vaCvenoT, rom algoriTmi iqneba sruli. sanam davamtkicebT

sisrules, jer davamtkicoT aseTi lema:

lema: lema: lema: lema: Tu sruldeba piroba )()( nhnh ∗≤ , maSin nebismier momentSi, sanam ∗A algoriTmi

daamTavrebs muSaobas, optimalur gzaze s wverodan miznis wveromde arsebobs iseTi

2 8 3

1 6 4

7 5

2 8 3 2 8 3 2 8 3

1 6 4 1 4 1 6 4

7 5 7 6 5 7 5

2 3 2 8 3 2 8 3

1 8 4 1 4 1 4

7 6 5 7 6 5 7 6 5

2 3 2 3

1 8 4 1 8 4

7 6 5 7 6 5

1 2 3

8 4

7 6 5

1 2 3

8 4

7 6 5


gauxsneli /n wvero, rom )()( / sfnf ≤ , sadac )(sf aris optimaluri gzis fasi s

wverodan miznis kn wveromde.

damtkiceba:damtkiceba:damtkiceba:damtkiceba: davuSvaT, ),...,,( 10 knnn iyos wveroebis mowesrigebuli mimdevroba, romelic

warmoadgens s optimalur gzas da /n aris pirveli gauxsneli wvero am gzaze. aseTi

wvero unda arsebobdes, radganac, Tu ∗A algoriTmma gaxsna kn wvero, mas daumTavrebia

muSaoba. maSin Semfasebeli funqciis ganmartebidan gamomdinare, gveqneba rom

)()()( /// nhngnf += . Cven viciT, rom algoriTmma ukve ipova optimaluri gza )( ∗ng ,

amitom )()( // ngng ∗= . Tu gaviTvaliswinebT pirobas )()( nhnh ∗≤ , miviRebT, rom

)()()()()()( ///// sfnhngnhngnf =+≤+= ∗∗∗, anu )()( / sfnf ≤ , ris damtkicebac gvindoda.

am lemis gamoyenebiT exla vaCvenoT, rom ∗A algoriTmi srulia, anu yovelTvis ipovnis

amoxsnas, Tu es amoxsna arsebobs. davamtkicoT sawinaaRmdegos daSvebis gziT, anu amocanas

amoxsna aqvs da algoriTmi mas ver poulobs. aq SeiZleba gvqondes ori SemTxveva:

1) algoriTmi amTavrebs muSaobas da ver poulobs amoxsnas da

2) algoriTmi ar amTavrebs muSaobas.

pirveli SemTxveva SeuZlebalia. marTlac, algoriTmis struqturidan gamomdinare, es

SemTxveva SeiZleba dadges mxolod maSin, rodesac sia “Riaa” iqneba carieli, magaram Cvens

mier damtkicebuli lemis Tanaxmad, sanam algoriTmi daamTavrebs muSaobas, siaSi “Riaa”

arsebobs iseTi gauxsneli /n wvero, romelic mdebareobs amoxsnis optimalur gzaze da

romlis Sefasebac naklebia optimaluri amoxsnis fasze, amitom, sanam algoriTmi

daamTavrebs muSaobas is aucileblad gaxsnis am wveros da aqedan gamomdinare,

avtomaturad ipovis amoxsnasac.

ganvixiloT meore SemTxveva, anu amoxsna arsebobs, algoriTmi mas ver poulobs da

arc amTavrebs muSaobas. davuSvaT, t aris romelime miznis wvero, romelic sawyisi

wverodan miiRweva raime sasruli k bijis Semdeg da misi minimaluri fasia )(sf .

nebismier gadasvlas erTi wverodan meoreSi aqvs raime minimaluri o>δ fasi mainc,

amitom nebismieri wverosTvis, romelic mdebareobs ufro Sors δ)(sfM = bijze,

gveqneba

)()()()( sfMngngnf =>≥≥ ∗ δ .

aqedan gamodis, rom arasodes ar iqneba gaxsnili wvero, romelic mdebareobs M bijze

Sors sawyisi wverodan (zemoT damtkicebuli lemis Tanaxmad) da Tu algoriTmi ar

amTavrebs muSaobas, es imas niSnavs, rom is xelaxla xsnis erTsa da imave wveroebs,

romlebic sawyisi wverodan daSorebulebi arian ara umetes M bijiT. aseTi wveroebis

simravle aRvniSnoT )(Mµ -iT. gzebis raodenoba sawyisi wverodan nebismier wveromde

sasrulia. ),( Mnν -Ti aRvniSnoT gzebis raodenoba sawyisi wverodan n wveromde, romelic

daSorebulia sawyis wveros araumetes M bijiT. )(

),(maxMn

Mnµ

νν∈

= iqneba is maqsimaluri


raodenoba, ramdenjerac SeiZleba gaixsnas erTi wvero, maSin νµ )(M bijis Semdeg yvela

wvero, romelic mdebareobs araumetes M bijisa sawyisi wverodan, aRmoCndeba siaSi

“daxurulia” da sia “Riaa” iqneba carieli, rasac unda mohyves algoriTmis gaCereba. aseT

SemTxvevaSi ki ZalaSi Seva pirveli SemTxveva, e. i. ∗A yovelTvis poulobs amoxsnas, Tuki

es amoxsna arsebobs.

vaCvenoT algoriTmis optimaluroba im gagebiT, rom algoriTmis mier napovni amoxsna

iqneba minimaluri gza sawyisi wverodan miznis wveromde. davuSvaT kvlav sawinaaRmdego,

anu algoriTmma ipovna amoxsna, romelic mTavrdeba raime t miznis wveroze, magram is ar

aris minimaluri gza, anu )()( sftf > -ze. magram lemis Tanaxmad siaSi “Riaa” arsebobs

iseTi gauxsneli /n wvero, rom )()()( / tfsfnf <≤ , amitom t wveros magivrad algoriTmi

gaxsnida /n wveros da ipovida optimalur amoxsnas.

BA rac Seexeba Sefasebis danarCen kriteriumebs, droiT da sivrciT sirTuleebs,

samwuxarod es parametrebi kvlavac asimptoturadaa damokidebuli mdgomareobaTa sivrcis

zomebze, amitom algoriTmis gamoyeneba xdeba araefeqturi didi zomis amocanebis amoxsnis

dros.

5.5. 5.5. 5.5. 5.5. ∗A algoriTmis informirebuloba. algoriTmis informirebuloba. algoriTmis informirebuloba. algoriTmis informirebuloba. algoriTmis informirebulobis qveS Cven gvesmis

Semdegi: davuSvaT, gvaqvs ori Semfasebeli funqcia )(1 nh da )(2 nh , iseTi, rom nebismieri

n wverosaTvis sruldeba piroba ),()()( 21 nhnhnh ∗≤≤ maSin algoriTmi, romelic iyenebs

)(2 nh evristikul funqcias, amocanis amoxsnis procesSi ar gaxsnis ufro met wveroebs,

vidre algoriTmi, romelic iyenebs )(1 nh evristikul funqcias. sxvanairad rom vTqvaT,

rac ufro mivuaxlovdebiT )(nh∗ funqcias qvevidan, miT ufro ukeTesi iqneba Cveni

algoriTmi.

davamtkicoT es debulebac sawinaaRmdegos daSvebiT. davuSvaT algoriTmma, romelic

iyenebda )(2 nh evristikul funqcias, ipovna amoxsna, magram gaxsna raime wvero //n ,

romelic ar gauxsnia algoriTmis, romelic iyenebda )(1 nh . es imas niSnavs, rom )(2 nh

evristikuli funqcis mqone algoriTmisaTvis am wveros Sefaseba

)()()()( //2

//// sfnhngnf ≤+= ∗,

xolo )(1 nh evristikuli funqciis mqone algoriTmisaTvis ki

)()()()( //1

//// sfnhngnf ≥+= ∗.

saidanac gamova, rom )()( 21 nhnh > , rac ewinaaRmdegeba Cvens daSvebas.


1. ra saxis informacia SeiZleba iyos gamoyenebuli Zebnis gasaumjobeseblad

da rogor SeiZleba am informacis mopoveba?


2. rogori amocanebis amosaxsnelad gamoiyeneba lokaluri Zebnis

algoriTmebi?

3. ra principiT muSaobs pikisaken aRmavali Zebnis algoriTmi?

4. ra nakli gaaCnia pikisaken aRmavali Zebnis algoriTms?

5. rogor algoriTmebs uwodeben “xarb” algoriTmebs?

6. ra principizea dafuZnebuli mowesrigebuli Zebnis algoriTmi?

7. daamtkiceT ∗A algoriTmis sisrule da optimaluroba.

8. ras niSnavs mowesrigebuli Zebnis algoriTmis informirebuloba?


1. ganixileT rvianis TamaSisaTvis ori SesaZlo Semfasebeli funqcia: 1) is

romelic moyvanilia leqciaSi da 2) mdgomareoba fasdeba im fiSkebis

raodenobiT, romlebic ar dganan Tavis adgilze, plus im svlebis raodenoba,

romlebic saWiroa am fiSkebis Tavis adgilze misayvanad (igulisxmeba umoklesi

gza). dawereT ∗A algoriTmis programa pirveli da meore Semfasebeli

funqciebiT da SeadareT erTmaneTs programis mier gaxsnili wveroebis

raodenoba pirvel da meore SemTxvevaSi.

2. moifiqreT evristikuli Sefasebeli funqcia, romelic saSualebas mogvcems

amovxsnaT ∗A algoriTmis saSualebiT rva lazieris amocana.

3. axseniT )(ng funqciis mniSvneloba.

4. SeecadeT SeadginoT Semfasebeli funqcia komivoiaJeris amocanisaTvis da

amoxseniT is ∗A algoriTmis gamoyenebiT.

leqleqleqleqcia #cia #cia #cia #6666

amocanebi amocanebi amocanebi amocanebi SezRudvaTa dakmayofilebaze.SezRudvaTa dakmayofilebaze.SezRudvaTa dakmayofilebaze.SezRudvaTa dakmayofilebaze.

6.1.6.1.6.1.6.1. amocanebi SezRudvaTa dakmayofilebazeamocanebi SezRudvaTa dakmayofilebazeamocanebi SezRudvaTa dakmayofilebazeamocanebi SezRudvaTa dakmayofilebaze. aqamde Cven vixilavdiT algoriTmebs,

romlebic amocanis amoxsnas eZeben mdgomareobaTa sivrceSi. am midgomis realizaciisaTvis

saWiro gaxda mdgomareobaTa Sefaseba evristikuli funqciebis saSualebiT, romlebic

mWidrod arian dakavSirebuli im problemur garemosTan, romelsac miekuTvneba mocemuli

amocana. amasTan, yovel nabijze saWiroa SevamowmoT, mivaRwieT Tu ara miznis

mdgomareobas. amave dros es mdgomareobebi warmoadgenen raRac “Sav yuTs”, erTnairi

Sinagani struqturiT. es struqtura mocemulia monacemebiT, romlebTanac wvdoma SeiZleba

ganxorcieldes mxolod im procedurebis saSualebiT, romlebic miekuTvneba mocemul

problemur garemos. amis garda, yvela es amocana iseTia, rom amocanis amoxsna

warmoadgens gzas sawyisi mdgomareobidan miznis mdgomareobamde. exla unda ganvixiloT

amocanebi egreT wodebul SezRudvaTa dakmayofilebazeSezRudvaTa dakmayofilebazeSezRudvaTa dakmayofilebazeSezRudvaTa dakmayofilebaze, romlebSic mdgomareobebi da

miznis Semowmeba Seesabameba standartul, struqturirebul da Zalian martiv warmodgenaswarmodgenaswarmodgenaswarmodgenas. . . .

amasTan am amocanebSi amoxsnas warmoadgens mxolod miznis mdgomareobaamoxsnas warmoadgens mxolod miznis mdgomareobaamoxsnas warmoadgens mxolod miznis mdgomareobaamoxsnas warmoadgens mxolod miznis mdgomareoba da ara gza

sawyisi mdgomareobidan miznis mdgomareobamde.Ees saSualebas mogvcems CamovayaliboT

Zebnis iseTi, ufro moxerxebuli algoriTmebi, romlebsac SeeZlebaT isargeblon

mdgomareobis aseTi struqturirebuli saxiT warmodgenis upiratesobiT da ZebnisaTvis

gamoiyenon zogadi daniSnulebis evristikuli funqciebi. agreTve arsebiTia isic, rom

miznis Semowmebis is standartuli warmodgena, romelic gamoiyeneba am algoriTmebSi da

romelic dakavSirebulia amocanis struqturaze, saSualebas gvaZlevs SevqmnaT amocanis

dekompoziciis meTodebi da davadginoT Sinagani kavSiri amocanis struqturasa da

amoxsnis sirTules Soris.

6.2.6.2.6.2.6.2. cvladebi da SezRudvebi.cvladebi da SezRudvebi.cvladebi da SezRudvebi.cvladebi da SezRudvebi. formalurad, nebismieri SezRudvaTa dakmayofilebSezRudvaTa dakmayofilebSezRudvaTa dakmayofilebSezRudvaTa dakmayofilebis is is is

amocana (Sda) amocana (Sda) amocana (Sda) amocana (Sda) ganisazRvreba nXXX ,..., 21 cvladebiTa cvladebiTa cvladebiTa cvladebiTa da mCCC ,...,, 21 SezRudvebis SezRudvebis SezRudvebis SezRudvebis

simravleebiT. TiToeul iX cvlads gaaCnia iD SesaZlo mniSvnelobaTa aracarieli

gansazRvris aregansazRvris aregansazRvris aregansazRvris are. TiToeuli jC SezRudva Seicavs cvladebis raime qvesimravles da

gansazRvravs am qvesimravlisaTvis dasaSveb kombinaciebs. amocanis mdgomareoba

ganisazRvreba cvladisaTvis mniSvnelobaTa miniWebisminiWebisminiWebisminiWebis gziT. miniWebas, romelic ar arRvevs

arcerT SezRudvas, ewodeba dasaSvebidasaSvebidasaSvebidasaSvebi an TavsebadiTavsebadiTavsebadiTavsebadi miniWeba.

sruli ewodeba iseT miniWebas, romelSic monawileobs yvela cvladi, xolo amocanis amocanis amocanis amocanis

amonaxsniamonaxsniamonaxsniamonaxsni ewodeba iseT srul miniWebas, romelic akmayofilebs yvela SezRudvas. garda

amisa, zogierT amocanebSi saWiroa iseTi amonaxsnis povna, romelic axdens miznis miznis miznis miznis

funqciisfunqciisfunqciisfunqciis optimizacias.

6.3.6.3.6.3.6.3. amocanis warmodgena.amocanis warmodgena.amocanis warmodgena.amocanis warmodgena. davuSvaT, mocemuli gvaqvs ruka, romelic Sedgeba Svidi

regionisagan da Cveni amocanaa gavaferadoT es ruka sami feris (wiTeli, mwvane, cisferi)

saSualebiT ise, rom mezobel regionebs ar hqondeT erTi da igive feri (ix. sur. #6.1).

CamovayaliboT es amocana SdaSdaSdaSda–s enaze. AaRvniSnoT regionebi cvladebiT:


7654321 ,,,,,, AAAAAAA . yvela cvladis dasaSveb mniSvnelobaTa simravle Sedgeba sami

ferisagan {wiTeli –1, mwvane _2, cisferi _3}. SezRudvebi moiTxoven, rom yvela wyvili

gaferadebuli iyos sxvadasxva ferad. magaliTad, 1A da 2A cvladebisaTvis dasaSvebia

ferTa Semdegi kombinaciebi: )}2,3();1,3();3,2();1,2();3,1();2,1{( . SesaZlebelia am SezRudvebis

ufro martivi saxiT Cawerac, magaliTad, 21 AA ≠ , Tuki algoriTmSi arsebobs iseTi

procedura, romelic SeZlebs mis wakiTxvas. . . .

sur. # 6.1. amocana rukis gaferadebaze

zogadad aseTi amocanebi SezRudvebze SesaZlebelia warmovadginoT grafis saxiT,

sadac kvanZebi Seesabamebian cvladebs, xolo rkalebi SezRudvebs (ix. sur. # 6.2).

amocanis SdaSdaSdaSda-sDAsaxiT warmodgena saSualebas gvaZlevs, mivaRwioT mniSvnelovan

upiratesobas amocanis mdgomareobaTa simravlis saxiT warmodgenasTan SedarebiT:

1. mdgomareobis warmodgena xdeba standartuli SabloniT (cvladebi, maTi

mniSvnelobebi da SezRudvebi), amitom Svilobilis ganmsazRvreli funqcia

(operatorebi) da miznis Semowmeba SeiZleba CavweroT universaluri formiT,

erTnairad yvela amocanisaTvis.

2. SeiZleba damuSavebuli iqnas efeqturi, standartuli evristikuli funqciebi,

romelTa Sesaqmnelad saWiro aRar iqneba damatebiTi codna konkretuli

problemuri garemos Sesaxeb.

3. amocanis amoxsnis procesis gasamartiveblad SeiZleba gamoviyenoT SezRudvaTa

grafis struqtura, rac saSualebas mogvcems eqsponencialurad SevamciroT

sirTule.

advili saCvenebelia, rom SdaSdaSdaSda klasis yvela amocana SeiZleba aRwerili iqnas iseve,

rogorc amocanebi miznis Zebnaze. Cven aRvwerdiT amocanas xuTi komponentis saSualebiT:

mdgomareobaTa simravle; sawyisi mdgomareoba; Svilobili wveros ganmsazRvreli funqcia

(operatorebis simravle); miznis mdgomareoba da gzis fasi. am SemTxvevaSi sawyisi sawyisi sawyisi sawyisi

1A 2A

4A

3A

5A

6A

7A

1A

leqcia #leqcia #leqcia #leqcia #6666. . . . amocanebi SezRudvaTa dakmayofilebazeamocanebi SezRudvaTa dakmayofilebazeamocanebi SezRudvaTa dakmayofilebazeamocanebi SezRudvaTa dakmayofilebaze 49

sur. # 6.2. amocanis warmodgena grafis saSualebiT.

mdgomareobamdgomareobamdgomareobamdgomareoba iqneba ccccarieliarieliarieliarieli miniWeba, romlis drosac arcerT cvlads ar mieniWeba

mniSvneloba. Svilobili wveros ganmsazRvreli funqcia Svilobili wveros ganmsazRvreli funqcia Svilobili wveros ganmsazRvreli funqcia Svilobili wveros ganmsazRvreli funqcia –––– romelime cvladisaTvis

dasaSvebi mniSvnelobis miniWebadasaSvebi mniSvnelobis miniWebadasaSvebi mniSvnelobis miniWebadasaSvebi mniSvnelobis miniWeba. miznis Semowmebis procedura tolfasia Semowmebisa,

mimdinare miniWebamimdinare miniWebamimdinare miniWebamimdinare miniWeba srulia Tu ara. gzis fasigzis fasigzis fasigzis fasi mudmivi sidide iqneba yvela gadasvlisaTvis

(yvela cvladisaTvis raime mniSvnelobis miniWebisaTvis).

yvela amoxsna unda warmoadgendes srul miniWebas da amitom unda imyofebodes n

doneze, sadac n aris cvladebis raodenoba. garda amisa xis siRrme aucileblad iqneba

agreTve n -is toli, amitom SdaSdaSdaSda amocanebis amoxsnis dros farTod gamoiyeneba siRrmeSi

gadarCevis algoriTmebi. am amocanebisaTvis damaxasiaTebelia agreTve is rom, araviTar

interess ar warmoadgens is gza, romliTac miiRweva amoxsna, amitomac SeiZleba

movaxdinoT amocanis formulireba srulsrulsrulsrul mdgomareobaTa enazemdgomareobaTa enazemdgomareobaTa enazemdgomareobaTa enaze, romelSic yvela

mdgomareoba warmoadgens srul miniWebas, romlebic an akmayofileben SezRudvebs an ara.

aseT SemTxvevaSi ufro mosaxerxebelia lokaluri Zebnis algoriTmebis gamoyeneba.

ufro martivi amocanebisaTvis damaxasiaTebelia diskretuli cvladebidiskretuli cvladebidiskretuli cvladebidiskretuli cvladebi, , , , romelTac

aqvT sasrulsasrulsasrulsasruliiii gansazRvris areebi gansazRvris areebi gansazRvris areebi gansazRvris areebi. . . . aseTia Cvens mier ganxiluli magaliTi. aseTivea rva

lazieris amocana, romelSic 821 ,...,, QQQ cvladebiT SegviZlia aRvniSnoT TiToeuli

lazieris pozicia 1, 2, . . ., 8 vertikalebze. TiToeuli cvladis mniSvnelobaTa simravle

iqneba – {1,2,3,4,5,6,7,8}. Tu nebismieri cvladis gansazRvris aris maqsimaluri zomaa d ,

maSin yvela SesaZlo srul miniWebaTa raodenoba izomeba sididiT O( nd ). miuxedavad imisa,

rom Sefaseba aqac eqponencialuria, algoriTmebi, romlebic gamoiyeneba SdaSdaSdaSda amocanebis

amosaxsnelad umetes SemTxvevaSi saSualebas gvaZleven amovxsnaT ramdenime rigiT ufro

rTuli amocanebi.

diskretul cvladebsac SeiZleba hqondeT usasrulo gansazRvris areusasrulo gansazRvris areusasrulo gansazRvris areusasrulo gansazRvris are. . . . aseT

SemTxvevaSi ukve SeuZlebelia SezRudvaTa aRwera cvladebis dasaSveb mniSvnelobaTa

kombinaciebis CamoTvliT. Aam SemTxvevaSi saWiroa gamoviyenoT SezRudvaTa aRweris enaSezRudvaTa aRweris enaSezRudvaTa aRweris enaSezRudvaTa aRweris ena.

yvelaze xSirad am mizniT gamoiyeneba algebruli aRwera. magaliTad, Tu ori cvladidan

1A

2A

4A 5A

3A

6A

7A


x da y , erTerTis mniSvnelobebi ar SeiZleba iyos naklebi raime mudmivi sididiT

meoreze, gveqneba SezRudva yax <+ . amave dros ukve aRar SeiZleba aseTi amocanebis

amoxsna ubralod yvela SesaZlo miniWebaTa CamoTvlis gziT, radganac aseT miniWebaTa

raodenoba iqneba usasrulo simravle. SdaSdaSdaSda amocanebSi Cven ar ganvixilavT amocanebs

mTelmniSvneliani cvladebiTa da wrfivi SezRudvebiT da amocanebs cvladTa uwyveti

gansazRvris areebiT. Epirveli tipis amocanebi Seiswavleba wrfiv programirebaSi, xolo

meore saxis – operaciaTa gamokvlevaSi.

6.4.6.4.6.4.6.4. SezRudvaTa tipebi.SezRudvaTa tipebi.SezRudvaTa tipebi.SezRudvaTa tipebi. garda cvladebis tipebis daxasiaTebisa, sasargebloa

ganvixiloT SezRudvaTa tipebic. SezRudvebi SeiZleba iyos unaruli,unaruli,unaruli,unaruli, anu exebodes

mxolod erT cvlads. . . . magaliTad, davuSvaT, rukaze 1A regioni ar SeiZleba SeiRebos

wiTlad, radganac mis mflobels ar uyvars wiTeli feri. unaruli SezRudva gadaiWreba

martivad, gansazRvris aridan Sesabamisi mniSvnelobis amogdebiT. ufro rTulia binaruli binaruli binaruli binaruli

SezRudvebiSezRudvebiSezRudvebiSezRudvebi, romlebic moqmedeben or cvladze. MmagaliTad, 21 AA ≠ . . . .

ufro maRali rigis SezRudvebSi monawileoben sami da ufro meti cvladebi. aseTi

amocanebis kargi magaliTia e.w. ricxviTi rebusebi, romlebSic ricxvebi Secvlilia

asoebiT. magaliTad, FOURTWOTWO =+ . aq moTxovna, rom eqvsive cvladi

( ORWUTF ,,,,, ) am gamosaxulebaSi Rebulobs sxvadasxva mniSvnelobebs, SeiZleba

Cawerili iqnas, rogorc SezRudva eqvsi cvladiT – yvelayvelayvelayvela gansxvgansxvgansxvgansxv ( ORWUTF ,,,,, ) an

sxvanairad binaruli SezRudvebis simravliT ( TF ≠ ). SezRudvebi Sekrebaze svetebSi aseve

Seicavs damatebiT cvladebs:

21

1

10

10

XUWWX

XROO

+=++⋅+=+

FX

XOTTX

=+=++

3

32 10

sadac 321 ,, XXX damatebiTi cvladebiadamatebiTi cvladebiadamatebiTi cvladebiadamatebiTi cvladebia, , , , mniSvnelobebiT 0 an 1, romelic gadaitaneba

Semdeg TanrigSi. maRali rigis SezRudvebi SeiZleba warmovadginoT SezRudvisSezRudvisSezRudvisSezRudvis

hipergrafishipergrafishipergrafishipergrafis saSualebiT ise, rogorc es moyvanilia sur. #6.3 rogorc am magaliTidanac

kargad Cans, maRali rigis SezRudvebi SeiZleba davSaloT binarul SezRudvebad

damatebiTi cvladebis Semotanis gziT, amitom SemdgomSi ganvixilavT mxolod binarul

SezRudvebs.

6.5.6.5.6.5.6.5. komutaturoba.komutaturoba.komutaturoba.komutaturoba. Cven vnaxeT, rom Sda Sda Sda Sda amocanebi SeiZleba warmovadginoT rogorc

Zebnis amocanebi da Sesabamisad SeiZleba maT amosaxsnelad gamoviyenoT Zebnis nebismieri

algoriTmi. vnaxoT ra moxdeba Tuki gamoviyenebT ganivi gadarCevis algoriTms, rodesac

cvladebis raodenobaa n da TiToeul maTgans SeuZlia miiRos d mniSvneloba. pirvel

etapze gveqneba dn ⋅ SesaZlo varianti, radganac nebismieri mniSvneloba SegviZlia

mivaniWoT nebismier cvlads. meore etapze gveqneba ukve dn ⋅− )1( varianti da sabolood,

miviRebT xes ndn ⋅! totiT, maSin rodesac sinamdileSi arsebobs mxolod d n

SesaZlo


sruli miniWeba.Y es xdeba imitom, rom ar iqna gaTvaliswinebuli yvela SdaSdaSdaSda amocanisaTvis

sur. # 6.3. SezRudvis yvelagansxvyvelagansxvyvelagansxvyvelagansxv ( ORWUTF ,,,,, ) hipergrafi.

aq rgolebiT aRniSnulia SezRudvebi, romlebic dakavSirebulebi arian maT

mier SezRudul cvladebTan

damaxasiaTebeli Tviseba – komutaturobakomutaturobakomutaturobakomutaturoba.... amocanas ewodeba komutaturuli, Tu amoxsnis

procesSi gamoyenebuli nebismieri konkretuli qmedebebis rigs ara aqvs mniSvneloba.

swored es Tviseba axasiaTebs SdaSdaSdaSda amocanebs, radganac ra rigiTac ar unda mivakuTvnoT

cvladebs mniSvnelobebi, Cven vRebulobT erTsa da imave nawilobriv miniWebas. amitom

yvela algoriTmSi, romelic gamoiyeneba SdaSdaSdaSda amocanebis amosaxsnelad, Svilobili

wveroebi warmoiqmneba imis gaTvaliswineboT, rom xis TiToeul kvanZSi xdeba mniSvnelobis

miniWeba mxolod erTi cvladisaTvis. magaliTad, Tu davubrundebiT rukis gaferadebis

amocanas, sawyis mdgomareobaSi ,11 =A A 21 =A da 31 =A variantebidan unda amovirCioT

erTerTi da ara 2,1 21 == AA variantebidan romelime. mxolod am pirobis dacviT

SegviZlia SevamciroT gadarCeva d n----mde.

6.6. Zebna ukan dabrunebiT.6.6. Zebna ukan dabrunebiT.6.6. Zebna ukan dabrunebiT.6.6. Zebna ukan dabrunebiT. GZebnas siRrmeSi, romlis drosac yovel jerze amoirCeva

mniSvnelobebi erTi cvladisaTvis da xdeba ukan dabruneba, rodesac aRar rCeba dasaSvebi

mniSvnelobebi, romelTa miniWebac SesaZlebelia am cvladisaTvis, ewodeba Zebna ukan Zebna ukan Zebna ukan Zebna ukan

dabrunebiTdabrunebiTdabrunebiTdabrunebiT. algoriTmi Zalian martivia. sawyis mdgomareobaSi (arcerT cvlads ara aqvs

miniWebuli raime mniSvneloba) aiReba pirveli cvladi da mieniWeba yvela dasaSvebi

mniSvnelobebi. meore etapze aiReba pirveli wvero da meore cvlads mieniWeba yvela

dasaSvebi mniSvneloba. Tu miiRweva iseTi sasruli mdgomareoba, romelSic yvela

cvlads aqvs miniWebuli dasaSvebi mniSvneloba, amocana amoxsnilia, Tu ara – algoriTmi

dabrundeba erTi nabijiT ukan da ganixilavs sxva wveros. cxadia es algoriTmi

warmoadgens arainformirebuli Zebnis algoriTms da amitom misi gamiyeneba didi

amocanebis amosaxsnelad araefeqturia. aseT SemTxvevebSi Zebnis informirebuli

algoriTmebis efeqturobis gaumjobesebis mizniT viyenebdiT evristikul informacias,

F T U W R O

1X 2X 3X


romelic gamomdinareobda Cveni codnidan mocemuli konkretuli amocanis Sesaxeb.

sur. # 6.4. algoriTmis agebuli xis nawili rukis gaferadebis amocanisaTvis

6.7. Zebna ukan dabrunebiT dmm6.7. Zebna ukan dabrunebiT dmm6.7. Zebna ukan dabrunebiT dmm6.7. Zebna ukan dabrunebiT dmm----is gamoyenebiTis gamoyenebiTis gamoyenebiTis gamoyenebiT.Eexla vnaxoT, rogor SeiZleba SdaSdaSdaSda

amocanebisaTvis movaxdinoT gadarCevis efeqturi Semcireba ise, rom gamoviyenoT ara raime

evristikuli informacia konkretuli amocanis Sesaxeb, aramed mxolod informacia,

romelic gamomdinareobs amocanis formalizaciis principebidan. amisaTvis davukvireT

rogor muSaobs zemoTganxiluli algoriTmi. is cvladebs irCevs im mimdevrobiT, ra

mimdevrobiTac isini Setanilia siaSi “cvladebi” da aniWebs maT dasaSveb mniSvnelobebs

aseve rigis mixedviT siidan “mniSvnelobebi”. es midgoma cxadia yovelTvis ver iqneba

efeqturi. igive Cveni magaliTis SemTxvevaSi, mas Semdeg, rac algoriTmi mianiWebs

mniSvnelobebs 1A da 2A cvladebs, mas 4A cvladisaTvis rCeba erTaderTi dasaSvebi

mniSvneloba, amitom logikurad ufro swori iqneba, Tu Semdeg etapze algoriTmi aiRebs

4A cvlads da ara 3A cvlads. marTlac, Tu mesame etapze algoriTmi aiRebs 4A cvlads,

yvela darCenil cvladebs garda 7A darCebaT erTaderTi dasaSvebi mniSvnelobebi da

amocana swrafad gadaiWreba. es daskvna, rom yovel etapze umjobesia amovarCioT cvladi

dasaSvebi mniSvnelobebis minimaluri raodenobebiT, SegviZlia CamovayaliboT pirveli

evristikis saxiT - ddddarCenil mniSvnelobaTa minimumi (dmm), arCenil mniSvnelobaTa minimumi (dmm), arCenil mniSvnelobaTa minimumi (dmm), arCenil mniSvnelobaTa minimumi (dmm), an sxvanairad cvladi yvelaze cvladi yvelaze cvladi yvelaze cvladi yvelaze

meti SezRudvebiT. meti SezRudvebiT. meti SezRudvebiT. meti SezRudvebiT. aseTi evristikis gamoyeneba iZleva kidev im upiratesobasac, rom Tu

romelime cvladis dasaSveb mniSvnelobaTa simravle gaxdeba nolis toli, algoriTmi

pirvel rigSi amoirCevs am cvlads, miva warumateblobamde da mokveTavs am tots.

davarqvaT am algoriTms Zebna Zebna Zebna Zebna ukan ukan ukan ukan dabrunebiTdabrunebiTdabrunebiTdabrunebiT dmmdmmdmmdmm––––iiiis gamoyenebiT. s gamoyenebiT. s gamoyenebiT. s gamoyenebiT. am algoriTmis

efeqturoba wina algoriTmTan SedarebiT SeiZleba gaizardos 3-dan 3000 jer amocanis

mixedviT.

6.8. xarisxovani evristika.6.8. xarisxovani evristika.6.8. xarisxovani evristika.6.8. xarisxovani evristika. samwuxarod, es evristika arafers ar gveubneba pirveli

cvladis amorCevaze, radganac xSir SemTxvevaSi (iseve rogorc Cvens magaliTSi), sawyis

mdgomareobaSi yvela cvlads gaaCnia erTi da igive dasaSveb mniSvnelobaTa simravle. am

SemTxvevaSi mosaxerxebelia xarisxovani evristikisxarisxovani evristikisxarisxovani evristikisxarisxovani evristikis gamoyeneba. es evristika cdilobs

11 =A 21 =A 31 =A

22 =A 32 =A

13 =A 33 =A


Seamciros xis datotvis koeficienti imis xarjze, rom pirvelad amoirCevs cvlads,

romelic monawileobs yvelaze met SezRudvebSi im cvladebTan, romlebsac jer ara aqvT

miniWebuli mniSvnelobebi. Cvens magaliTSi aseT cvlads warmoadgens 4A cvladi. es

evristika dmmdmmdmmdmm evristikasTan SedarebiT naklebad amcirebs gadarCevas, magram is Zalian

sasargebloa gaurkvevel situaciebSi.

Mmas Semdeg, rac amovirCevT romelime cvlads, saWiroa davadginoT misi mniSvnelobebis

miniWebis rigi. amisaTvis SeiZleba gamoviyenoT kidev erTi efeqturi evristika -

minimalurad SemzRudavi mniSvnelobis minimalurad SemzRudavi mniSvnelobis minimalurad SemzRudavi mniSvnelobis minimalurad SemzRudavi mniSvnelobis amorCevis evristikaamorCevis evristikaamorCevis evristikaamorCevis evristika. Aes evristika upiratesobas

aniWebs cvladis im mniSvnelobebs, romlebic minimalurad zRudaven danarCeni

cvladebisaTvis mniSvnelobaTa miniWebis variantebs. imave magaliTSi Tu pirvel cvlads

miniWebuli aqvs mniSvneloba erTi, meore cvlads ki mniSvneloba – ori da vixilavT mesame

cvlads, dasaSvebi ori variantidan es evristika amoirCevs mniSvnelobas erTi, radgan

samis miniWeba meoTxe cvlads aRar utovebs dasaSveb mniSvnelobas. Tu Cven veZebT

amocanis yvela amoxsnas, an amocanas ar gaaCnia amonaxseni, maSin am evristikis gamoyenebas

azri ara aqvs, yvela danarCen SemTxvevaSi ki es evristikac amcirebs gadarCevas.

sur. # 6.5. algoriTmis muSaobis pirveli etapi.

vnaxoT, rogor imuSavebs aseTi evristikebiT aRWurvili algoriTmi Cveni magaliTis

SemTxvevaSi. xarisxovani evristikis gamoyenebiT is pirvel cvladad amoirCevs 4A

cvlads, radganac is dakavSirebulia xuT cvladTan. minimalurad SemzRudavi

mniSvnelobis amorCevis evristika aq ver imuSavebs imitom, rom yvela danarCeni cvladebis

(garda 7A ) dasaSveb mniSvnelobaTa simravle izRudeba erTnairad. aqedan gamomdinare,

pirveli etapis Semdeg xes eqneba Semdegi saxe (ix. sur. # 6.5.).

sur. # 6.6. algoriTmis muSaobis meore etapi.

14 =A 24 =A 34 =A

2

1

1

4

==

A

A

3

1

1

4

==

A

A

1

2

1

4

==

A

A

3

2

1

4

==

A

A

1

3

1

4

==

A

A

2

3

1

4

==

A

A

14 =A 24 =A 34 =A


meore etapze algoriTmi eZebs cvlads, romlis dasaSveb mniSvnelobaTa simravle

minimaluria. aseTebia ,,,,, 65321 AAAAA amitom is amoirCevs 1A -s da miiReba Semdegi xe (ix

sur. # 6.6.).

mesame etapze erTi (minimaluri) dasaSvebi mniSvneloba eqneba 3A cvlads, Semdeg

etapze 4A -s da ase gagrZeldeba sanam algoriTmi ar mianiWebs mniSvnelobebs pirvel

eqvs cvlads. Semdeg darCeba mxolod meSvide cvladi, romelmac SeiZleba miiRos sami

mniSvneloba damoukideblad sxva cvladebisagan, amitom gveqneba amocanis Tvrameti

sxvadasxva amoxsna (ix.sur. # 6.7).

............

sur. #6.7 rukis gaferadebis amocanis amoxsna

6.9. winaswari Semowmeba.6.9. winaswari Semowmeba.6.9. winaswari Semowmeba.6.9. winaswari Semowmeba. aqamde ganxilul algoriTmSi SezRudva, romelic vrceldeboda

romelime cvladze, mxedvelobaSi miiReboda mxolod maSin, rodesac xdeboda am

34 =A 24 =A 34 =A

2

1

1

4

==

A

A

3

1

1

4

==

A

A

1

2

1

4

==

A

A

3

2

1

4

==

A

A

1

3

1

4

==

A

A

2

3

1

4

==

A

A

3

2

1

2

1

4

===

A

A

A

2

3

1

2

1

4

===

A

A

A

2

3

2

1

3

2

1

4

====

A

A

A

A

3

2

3

2

1

5

3

2

1

4

=====

A

A

A

A

A

2

3

2

3

2

1

6

5

3

2

1

4

======

A

A

A

A

A

A

1

2

3

2

3

2

1

7

6

5

3

2

1

4

=======

A

A

A

A

A

A

A

2

2

3

2

3

2

1

7

6

5

3

2

1

4

=======

A

A

A

A

A

A

A

3

2

3

2

3

2

1

7

6

5

3

2

1

4

=======

A

A

A

A

A

A

A


cvladisaTvis mniSvnelobis miniWeba. magram Tu zogierT SezRudvas ganvixilavT ufro

adreul etapebze, an saerTod Zebnis dawyebamde, SesaZlebelia mkveTrad SevamciroT Zebnis

sivrce.

erTerT saSualebas Zebnis dros SezRudvebis ukeT gamoyenebisa warmoadgens

winaswariwinaswariwinaswariwinaswari Semowmeb Semowmeb Semowmeb Semowmebisisisis meTodi, romelic mdgomareobs SemdegSi: cvladisaTvis raime

mniSvnelobis miniWebisas xdeba yvela im cvladis Semowmeba, romlebsac jer ara aqvT

miniWebuli mniSvneloba da romlebic SezRudviT dakavSirebulni arian am cvladTan. maTi

gansazRvris aredan amoiSleba is mniSvnelobebi, romlebic SeuTavsebelni arian

cvladisTvis miniWebul mniSvnelobasTan. sur. # 6.8. mocemulia winaswariwinaswariwinaswariwinaswari SemowmebisSemowmebisSemowmebisSemowmebis

meTodis gamoyeneba Cvens mier zemoT ganxiluli magaliTisaTvis. pirvel striqonSi

mocemulia sawyisi gansazRvris areebi Zebnis dawyebamde. meore striqonSi gansazRvris

areebi mas Semdeg, rac pirvel cvlads mivaniWeT mniSvneloba 1. mesame striqonSi – pirvel

cvlads mieniWa mniSvneloba erTi da mesame cvlads – 2. meoTxe striqonSi pirvels –1,

mesames – 2, mexuTs – 3. rogorc am magaliTidan Cans, mas Semdeg, rac

1A 2A 3A 4A 5A 6A 7A

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

1 2 3 1 2 3 2 3 1 2 3 1 2 3 1 2 3

1 3 2 3 1 3 1 2 3 1 2 3

1 3 2 3 1 2 1 2 3

sur. # 6.8. winaswari Semowmebis meTodis cxriliN

pirvel cvlads mivaniWeT mniSvneloba 1 da mesames mniSvneloba –2, meore da meoTxe

cvladebs darCaT erTaderTi dasaSvebi mniSvnelobebi. Ees ra Tqma unda amcirebs Zebnis

xis datotvas, rasac aucileblad gamoiyenebs dmmdmmdmmdmm evristika. meore, rac aseve Zalian

mniSvnelovania, aris is, rom mexuTe cvladisaTvis mniSvnelobis 3 miniWebis Semdeg meoTxe

cvladis dasaSveb mniSvnelobaTa simravle aRmoCnda carieli, rac imas niSnavs, rom es

kombinacia SeuTavsebelia SezRudvebTan, amitom algoriTmi aRar gaagrZelebs mis

ganxilvas da dabrundeba ukan.

Mmiuxedavad imisa, rom winaswari Semowmebiswinaswari Semowmebiswinaswari Semowmebiswinaswari Semowmebis meTodi saSualebas gvaZlevs aRmovaCinoT

bevri Seusabamoba, mas mainc ar SeuZlia yvelafris danaxva. magaliTad, mesame striqonSi,

pirveli cvladisaTvis 1 miniWebisa da mesame cvladisaTvis 2 minWebis Semdeg meore da

meoTxe cvladebs rCebaT mxolod mniSvneloba 3. es regionebi ki erTmaneTis mezoblebi

arian da ar SeuZliaT miiRon erTi da igive mniSvnelobebi. aseT SemTxvevebSi

SesaZlebelia gamoviyenoT sxvadasxva meTodebi, romlebic gaerTianebulni arian erTi

saxelis qveS SezRudvaTa gavrceleba.SezRudvaTa gavrceleba.SezRudvaTa gavrceleba.SezRudvaTa gavrceleba. Yyvelaze swrafi aseT meTodebs Soris aris

rkalebis Tavsebadobisrkalebis Tavsebadobisrkalebis Tavsebadobisrkalebis Tavsebadobis Semowmeba. am SemTxvevaSi rkalis qveS gvesmis orientirebuli

gadasvla SezRudvaTa grafze, iseTi, rogoricaa magaliTad rkali 6A -dan 4A -ze.

gansazRvris Tanaxmad, rkali erTi wverodan (erTi cvladidan) meorisken Tavsebadia, Tu


pirveli wveros (pirveli cvladis) yoveli mniSvnelobisaTvis arsebobs meore cvladis

raime mniSvneloba, romelic dasaSvebia (Tavsebadia) pirveli cvladis mniSvnelobasTan.

Cveni magaliTisaTvis davuSvaT, 5A cvladis dasSvebi mniSvnelobaa {1,3} da 4A cvladis ki-3

(rogorc esaa winaswari Semowmebis cxrilis mesame striqonSi). maSin orientirebuli

rkali 4A -dan 5A -Si Tavsebadia, radganac Tu 4A -s mivaniWebT mniSvnelobas 3, 5A -s

SeiZleba mivaniWoT 1, magram piriqiT orientirebuli rkali ukve aRaraa Tavsebadi,

radganac, Tu 5A -s mivaniWeT mniSvneloba 3, maSin 4A -s aRar darCeba dasaSvebi

mniSvneloba.

6.10. amocanis 6.10. amocanis 6.10. amocanis 6.10. amocanis dekompoziciadekompoziciadekompoziciadekompozicia. . . . arseboben aseTi tipis amocanebis amoxsnis ufro swrafi

meTodebi, romlebic iyeneben amocanis struqturas da axdenen amocanis dekompoziciasdekompoziciasdekompoziciasdekompozicias

qveamocanebad, romlbic Semdeg calcalke amoixsneba. Cvens mier ganxilul magaliTSi,

pirveli eqvsi regionis gaferadeba aranair gavlenas ar axdens meSvide regionze, anu es

qveamocanebi arian damoukidebeli qveamocanebi, damoukidebeli qveamocanebi, damoukidebeli qveamocanebi, damoukidebeli qveamocanebi, amas aCvenebs amocanis grafic, romelzec

meSvide regioni ar aris dakavSirebuli arcerT sxva regionTan. maSin Cveni ZiriTadi

amocana SeiZleba gavyoT or qveamocanad: pirveli eqvsi regionis gaferadeba da meSvide

regionis gaferadeba. am SemTxvevaSi amocanis amoxnis siRrme Semcirdeba Svididan eqvsamde.

es ra Tqma unda arc Tu ise bevria, magram warmovidginoT, rom gvaqvs amocana, romelic

Seicavs n cvlads da es amocana iyofa iseT damoukidebel qveamocanebad, sadac

TiToeuli qveamocana Seicavs c cvlads (radganac qveamocanebi damoukidebelia, erTi

qveamocanis cvladebi ar monawileoben meore qveamocanaSi), amitom sul gveqneba cn

qveamocana da TiToeuli qveamocanis amoxsna moiTxovs maqsimum cd variants, amitom mTeli

amocanis amoxsnis sirTule iqneba )( cndO c, romelic wrfivadaa damokidebuli n -ze

gansxvavebiT ).( ndO es ra Tqma unda mniSvnelovnad amcirebs amocanis amoxsnis dros.

amocanis daSla damoukidebel qveamocanebad Zalian kargi da swrafi meTodia, magram

samwuxarod aseTi amocanebi gvxvdeba Zalian iSviaTad, umravles SemTxvevebSi qveamocanebi

damokidebulia erTmaneTze da qmnian grafs. umartives SemTxvevaSi es grafi SeiZleba iyos

xexexexe, rodesac nebismieri ori qveamocana dakavSirebuli erTmaneTTan mxolod erTi gziT (ix

sur. # 6.9).

a) b)

sur. # 6.9. a) xiseburi struqtura; b) cvladebis wrfivi mowesrigeba fesviT A

B

C

D

E

F

A

A B C D E F


aseT SemTxvevaSi, arsebobs algoriTmi, romlis sirTulec wrfivadaa damokidebuli

cvladebis raodenobaze. es algoriTmi Sedgeba Semdegi etapebisagan:

1. amoirCie xis fesvad nebismieri cvladi da moawesrige cvladebi fesvidan

foTlebamde ise, rom TiToeuli kvanZis mSobeli kvanZi xeze win uswrebdes am kvanZs

(ix. sur. # 6.9 b). aRniSne cvladebi am mimdevrobiT, rogorc nXXX ,..., 21 , maSin

yvela cvlads garda fesvisa, eyoleba mxolod erTi mSobeli cvladi.

2. ciklSi j icvleba n -dan 2-mde gamoiyene rkalebis Tavsebadobis Semowmeba ),( ji XX

rkalebisaTvis, sadac iX aris mSobeli kvanZi jX kvanZisaTvis da Tu saWiroa

amoyare mniSvnelobebi iX -s gansazRvris aridan.

3. ciklSi j icvleba 1-dan n -mde mianiWe jX nebismieri mniSvneloba, romelic

Tavsebadia iX -s mniSvnelobasTan, sadac iX aris mSobeli kvanZi.

exla vnaxoT, SesaZlebelia Tu ara miviyvanoT rTuli grafebi xisebur struqturamde.

arsebobs ori gza amis misaRwevad: pirveli moiTxovs kvanZebis mocilebas, meore – ki

kvanZebis gareTianebas. davubrundeT Cvens magaliTs. Tu Cven SevZlebT 4A cvladis

moSorebas. maSin danarCeni cvladebi mogvcemen grafs (is. sur. # 6.10.).

sur. # 6.10. grafis xed gadaqcevis pirveli gza kvanZis mocilebiT

am kvanZis moSoreba SesaZlebelia, Tu Cven 4A cvlads davufiqsirebT raime

mniSvnelobas da danarCeni cvladebis (garda 7A ) gansazRvris areebidan amoviRebT am

mniSvnelobas. ufro rTul SemTxvevebSi SesaZlebelia erTi cvladis amoReba ar iyos

sakmarisi xis misaRebad, amitom zogadad algoriTms eqneba Semdegi saxe:

1. amovirCioT iseTi qvesimravle S cvladebis simravlidan, rom SezRudvaTa

darCenili grafi warmodgendes xes (S -s ewodeba ciklis gawyvetis simravleciklis gawyvetis simravleciklis gawyvetis simravleciklis gawyvetis simravle).

2. S -Si cvladebisaTvis yvela SesaZlo miniWebebisaTvis, romlebic akmayofileben

SezRudvebs S -Si, Seasrule Semdegi:

1A

2A

3A

5A

6A 7A


3. darCenili cvladebis mniSvnelobaTa simravlidan amoiRe yvela mniSvnelobebi,

romlebis araTavsebadia S -Si miniWebul mniSvnelobebTan;

4. Tu darCenil amocanas aqvs amoxsna, gamoitane es amoxsna S -Si Sesrulebul

miniWebebTan erTad.

Tu ciklis gawyvetis simZlavrea c , maSin algoriTmis sirTule iqneba

))(( 2dcndO c − . im SemTxvevaSi, rodesac grafi Tavisi formiT “Zalian axlosaa xesTan,

c iqneba patara, xolo drois ekonomia Zebnis ukan dabrunebis algoriTmTan SedarebiT,

Zalian didi. yvelaze cud SemTxvevaSi c SeiZleba iyos )2( −n -is toli. ciklis

gawyvetis amocana warmoadgens NP sirTulis amocanas, magram cnobilia ramdenime efeqturi

algoriTmi am amocanis amosaxsnelad.

sur. # 6.11. grafis xiseburi dekompozicia

meore gza, romelic SeiZleba gamoviyenoT xiseburi struqturis misaRebad efuZneba

SezRudvaTa grafis xiseburi dekompoziciisxiseburi dekompoziciisxiseburi dekompoziciisxiseburi dekompoziciisa a a a da dakavSirebul qveamocanaTa dakavSirebul qveamocanaTa dakavSirebul qveamocanaTa dakavSirebul qveamocanaTa simravlis

1A

A

1A

2A

4A

2A 3A

4A

4A 3A

5A

4A 5A

6A

7A


Seqmnas. TiToeuli qveamocana gadaiWreba damoukideblad da Semdeg xdeba miRebuli

Sedegebis kombinaciebis Semowmeba. Tu qveamocanebi ar iqneba Zalian didi, maSin

algoriTmi muSaobs sakmarisad warmatebulad. ganvixiloT es midgoma kvlav Cveni

magaliTis SemTxvevaSi (ix. sur. # 6.11.). aq moxda xiseburi struqturis miReba sam-sami

cvladebis gaerTianebiT dakavSirebul qveamocanaTa simravleSi. Tu dekompoziciis Semdeg

romelime qveamocanas ara aqvs amoxsna, maSin cxadia, arc mTlian amocanas ar eqneba

amoxsna Tu SevZeliT qveamocanaTa amoxsna, maSin SegviZlia vcadoT ZiriTadi amocanis

amoxsna Semdegi gziT. TiToeuli qveamocana ganixileba rogorc “megacvladi”“megacvladi”“megacvladi”“megacvladi”, romlis

gansazRvris aresac warmoadgens am qveamocanis amonaxsnebi. magaliTad, pirveli

qveamocanaa sami regionis gaferadeba sami feriT, ise, rom mezobeli regionebi ar iyos

gaferadebuli erTi da igive feriT, amitom am qveamocanas aqvs eqvsi amoxsna. Sesabamisad,

pirveli megacvladis mniSvnelobebis simravle Seicavs am eqvs amoxsnas. amis Semdeg

qveamocanebis SezRudvebis dasadgenad gamoiyeneba zemoTmoyvanili xeebis algoriTmi.

SezRudvebi, romlebic akavSireben qveamocanebs, miuTiTeben, rom qveamocanaTa amoxsnebi

unda SeTanxmebuli iyos maTi saerTo cvladebis mimarT. magaliTad, Tu viwyebT pirveli

qveamocanis amonaxsniT ,3,2,1 421 === AAA erTaderTi Tavsebadi amonaxsni meore

qveamocanisaTvis SeiZleba iyos 3,1,2 432 === AAA .

SezRudvaTa nebismieri grafisaTvis SesaZlebelia didi raodenobis xiseburi

dekompozicia. dekompoziciis amorCevis dros unda vecadoT, rom qveamocanaTa raodenoba

iyos cota. xiseburi dekompoziciis xis siganexis siganexis siganexis sigane erTiT naklebi unda iyos yvelaze didi

qveamocanis zomaze. TviT grafis xis sigane ganisazRvreba rogorc minimaluri xis sigane

yvela mis xisebur dekompoziciebs Soris. Tu grafis xis sigane tolia w da mocemulia

Sesabamisi xiseburi dekompozicia, maSin amocanis sirTule iqneba )( 1+wndO , rac imas

niSnavs, rom amocanebi SezRudvaTa dakmayofilebaze, romelTa SezRudvaTa grafi

xasiTdeba xis sasruli siganiT, SeiZleba amoixsnas polinomialur droSi. samwuxarod,

minimaluri xis siganis mqone dekompoziciis moZebnis amocana warmoadgens NP sirTulis

amocanas, magram arseboben evristikuli meTodebi, romlebic warmatebiT gamoiyeneba

praqtikaSi.Q

sakontrolosakontrolosakontrolosakontrolo kiTxvebi: kiTxvebi: kiTxvebi: kiTxvebi:

1. ra gansxvavebaa amocanis warmodgenaSi mdgomareobaTa sivrcesa da

SezRudvebis dakmayofilebaze?

2 CamoTvaleT ra upiratesobebiB aqvs Sda Sda Sda Sda warmodgenas?

3 rogori SeiZleba iyos cvladebis mniSvnelobebi da SezRudvebi?

4 rogor amocanebs ar ganvixilavT ganvixilavT amocanebSi SezRudvaze?

5 moiyvaneT erTi da igive amocanis warmodgenis magaliTi mdgomareobaTa sivrceSi

da Sda Sda Sda Sda warmodgenaSi.

6 aRwereT algoriTmi Zebna ukan dabrunebiT

7 aRwereT evristikebi, romlebic gamoiyeneba Sda Sda Sda Sda algoriTmebSi.


8 riT gansxvavdeba es evristikebi mdgomareobaTa sivrcis evristikebisagan?

9 ras niSnavs amocanis dekompozicia?

10 rogor qveamocanebs ewodeba damoukidebeli qveamocanebi?

11 ras niSnavs grafis xiseburi dekompozica/

12 rogori algoriTmi SeiZleba gamoviyenoT amocanis amosaxnelad, Tu SezRudvebis

grafis nacvlad gveqneba xe.

13 ras niSnavs amocanis dekompozicia?

14 rogor qveamocanebs ewodebaT damoukidebeli qveamocanebi?

15 ra meTodebi arsebobs rTuli grafis xisebur struqturaze misayvanad?


1. SeadgineT rkalebis Tavsebadobis Semowmebis algoriTmi SeecadeT daweroT

Sesabamisi programa.

2. CamoayalibeT rva lazieris amocana SdaSdaSdaSda-s enaze da SeadareT, rodis ufro advilad

miiRweva amoxsna, roca amocana warmodgenilia mdgomareobaTa sivrceSi, Tu SdaSdaSdaSda-s

enaze?

3. moifiqreT, rogor SeiZleba gamoviyenoT lokaluri Zebnis algoriTmi

amocanebisaTvis, romlebic warmoidgineba SdaSdaSdaSda-s enaze?

4. amoxseniT leqciaSi moyvanili magaliTi amocanis dekompoziciis meTodis

gamoyenebiT da SeadareT amoxsnas, romelic mocemulia leqciaSi.

leqcia leqcia leqcia leqcia #7#7#7#7

Zebna wiZebna wiZebna wiZebna winaaRmdegobis SemTxvevaSinaaRmdegobis SemTxvevaSinaaRmdegobis SemTxvevaSinaaRmdegobis SemTxvevaSi

7.17.17.17.1 TamaSebi, rogorc konkurentuli problemuri garemo. TamaSebi, rogorc konkurentuli problemuri garemo. TamaSebi, rogorc konkurentuli problemuri garemo. TamaSebi, rogorc konkurentuli problemuri garemo. Cven agentTa TeoriaSi (leqcia

#2), ganvixileT multiagenturi garemo, romelSic agents uxdeboda mxedvelobaSi mieRo

sxva agentebis qmedebebi, daedgina Tu ra gavlenas iqoniebda es qmedebebi mis sakuTar

gadawyvetilebebze da amis mixediT moexdina maTi koreqcia. multiagenturi garemo Tavisi

SinaarsiT SeiZleba iyos rogorc kooperaciulikooperaciulikooperaciulikooperaciuli,,,, aseve konkurentuli.konkurentuli.konkurentuli.konkurentuli. pirvel SemTxvevaSi

agentebi urTierTTanamSromloben dasaxuli miznebis misaRwevad, meore SemTxvevaSi ki maTi

miznebi imdenad gansxvavebulia, rom erTi agentis mier miznis miRweva avtomaturad iwvevs

imas, rom meore agenti an ver miaRwevs miznas, an miaRwevs mxolod nawilobriv. xelovnur

inteleqtSi Zebnis amocanebs iseT konkurentul multiagentur garemoSi, sadac agentTa

miznebi urTierTsawinaaRmdegoa, uwodeben Zebnas winaaRmdegobis pirobebSi Zebnas winaaRmdegobis pirobebSi Zebnas winaaRmdegobis pirobebSi Zebnas winaaRmdegobis pirobebSi da radganc

aseTi garemos yvelaze xSiri magaliTebia inteleqtualuri TamaSebi – zogjer TamaSebsTamaSebsTamaSebsTamaSebs.

TamaSebi Tavisi stuqturiT gansxvavdebian erTmaneTisagan. magaliTad Wadrakis, an

SaSis TamaSi arsebiTad gansxvavdeba prefenansis TamaSisagan da aq saqme marto imaSi ki ar

aris, rom erT SemTxvevaSi saqme gvaqvs Wadrakis figurebTan, xolo meore SemTxvevaSi

baqosTan. gansxvaveba ufro Rrmaa. Wadrakis TamaSis dros aris ori mowinaaRmdege,

romelTa miznebi diametralurad gansxvavdeba erTmaneTisagan, anu antagonisturiantagonisturiantagonisturiantagonisturiaaaa.... erTi

moTamaSis mogeba avtomaturad iwvevs meoris wagebas. magaliTad prefenansis TamaSis dros

ki SesaZlebelia ramdenime moTamaSe gaerTiandes danarCenebis winaaRmdeg, anu Seqmnan

korporacia da gauCndeT saerTo mizani (magaliTad, mizeris dros). garda amisa, Wadrakis

TamaSi mimdinareobs dafaze, da drois nebismier momentSi moTamaSeebs gaaCniaT sruli

informacia TamaSis mimdinareobis Sesaxeb, maSin, rodesac prefenansis TamaSis dros

moTamaSes ar gaaCnia sruli informacia TamaSis Sesaxeb, radganac man zustad ar icis ra

kartebi uWiravT danarCen moTamaSeebs da ra kartebia bazarSi.

7.2. 7.2. 7.2. 7.2. TamaSebi sruli informaciiT.TamaSebi sruli informaciiT.TamaSebi sruli informaciiT.TamaSebi sruli informaciiT. TamaSTa maTematikur TeoriaSi pirveli tipis TamaSebs

uwodeben ori mowinaaRmdegis TamaSs nulovani jamiT da sruli informaciiT. problemuri

garemos enaze es Seesabameba determinirebul, mTlianad dakvirvebad, mimdevrobiT garemos,

romelSic moqmedebs urTierTsawinaaRmdego miznebis mqone ori agenti. cxadia aseT

SemTxvevaSi Zebnis zemoTganxiluli evristikuli algoriTmebi ver mogvcemen sasurvel

Sedegs, vinaidan yvela es algoriTmi yovel nabijze aumjobesebs Tavis parametrebs da ise

eZebs amonaxsns, rac am SemTxvevaSi SeuZlebelia. saerTod TamaSebi imiTac gansxvavdeba

sxva amocanebisagan, rom Zalian Znelia maTi amoxsna. ase magaliTad Wadrakis TamaSSi

gantotvis koeficienti saSualod udris 35, xolo TamaSi xSirad grZelda 50 svlamde

TiToeuli moTamaSis mxridan, amitom Zebnis xe Seicavs daaxloebiT 15410 wveros (Tumca

TviT Zebnis grafi Seicavs “mxolod” 4010 gansxvavebul wveros. SedarebisaTvis Cvens

galaqtikaSi molekulebis raodenoba ar aRemateba 8510 -s).

TamaSTa TeoriaSi advilad mtkicdeba, rom aseTi TamaSebisaTvis arsebobs erTaderTi


strategia, romelic saukeTesoa moTamaSisaTvis da rogorc ar unda iTamaSos

mowinaaRmdegem es strategia yovelTvis miiyvans mas mocemul TamaSSi obieqturad arsebul

saukeTeso Sedegamde. imisaTvis, rom vnaxoT Tu rogor unda movZebnoT aseTi optimaluri

strategia, ganvixiloT iseTi martivi TamaSi, rogoricaa e.w. “krestiki – noliki”. am

TamaSSi gvaqvs dafa cxra ujriT (sami samze), romelSic mowinaaRmdegeni rigrigobiT

svaven “jvars” da “nols”. TamaSi mTavrdeba maSin, rodesac erTerTi mowinaaRmdege

horizontalurad, vertikalurad an diagonalze dasvavs sam “jvars” an “nols”, an rodesac

Seivseba yvela ujra. yvela SesaZlo strategiebis raodenoba am TamaSSi tolia

381024!9123456789 ==×××××××× , magram imis gaviTvaliswinebT, rom es TamaSi

simetriulia diagonalis mimarT, maSin strategiebis raodenoba SegviZlia SevamciroT

720!6 = -mde.

7.3.7.3.7.3.7.3. minimaqsisis procedura.minimaqsisis procedura.minimaqsisis procedura.minimaqsisis procedura. rogor SeiZleba movZebnoT am TamaSSi is erTaderTi

strategia, romlis arsebobasac amtkicebs TamaSTa Teoria? amisaTvis unda avagoT TamaSis

sruli xe, anu minimum is 720 strategia, romelic gaaCnia am elementarul TamaSs. mas

Semdeg, rac avagebT TamaSis srul xes, yvela damamTavrebeli wvero SegviZlia SevafasoT

TamaSis wesebidan gamomdinare. amis Semdeg viwyebT saukeTeso svlebis mimdevrobis, anu

strategiis amorCevas. amisaTvis viqceviT Semdegnairad: davuSvaT DdamamTavrebel

wveroebSi gadavyevarT mowinaaRmdegis svlebs, cxadia, rom mowinaaRmdege ecdeba miaRwios

warmatebas, rac niSnavs Cvens damarcxebas, amitom yvela SesaZlo poziciebidan, romlebSic

gadavyavarT mowinaaRmdeges, Cven unda amovarCioT poziciebi minimaluri SefasebebiT da es

Sefasebebi mivaweroT poziciebs, romlebic dganan erTi safexuriT zeviT. am poziciebSi

ukve gadavdivarT Cveni svlebis Sedegad, amitom yvela SesaZlo poziciebs Soris unda

amovarCioT poziciebi maqsimaluri SefasebebiT da es Sefasebebi gadmovitanoT erTi

safexuriT zeviT. ase unda gavagrZeloT, sanam ar mivaRwevT sawyis pozicias. am

proceduras ewodeba minimaqsis proceduraminimaqsis proceduraminimaqsis proceduraminimaqsis procedura da saSualebas gvaZlevs vipovoT is erTaderTi

strategia, romelic miuxedavaT imisa, Tu ras iTamaSebs mowinaaRmdege, yovelTvis

migviyvans sasurvel Sedegamde. ganvixiloT magaliTi. davuSvaT, mocemuli gvaqvs TamaSis

xe (ix. sur. # 7.1), romlis damaTavrebel poziciebSi TamaSis wesebis Tanaxmad gvaqvs

TamaSis Sedegebi, anu damamTavrebeli poziciebis Sefasebebi. Sefasebebi aRebulia 1S

sur. # 7.1. TamaSis xe damamTavrebeli wveroebiT

3

-2 2 3

-2 5 10 11 2 2 3 4 min

max

leqcia #leqcia #leqcia #leqcia #7777. . . . Zebna winaaRmdegobis SemTxvevaSiZebna winaaRmdegobis SemTxvevaSiZebna winaaRmdegobis SemTxvevaSiZebna winaaRmdegobis SemTxvevaSi 63

moTamaSisaTvis da saukeTeso strategiis amorCevac xdeba misTvis. radganac damamTavrebel

poziciebSi gadavdivarT mowinaaRmdegis svlis Sedegad, SesaZlo poziciebidan unda

amovarCioT minimaluri Sefasebebi. gveqneba Sefasebebi 3;2;2− . es Sefasebebi unda

mivaweroT erTi safexuriT zemoT mdgom poziciebs. am poziciebSi ukve gadavdivarT 1S

moTamaSis svlis Sedegad, amitom unda amovirCioT maT Soris maqsimaluri Sefaseba, rac

mogvcems saukeTeso strategias mocemuli xisTvis. unda avRniSnos, rom es strategia

saSualebas gvaZlevs, yovelTvis miviRoT is garantirebuli mogeba, romelic

gamomdinareobs TamaSis pirobebidan, imis gaTvaliswinebiT, rom zustad aseve TamaSobs

mowinaaRmdege, magram Tu mowinaaRmdegisaTvis ucnobia misi optimaluri strategia, Cven

SeiZleba miviRoT ufro meti mogebac (mocemul magaliTSi SeiZleba samis magivrad

movigoT oTxi, Tu mowinaaRmdege iTamaSebs arasworad).

7.4.7.4.7.4.7.4. Semoklebuli minimaqsis procedura. Semoklebuli minimaqsis procedura. Semoklebuli minimaqsis procedura. Semoklebuli minimaqsis procedura. aSkaraa, rom TamaSis optimaluri strategiis

moZebnis aseTi algoriTmi SeuZlebelia gamoviyenoT met-naklebad saintereso

TamaSebisaTvis, radganac praqtikulad SeuZlebelia avagoT aseTi TamaSebis sruli xe. Tu

Cven uars vityviT garantirebulad optimaluri strategiis moZebnaze, igive procedura

SesaZlebelia gamoviyenoT maSinac, rodesac avagebT TamaSis ara srul xes, aramed mis

fragments, davuSvaT sawyisi poziciidan raime mocemul d siRremze. ase iqceva albaT

adamianic, rodesac is TamaSobs magaliTad Wadraks, SaSs an raime sxva TamaSs. am

algoriTms ewodeba Semoklebuli minimaqsis procedura.Semoklebuli minimaqsis procedura.Semoklebuli minimaqsis procedura.Semoklebuli minimaqsis procedura.

aseTi midgomis dros warmoiSveba ori problema. pirveli, ra doneze unda SevwyvitoT

axali poziciebis ageba, anu ra doneze unda gadavWraT xe. ra Tqma unda am SemTxvevaSi

unda gaTvaliswinebuli iqnas kompiuteris simZlavreebi da TamaSis xis datotvis

koeficienti, magram marto es ar aris sakmarisi. warmovidginoT, rom Wadrakis

TamaSisaTvis SemoviReT raime d done, romelzedac vWriT xes. am doneze erT erT

poziciaSi iwyeba lazierebis gacvlis kombinacia, mowinaaRmdegem ukve aiyvana Cveni

lazieri da Semdeg svlaze igives gavakeTebT Cvenc. magram es Semdegi pozicia ukve aRar

Sedis Semoklebuli minimaqsis proceduris im poziciaTa simravleSi, romelSic is eZebs

saukeTeso svlas. TavisTavad cxadia, rom situacia dawunebuli iqneba, maSinac ki, rodesac

am gzas mivyavarT saboloo gamarjvebisaken. aseTi SemTxvevebis Tavidan asacileblad

SemoRebulia e.w. mkvdari poziciismkvdari poziciismkvdari poziciismkvdari poziciis cneba. pozicias ewodeba mkvdari, Tu misi Sefaseba

radikalurad ar gansxvavdeba misi Svilobili poziciebis Sefasebebisagan. mkvdari

poziciis cneba saSualebas gvaZlevs gadavWraT xe sxvadasxva doneze da Tavidan aviciloT

Secdomebi optimaluri gzis Zebnis dros.

meore problema exeba poziciebis Sefasebas. damamTavrebel poziciebSi Sefaseba

advili gasakeTebelia, radganac is gamomdinareobs TamaSis wesebidan, magram

daumTavrebeli TamaSis dros Sefasebebis gasakeTeblad Cven kvlav unda gamoviyenoT

evristikuli Semfasebeli funqcia, romelic aigeba Cveni an specialistebis mosazrebebidan

gamomdinare da romelic nebismier pozicias Seusabamebs raime ricxvs. rogorc wesi aseT

Semfasebel funqcias aqvs polinomis saxe:


=)(nf ∑=

m

iii xa

1

sadac n aris pozicia, ix -uri aris parametri, romliTac xdeba am poziciis Sefaseba,

xolo ia - ki am parametris xvedriTi wona Semfasebel funqciaSi. m aris parametrebis

raodenoba, romlebic monawileoben poziciis SefasebaSi. unda aRiniSnos, rom aseTi

funqciis Sedgena arc ise martivia, radganac parametrebi, romlebiTac fasdeba

mdgomareoba, rogorc wesi arian xarisxovani saxis da maTTvis ricxviTi mniSvnelobebis

Sefardeba sakmaod rTuli procesia. aseve rTulia woniTi koeficientebis SerCeva, xSirad

es dakavSirebulia xangrZliv manqanur eqsperimentebTan.

mas Semdeg, rac Cven gveqneba Semfasebeli funqcia, ukve SesaZlebeli iqneba minimaqsis

proceduris gamoyeneba gadaWril, anu qvexeze. ganvixiloT aseTi funqciis Sedgenisa da

gamoyenebis magaliTi kargad cnobili “krestiki-nolikis” TamaSisaTvis. davuSvaT, 1S iyos

moTamaSe, romelic svavs “× ”-ebs, xolo 2S - moTamaSe, romelic svavs “0”-ebs. Cven

funqcias vadgenT 1S moTamaSisaTvis. SemovitanoT )(nf Semfasebeli funqcia im

poziciebisaTvis, romlebic ar arian damamTavrebeli poziciebi Semdegi saxiT:

)()()( 21 nfnfnf −= , sadac )(1 nf aris im sruli striqonebis, svetebis da diagonalebis

raodenoba, romlebic Riaa 1S moTamaSisaTvis, xolo )(2 nf ki – im sruli striqonebis,

svetebisa da diagonalebis raodenoba, romlebic Riaa 2S moTamaSisaTvis. Tu n aris

damamTavrebeli pozicia, romelSic igebs 1S moTamaSe, maSin ∞=)(nf , xolo Tu n aris

damamTavrebeli pozicia, romelSic igebs 2S moTamaSe – −∞=)(nf . magaliTad, davuSvaT,

gvaqvs pozicia

×

× 0

maSin 1S moTamaSisaTvis Riaa pirveli da meore striqonebi, pirveli da mesame svetebi da

orive diagonali, 2S moTamaSisaTvis Riaa mesame striqoni, meore sveti da erTi

diagonali, amitom .336)( =−=nf

ganvixiloT, rogor SeiZleba Semoklebuli minimaqsis algoriTmis gamoyeneba am

TamaSisaTvis. davuSvaT TamaSs iwyebs 1S moTamaSe da ganixilavs TamaSs samis tol

siRrmeze. Tu gaviTvaliswinebT simetrias, romelic axasiaTebs am TamaSs, maSin arsebobs

xuTi gansxvavebuli svla, romelic 1S moTamaSes SeuZlia iTamaSos sawyis poziciaSi.

Sesabamisad miiReba xuTi gansxvavebuli pozicia 1P , 2P , 3P , 4P da 5P .

ganvixiloT ra sapasuxo svlebis gakeTeba SeuZlia mowinaaRmdeges TiToeul svlaze da

SevafasoT miRebuli poziciebi Semfasebeli funqciiT.


1P 2P 3P 4P 5P

1P =-1

×

× 0 × 0 × × ×

0 0

0

1)( 1 =nf 0)( 2 =nf 1)( 3 −=nf 1)( 4 =nf 0)( 5 =nf

2P = -2

1)( 1 −=nf 1)( 2 −=nf 2)( 3 −=nf 0)( 4 =nf 0)( 5 =nf

3P =-1

0)( 1 =nf 1)( 2 =nf 1)( 3 −=nf 0)( 4 =nf 0)( 5 =nf

× × ×

× ×

×

0 × × 0 × × × 0 0 0

×

0 × 0 × × × × 0 0

0


4P =2

×

1)( 1 =nf 2)( 2 =nf 2)( 3 =nf 2)( 4 =nf 1)( 5 =nf

5P =-2

1)( 1 −=nf 0)( 2 =nf 1)( 3 −=nf 2)( 4 −=nf 1)( 5 −=nf

e.i. 1P svlis TamaSis SemTxvevaSi 1S moTamaSis mogeba iqneba -1-is toli. gamovTvaloT

analogiurad danarCeni oTxi SemTxvevac.

amis Semdeg Semoklebuli minimaqsis proceduris proceduris gamoyenebiT SesaZlebeli

iqneba moiZebnos mocemuli Semfasebeli funqciisaTvis yvelaze optimaluri strategia (ix.

sur. # 7.2)

P

11 −=P 22 −=P 13 −=P 24 =P 25 −=P

sur. # 7.2. Semoklebuli minimaqsis procedura “krestiki – nolikis” TamaSisaTvis.

aRvniSnoT, rom Semoklebuli minimaqsis procedura, gansxvavebiT minimaqsis

procedurisagan, ukve aRar iqneba optimaluri da SeiZleba zogierT SemTxvevaSi srulic.

0 0 0

× × × × 0 × 0

×

× × ×

× ×

0 0 0

× × × 0 × × 0


droiTi da sivrculi parametrebi rogorc minimaqsis proceduris, aseve Semoklebuli

minimaqsis procedurisa, Sefasdeba ),( mbO sadac b aris datotvis koeficienti, xolo m

- ki xis siRrme.

7.5.7.5.7.5.7.5. alfa alfa alfa alfa –––– beta beta beta beta procedura. procedura. procedura. procedura. aqamde ganxilul Zebnis yvela algoriTmSi, dawyebuli ganivi

gadarCevis algoriTmiT damTavrebuli amocanebiT SezRudvaTa dakmayofilebaze, amocanis

amoxsnis grafi (an xe) yovelTvis moicemoda aracxadi saxiT da evristikuli

programirebis ZiriTadi principis Tanaxmad, grafis (xis) agebis da Zebnis procesebi iyo

gaerTianebuli, rac warmoadgens evristikuli Zebnis mniSvnelovan upiratesobas grafze

Zebnis meTodebTan SedarebiT. rogorc vxedavT, Semoklebuli minimaqsis proceduraSi es

principi darRveulia.

Cven exla ganvixilavT proceduras, romelSic es principi kvlav aRdgenilia da

romelic saSualebas gvaZlevs gavxsnaT ufro naklebi wveroebi, vidre es xdeba

Semoklebuli minimaqsis algoriTmSi da movZebnoT zustad is amoxsna, romelsac

gvapovninebda es algoriTi erTi da igive Semfasebeli funqciis SemTxvevaSi. am

proceduras, romeli Zalian waagavs siRrmeSi gadarCevis algoriTms ewodeba alfa alfa alfa alfa –––– beta beta beta beta

proceduraproceduraproceduraprocedura. . . . Aam proceduris muSaobis principis gasagebad ganvixiloT magaliTi. davuSvaT,

gvaqvs pozicia (ix. sur. # 7.3.), romelSic svla unda gaakeTos 1S moTamaSem da is iwyebs

sur. # 7.3. alfa-beta proceduris muSaobis pirveli etapi

xis agebas, romelSic yovel wveros aqvs sami Svilobili wvero. 1S moTamaSe aagebs

sawyisi wveros pirvel Svilobil wveros, Semdeg mis Svilobil wveros da bolo doneze

samive Svilobil wveros. Seafasebs am wveroebs da radganac gadasvla xdeba misi svliT

maqsimalur Sefasebas amoitans ori doniT maRla. am Sefasebas ewodeba winaswari Sefaseba.

amis Semdeg is ganixilavs Semdeg tots (ix. sur. # 7.4.), Cayveba bolomde da miiRebs ra

Sefasebas, romelic metia winaswar Sefasebaze, aRar ganixilavs sxva wveroebs, radganac am

doneze aris mowinaaRmdegis svla da unda amorCeuli iyos svla minimaluri SefasebiT. es

iqneba beta mokveTa.

CamovayaliboT alfa _ beta procedura: im doneze, romlezedac 1S moTamaSe irCevs

6

6

5 4 6


maqsimums, xdeba alfa mokveTa, anu algoriTmi aRar gaxsnis wveros mTlianad, Tu misi

romelime Svilobili wveros Sefaseba naklebia vidre ukve gaxsnili wveros Sefaseba.

sur. # 7.4. alfa – beta proceduris mier moikveTa ori wvero

analogiurad, im doneze, romelzec 1S moTamaSe irCevs minimums, algoriTmi aRar gaxsnis

wveros mTlianad, Tu misi romelime Svilobili wveros Sefaseba metia vidre ukve

gaxsnili wveros Sefaseba. alfa – beta mokveTa SeiZleba gamoyenebuli iqnes nebismieri

siRrmis xeebisaTvis da Zalian xSirad is mokveTs mTel qvexeebs. proceduram saxeli miiRo

im ori parametris mixedviT, romlebic warmoadgenen zeda da qveda sazRvrebs:

αααα = = = = saukeTeso variantis Sefaseba, romelic mocemul momentamde iyo napovni 1S

moTamaSis mier im doneze, sadac is irCevs maqsimums;

ββββ = saukeTeso variantis Sefaseba, romelic mocemul momentamde iyo napovni 1S

moTamaSis mier im doneze, sadac is irCevs minimums.

sur. # 7.5. alfa – beta procedura. marTkuTxedebiT aRniSnulia

wveroebi, romlebSic gadavdivarT mowinaaRmdegis svliT.

6

6

5 4 6

7

7

A 3=f

B 3=f

F 2=f

C 3=f

D 12=f

E 8=f

G 2=f

I 4=f

K 6=f


alfa – beta proceduraSi arsebiTi mniSvneloba aqvs wveroebis gaxsnis mimdevrobas.

marTlac, ganvixiloT magaliTi (ix. sur. #7.5.). Tu viyenebT alfa – beta proceduras, maSin

algoriTmi aagebs B wveros, Semdeg mis Svilobil wveroebs C,D,E da amoarCevs maT Soris

minimalur Sefasebas, romelsac gadaitans rogorc B, aseve A wveroebSi. Aamis Semdeg is

aagebs F wveros, mis Svilobil G wveros, miiRebs mis Sefasebas, gadmoitans G wveroSi,

Seadarebs mas B wveros Sefasebas da radganac am doneze xdeba maqsimumis moZebna, aRar

gaxsnis I da K wveroebs. magram Tu F wveros Svilobili wveroebi ganlagdebodnen

Sebrunebuli mimdevrobiT, maSin algoriTms mouwevda yvela Svilobili wveros gaxsna da

misi efeqtianoba iqneboda iseTive, rogoric Semoklebuli minimaqsis proceduris. aqedan

gamomdinare, SegviZlia davaskvnaT, rom ukeTesia algoriTmma pirvel rigSi gamoikvlios is

wveroebi, romlebic albaT SeiZleba gaxdnen saukeTesoebi. cxadia, rom SeuZlebelia

wveroebis absoluturad mowesrigeba, magram raRac albaTobiT es mainc SesaZlebelia.

magaliTad, Wadrakis SemTxvevaSi SeiZleba gamoviyenoT martivi funqcia, jer ganvixiloT

svlebi, romlebic dakavSirebulia figurebis ayvanasTan, Semdeg muqarebTan, svlebi win da

ase Semdeg. aseT SemTxvevaSi algoriTmis sivrciTi (da Sesabamisad DdroiTi) sirTule

gaxdeba )( 2m

bO da ara )( mbO , rogorc es aris minimaqsis proceduris dros. es niSnavs,

rom datotvis koeficienti iqneba ara b , aramed b ....

rogorc viciT, Tu amocanis amoxsnis procesSi vRebulobT grafs da ara xes, es

gamoiwvevs sivrciTi da droiTi sirTuleebis eqsponencialur zrdas.BTamaSebSi svlebis

sxvadasxva mimdevrobebs xSirad mivyavarT erTsa da imave poziciaSi. Aam movlenas

uwodeben transpozicias.transpozicias.transpozicias.transpozicias. vinaidan SeuZlebelia Tavidan aviciloT es momenti, kargi iqneba,

Tu specialur cxrilSi SevinaxavT poziciis Sefasebas. AaseT cxrils uwodenen

transpozitranspozitranspozitranspoziciis cxrilsciis cxrilsciis cxrilsciis cxrils. . . . es cxrili Zalian waagavs sias “daxurulia”, romelic

gamoiyeneboda Zebnis algoriTmebSi da mas SeuZlia TiTqmis orjer gazardos alfa – beta

proceduris siRrme iseT TamaSSi, rogoricaa Wadraki.

7.6. TamaSebi arasruli informaciiT.7.6. TamaSebi arasruli informaciiT.7.6. TamaSebi arasruli informaciiT.7.6. TamaSebi arasruli informaciiT. realur cxovrebaSi xSirad xdeba araprognozirebadi

movlenebi, ris gamoc adamianebi aRmoCndebian xolme sxadasxva moulodnel situaciebSi. es

araprognozirebadoba bevr TamaSSi asaxulia masSi SemTxveviTobis elementis CarTvis

gziT. amitom aseTi TamaSebis ganxilva sasargebloa imis dasadgenad, Tu gadawyvetilebis

miRebis rogori meqanizmebi moqmedeben aseT SemTxvevebSi. Nnardis TamaSi warmoadgens

swored aseT TamaSs. Yyoveli svlis win moTamaSe agorebs kamaTels imis dasadgenad, Tu

ra svlebis gakeTeba SeuZlia mas mocemul poziciaSi.

sur. # 7.6. gamosaxula erTerTi SesaZlo pozicia. TeTri qvebi moZraoben saaTis isris

mimarTulebiT, xolo Savi qvebi saaTis isris sawinaaRmdego mimarTulebiT. davuSvaT, 1S

moTamaSes, romelic TamaSobs TeTri qvebiT, mouvida SaSi beSi (eqvsi da xuTi), maSin mas

SeuZlia gaakeTos Semdegi svlebi: (5-10;5-11), (5-10;10-16), (5-11;19-24), (5-11,11-16). miuxedavad imisa,

rom 1S moTamaSem icis Tavisi svlebi, mas ar SeuZlia aagos TamaSis xe, radganac misTvis

ucnobia, ras gaagorebs mowinaaRmdege da rogori iqneba misi dasaSveb svlaTa simravle.

amitom nardis TamaSis xe garda 1S da 2S moTamaSeebis wveroebisa, agreTve unda


Seicavdes kamaTlebiskamaTlebiskamaTlebiskamaTlebis gagorebis gagorebis gagorebis gagorebis wveroebsac wveroebsac wveroebsac wveroebsac. . . . yoveli gagorebis dros mosalodnelia 36

0 1 2 3 4 5 6 7 8 9 10 11 12

25 24 23 22 21 20 19 18 17 16 15 14 13

sur. # 7.6.. nardis TamaSSi Seqmnili erT erTi pozicia

kombinacia, sadac wyvilis mosvlis albaToba tolia 361 , xolo danarCeni kombinaciebis

ki 181 . TamaSis xes eqneba Semdegi saxe:

1S

gagoreba ……………..……………………

2S . . . . . .

(1,1) (1,2) (1,3) (6,6)

gagoreba ……… . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .

sur. # 7.7. nardis TamaSis xis struqtura

……..


ra Tqma unda am SemTxvevaSic moTamaSe cdilobs ipovos iseTi svla, romelic miiyvans

mas saukeTeso Sedegamde, magram aq ukve wveroebs aRar aqvT gansazRvruli mniSvnelobebi,

aq SeiZleba laparaki mxolod SesaZlo, mosalodnel mniSvnelobebzemosalodnel mniSvnelobebzemosalodnel mniSvnelobebzemosalodnel mniSvnelobebze, romelSic

mosalodneli Sedegi gamoiTvleba kamaTlis gagorebis yvela SesaZlo Sedegebis

gaTvaliswinebiT. amitom, am SemTxvevaSi Cven ukve saqme gvaqvs TamaSis mosalodnel mosalodnel mosalodnel mosalodnel

minimaqsur mniSvnelobaminimaqsur mniSvnelobaminimaqsur mniSvnelobaminimaqsur mniSvnelobasTansTansTansTan....

iseve, rogorc minimaqsis, an alfa – beta proceduris gamoyenebis dros, nardis

TamaSis SemTxvevaSic Cven unda SevwyvitoT xis ageba raRac momentSi da gamoviyenoT

Semfasebeli funqcia wveroebis Sesafaseblad. erTi SexedviT meti araferi ar icvleba,

garda imisa, rom aq veZebT mosalodnel minimaqsur mniSvnelobas, magram sinamdvileSi

wilisyris (kamaTlis gagorebis) kvanZebis arseboba mniSvnelovnad cvlis saukeTeso svlis

amorCevas. ganvixiloT magaliTi. davuSvaT, mocemuli gvaqvs erTi da igive qvexe, magram

Semfasebeli funqcia aris sxvadasxva (ix. sur. # 7.8).

1S A B A B (2,1) (1,3) GGGG gagoreba gagoreba gagoreba gagoreba (2,1) (1,3) 0,9 0,1 0,9 0,1 0,9 0,1 0,9 0,1

2 3 1 4 2S 20 30 1 400 20 20 30 30 1 1 400 400

2 2 3 3 1 1 4 4 a) b)

sur. # 7.8 a) albaT umjobesia strategia A

b) albaT umjobesia strategia B

Tu programaSi winaswar iqneboda cnobili, Tu ra Sedegi gveqneba yoveli wilisyris

Semdeg, maSin amonaxsnis Zebna iqneboda analogiuri wilisyris gareSe Zebnisa, romelsac

minimaqsis algoriTmi asrulebs )( mbO droSi. magram, radgan moslodneli

minimaqsuri mniSvnelobis algoriTmSi ganixileba yvela SesaZlo mimdevrobebi wilisyris

Sedegebisa, mis Sesrulebas sWirdeba )( mmnbO dro, sadac n aris wilisyris sxvadasxva

variantebis raodenoba. es gacilebiT arTulebs Zebnas da gvaiZulebs maqsimalurad

SevzRudoT xis siRrme, rac uaryofiTad moqmedebs met- naklebad kargi strategiis

amorCevaze.



1. rogor garemoSi uxdeba moqmedeba agents TamaSebis dros

2. rogor TamaSebs ewodebaT TamaSebi sruli informaciiT?

3. ratom ver gamoviyenebT Zebnis informirebul algoriTmebs TamaSebSi?

4. aRwereT minimaqsis procedura. ra arsebiTi gansxvavebaa minimaqsisa da alfa-beta

procedurebs Soris?

5. CamoayalibeT romel garemoSi uxdeba moqmedeba nardis moTamaSe agents.

6. romeli TamaSi ufro Znelia alfa-beta procedurisaTvis, Wadrakis Tu nardis?

adamianisaTvis?

savarjisavarjisavarjisavarjiSoebi:Soebi:Soebi:Soebi:

1. dawereT programa alfa-beta procedurisaTvis.

2. “krestiki-nolikisaTvis” Semfasebel funqcias aqvs Semdegi saxe: 321 255)( xxxnf ++= ,

sadac 1x aris sxvaoba Tavisufal striqonebs, svetebsa da diagonalebs Soris

pirveli da meore moTamaSeebisaTvis (is rac iyo aRwerili leqciaSi), 2x - aseTive

sxvaoba rodesac striqonSi, svetSi an diagonalze dgas erTi fiSka (pirveli

moTamaSisTvis “krestiki”, meore moTamaSisTvis “noliki” da 3x - aseTive sxvaoba,

rodesac dakavebulia ori ujra. SeadareT es Semfasebeli funqcia leqciaSi moyvanil

Semfasebel funqcias da axseniT romeli Semfasebeli funqciaa ukeTesi da ratom?

3. arsebobs Zveli induri TamaSi kalaxi, romelic warmoadgens dafas ToTxmeti

RrmuliT, TormetSi yria eqvs-eqvsi qva (ix. sur. # 7.9) eqvsi ujra da erTi kalaxi

1S

2S

sur. # 7.9. kalaxis saTamaSo dafa.

6 6 6 6 6 6

1K 2K

6 6 6 6 6 6


(carieli ujra) ekuTvnis erT moTamaSes, eqvsi ujra da meore kalaxi – meore

moTamaSes. TamaSis mizania sakuTar kalaxSi moagrovos moTamaSem mowinaaRmdegeze

meti qva.

TamaSis wesebi aseTia: moTamaSe iRebs Tavisi erTerTi ujridan yvela qvas da

saaTis isris sawinaaRmdego mimarTulebiT TiTo TiTos awyobs rogorc Tavis, aseve

mowinaaRmdegis ujrebSi da Tavis kalaxSi, gamotovebs mxolod mowinaaRmdegis

kalaxas. Tu bolo qva Cavardeba Tavis kalaxSi, moTamaSes eZleva kidev erTi svlis

gakeTebis ufleba, Tu ara – svla gadaecema mowinaaRmdeges. Tu bolo qva Cavardeba

moTamaSis cariel ujraSi, maSin es qva da yvela qva, romelic yria am ujris

mopirdapired mdebare mowinaaRmdegis ujraSi, gaditaneba am moTamaSis kalaxSi da

svla gadaecema mowinaaRmdegs. yvela danarCen SemTxvevaSi moTamaSeebi svlebs

akeTeben rigrigobiT. SeadgineT am TamaSisaTvis Semfasebeli funqcia. dawereT

programa, romelic iTamaSebs am TamaSs.

leqcia #8 leqcia #8 leqcia #8 leqcia #8

codniscodniscodniscodnis kompiuterul sistemebSi kompiuterul sistemebSi kompiuterul sistemebSi kompiuterul sistemebSi warmodgeniswarmodgeniswarmodgeniswarmodgenis problemaproblemaproblemaproblema

8.1.8.1.8.1.8.1. codnis warmodgenis aucilebloba.codnis warmodgenis aucilebloba.codnis warmodgenis aucilebloba.codnis warmodgenis aucilebloba. Cven ganvixileT mizanze dafuZnebuli agentebi,

romlebic problemaTa gadasawyvetad iyenebdnen Zebnis algoriTmebs. rogorc vnaxeT, aseTi

agentebi ar iZlevian saSualebas gadavWraT yvela problema, radganac es algoriTmebi

arian eqsponencialuri da amocanis zomebis zrdasTan erTad maTi efeqtianoba Zalian

swrafad mcirdeboda. Cven exla daviwyebT iseTi agentebis Seswavlas, romlebic moqmedeben

codnis safuZvelze (SemoklebiT codnaze dafuZnebuli agenticodnaze dafuZnebuli agenticodnaze dafuZnebuli agenticodnaze dafuZnebuli agenti). codnis warmodgena da

msjelobis procesebi warmoadgenen xelovnuri inteleqtis centralur sakiTxebs.

TavisTavad cxadia, rom adamianebi sicocxlis ganmavlobaSi swavloben, agroveben codnas

da es codna uadvilebT maT miaRwion dasmuli amocanebis gadawyvetas. arsebiTia agreTve,

rom adamianebs gaaCniaT gansjis unari. codna da gansjis unari aseve mniSvnelovania

xelovnuri agentebisaTvis, radganac uzrunvelyofs warmatebuli qcevis formirebas,

romlis miRwevac sxva gziT albaT SeuZlebeli iqneboda. ase magaliTad, Tu amocanaTa

amomxsnel agents ecodineba Tavisi qmedebebis Sedegebi, mas SeeZleba warmatebulad

imoqmedis rTuli garemos pirobebSic da ar eZebos gza baTumidan Tbilisamde brmad,

rogorc amas akeTebda mizanze damyarebuli agenti. magram amocanaTa amomxsneli agentebis

codna aris Zalian specifikuri da mouqneli. Wadrakis moTamaSe programas SeuZlia

gaTvalos mefis dasaSvebi svlebi (im feris, romeli feriTac is TamaSobs), magram mas ar

gaaCnia mravali sxva sasargeblo codna, magaliTad, rom arc erT figuras ar SeuZlia

erTdroulad idges or ujraze. codnaze damyarebul agentebs SeuZliaT Zalian zogad

formaSi gamoxatuli codnis gamoyeneba, am codnis kombinirebacodnis kombinirebacodnis kombinirebacodnis kombinireba da rekombinireba

sxvadasxva garemo pirobebis Sesabamisad.

codna da gansja TamaSoben gadamwyvet rols maSinac, rodesac agents uxdeba

moqmedeba nawilobriv dakvirvebad problemur garemoSi. codnaze damyarebul agents unari

aqvs SeuTavsos erTmaneTs codna da mocemul momentSi miRebuli aRqma, raTa gamoavlinos

mimdinare mdgomareobis dafaruli aspeqtebi manamade, sanam is daiwyebs moqmedebas. Zalian

mniSvnelovania isic, rom aseTi agentebi arian Zalian moqnilebi. maT SeuZliaT miiRon da

Seasrulon axali amocanebi, romlebic Camoyalibebulia cxadad dasmuli miznis saxiT,

garda amisa Tavisi codnis ganaxlebis gziT maT SeuZliaT Seeguon im garemos cvlilebas,

romelSic isini moqmedeben .

codnaze damyarebuli nebismieri agentis centralur komponents cxadia warmoadgens

misi codnis baza.codnis baza.codnis baza.codnis baza.Aswored aseTi bazis organizeba kompiuterul sistemaSi warmoadgens

xelovnuri inteleqtis erTerT ZiriTad problemas.

iseve, rogorc problemaTa gadawyvetis dros Cven gvainteresebda Tu rogor wyvetda

aseT problemebs adamiani, aqac ra Tqma unda sainteresoa, Tu rogoraa organizebuli

codna adamianSi.

8.2.8.2.8.2.8.2. semantikuri qselebi.semantikuri qselebi.semantikuri qselebi.semantikuri qselebi. Afsiqoligiidan cnobili asocionisturi Teoriis Tanaxmad,

obieqtis mniSvneloba ganisazRvreba sxva obieqtebTan asociaciis terminebSi. am Teoriis

Tanaxmad, obieqtebis aRqma xdeba cnebebis saSualebiT. cnebebi warmoadgenen garemos

leqcia #leqcia #leqcia #leqcia #8888. codnis warmodgenis problema kompiuterul sistemebSi. codnis warmodgenis problema kompiuterul sistemebSi. codnis warmodgenis problema kompiuterul sistemebSi. codnis warmodgenis problema kompiuterul sistemebSi 75

Sesaxeb Cveni codnis mniSvnelovan nawils da dakavSirebulebi arian sxva cnebebTan

asociaciebis saSualebiT. es kavSirebi warmoadgenen obieqtis Tvisebebs da qcevas.

magaliTad, cdebis safuZvelze Cven vaxdenT cneba “Tovlis” asocirebas sxva cnebebTan,

davuSaT iseTebTan, rogorebica: “sicive”, TeTri”, “Tovlis adamiani”, “yinuli” da ase

Semdeg. Cveni codna Tovlis Sesaxeb da gamonaTqvamis “Tovli TeTria” WeSmariteba iqmneba

am asociaciis qselidan.

SeuZliaT sunTqvasunTqvasunTqvasunTqva aqvT

cxovelebi cxovelebi cxovelebi cxovelebi tyavityavityavityavi SeuZliaT

moZraoba moZraoba moZraoba moZraoba

TevzebiTevzebiTevzebiTevzebi

SeuZliaT frenafrenafrenafrena aqvT Citebi Citebi Citebi Citebi frTebi frTebi frTebi frTebi

aqvT

b b b bumbuliumbuliumbuliumbuli

Kiadoni Kiadoni Kiadoni Kiadoni strausistrausistrausistrausi

SeuZlia aris aris ar SeuZlia

simRera simRera simRera simRera yviTeli yviTeli yviTeli yviTeli maRali frena maRali frena maRali frena maRali frena

sur. #8.1. kolinsisa da kvilinis mier Sedgenili semantikuri qseli

aseve fsiqologiidanaa cnobili, rom es asociacebi qmnian ierarqiul struqturebsierarqiul struqturebsierarqiul struqturebsierarqiul struqturebs.

1969 wels kolinsma da kvilianma Caatares cdebi, romlis arsi mdgomareobda imaSi, rom

isini cdis pirebs aZlevdnen iseT SekiTxvebs frinvelebis Tvisebebis Sesaxeb, rogoricaa

magaliTad “iadoni es Citia?” “SeuZlia iadons frena?” “strausi maRalia?” da sxva.

zomavdnen ra dros, romelic sWirdebodaT cdis pirebs pasuxebis mosafiqreblad. maT

aRmoaCines, rom im kiTxvebze pasuxis gasacemad, romlebic exeba mocemuli obieqtis

konkretul Tvisebebs, cdis pirebs dasWirdaT ufro cota dro, vidre im kiTxvebze,

romlebic exeba ufro zogad Tvisebebs, damaxasiaTebels ara marto am konkretuli

obieqtisaTvis. magaliTad, kiTxvas “iadoni yviTelia?” sWirdeba gacilebiT cota dro,

vidre kiTxvas “SeuZlia iadons frena?”, maSin, rodesac analogiuri SekiTxva “SeuZlia Tu


ara frena strauss?” moiTxovs gacilebT cota dros. cdis avtorebi amas xsnian imiT, rom

adamianebi informacias imaxsovreben maqsimalurad abstraqtul doneze. imis magivrad, rom

daimaxsovron iadons SeuZlia Tu ara frena, isini imaxsovreben, rom iadoni aris Citi,

xolo Citebs (ZiriTadad) SeuZliaT frena. am cdis safuZvelze maT SemogvTavazes

semantikuri qseli, romelic organizebulia ierarqiuli principiT, da aRwers adamianis

Tavis tvinSi codnis Senaxvis SesaZlo sqemas. D

rogorc am qselidan Cans, imisaTvis, rom cdis pirma upasuxos SekiTxvas, SeuZlia Tu

ara iadons sunTqva, adaminama Tavis semantikur qselSi unda gairos gza Y”iadoni” →

“Citi” → “cxoveli” ← “sunTqavs”. semantikuri qselebis es principi formalizebuli iqna

memkvidreobiT struqturebSimemkvidreobiT struqturebSimemkvidreobiT struqturebSimemkvidreobiT struqturebSi. . . . es struqturebi saSualebas gvaZleven davimaxsovroT

informacia abstraqciis yvelaze maRal doneze, rac amcirebs codnis bazis zomebs da

saSualebas gvaZlevs Tavidan aviciloT winaaRmdegobebi. magaliTad, Tu Cven vagebT

codnis bazas Citebis Sesaxeb, maSin SegviZlia ganvsazRvroT yvela CitisaTvis

damaxasiaTebeli iseTi zogadi Tvisebebi, rogorica “SeuZliaT frena”, “aqvT frTebi” da a.

S. davimaxsovroT es informacia Citebis abstraqciis doneze da mivceT SesaZlebloba

Citebis konkretul warmomadgenels memkvidreobiT miiRos es Tvisebebi. es ra Tqma unda

amcirebs codnis bazis zomas, imitom rom am Tvisebebs ganvsazRvraT mxolod erTxel da

ara yoveli konkretuli warmomadgenelisaTvis cal - calke. es mosaxerxebelia agreTve

codnis bazaSi cvlilebebis Setanis drosac. Tu Cven bazas vumatebT Citebis romelime

konkretul warmomadgenels an mTlianad qveklass, klasisaTvis aRwerili Tvisebebi

avtomaturad gavrceldeba am qveklaszec.M

sur. 8.2. cnebebis tirilitirilitirilitirili da komfortis komfortis komfortis komfortis TanakveTis grafi.

semantikuri qselebis aRweris yvelaze moxerxebuli formaa grafebi, radganac

SesaZlebelia cnebebs Soris arsebuli damokidebulebebis aRwera kvanZebisa da rkalebis

tirili2 tirili

komforti 3

komforti

da aqvs akeTebs xmebs sevda

tirili 2

iZleva da akeTebs 2 naklebi sevda

komforti 3

sevda


saSualebiT. kvilianis mier Sedgenil codnis bazaSi, romelic Seiqmna samociani

wlebis bolos da romelic organizebuli iyo leqsikonis principis Sesabamisad, grafis

sur. # 8.3 sami sibrtye, romlebic warmoadgenen sityva ““““plant”- is sam ganmartebas.

Plant: 1. cocxali struqtura, romelic araa cxoveli, xSirad aqvs foTlebi,

Rebulobs sakvebs haeridan, wylidan da miwidan.

2. mowyobiloba, romelic gamoiyeneba raime sawarmoo procesSi.

3. movaTavsoT (Tesli, mcenare da a.S.) miwaSi gasazrdelad.

TiToeuli kvanZi Seesabameboda sityvebiT aRweril cnebas, xolo rkalebis saSualebiT

aRiwereboda asociaciuri kavSirebi sxva cnebebTan. codnis baza iyo organizebuli

sibrtyeebiT, sadac TiToeuli sibrtye warmoadgenda grafs, romelic axasiaTebda erT

cnebas. am qselidan erTerTi cnebis magaliTi moyvanilia sur. # 8.2.

programa iyenebda am bazas mimarTebis mosaZebnad sityvaTa wyvils Soris. amisaTvis

is axorcielebda Zebnas siganeSi, sanam ar ipovnida saerTo cnebas, anu TanakveTis kvanZs.

gzebi saerTo kvanZamde warmoadgendnen mimarTebebs cnebebs Soris. magaliTad, sur. #8.2.

or or Plant 2 Plant 3 = A structure and live animal with 3 get 3 =A from 3 food or air water earth

Plant 1

put S person N9 =8D or seed parth object earth for 4 grow

Plant 3

= A apparatus use people =A for 5 process in industru

Plant 2


naCvenebia TanakveTis kvanZi, or cnebas, tiriltiriltiriltirilsasasasa da komfortskomfortskomfortskomforts Soris. gamoiyena ra am

gzebis TanakveTa, programam daaskvna, rom:

"tirili sxva danarCenTan erTad dakavSirebulia samwuxaro xmebis warmoqmnasTan.

mosvenebas SeuZlia Seamciros mwuxareba."

avtori Tvlida, rom aseTi midgoma semantikisadmi uzrunvelyofda sistemis mier

bunebrivi enis gagebis Semdeg SesaZleblobebs:

1. inglisuri teqstis azris gageba TanakveTis kvanZebis agebis gziT.

2. sityvis mniSvnelobis amorCeva, winadadebis sxva sityvebTan gadakveTamde umoklesi

gzis amorCevis safuZvelze. magaliTad inglisur winadadebaSi “Tom went home to water

his new plant” ( “tomi movida saxlSi Tavisi axali nargavebis mosarwyavad”), sistemas

SeuZlia amoirCios sityva “plant”- is mniSvneloba cnebebis “water” da “plant”

TanakveTaze dayrdnobiT.

3. SekiTxvaSi mocemuli cnebebis asociaciebze dayrdnobiT, sistema SesZlebs

moqnilad upasuxos SekiTxvebs.

miuxedavad imisa, rom am da sxva misma msgavsma sistemebma naTlad aCvenes grafebis

gamoyenebis efeqturoba asociaciuri azris modelirebis dros, isini SezRudulni iyvnen

metismetad zogadi formalizmis gamo. codnis struqturireba rogorc wesi xdeboda

specifikuri damokidebulebebis terminebSi, iseTi, rogorica klasi – qveklasi, agenti –

zmna – obieqti.

8.38.38.38.3 freimebi.freimebi.freimebi.freimebi. gansxvavebuli idea codnis kompiuterul sistemaSi warmodgenaze wamoayena

cnobilma amerikelma mecnierma m. minskma. man SemogvTavaza freimebis Teoria, romlis

ZiriTadi mamoZravebli idea mdgomareobs imaSi, rom rodesac adamiani cdilobs Seicnos

misTvis axali situacia, an axleburad Sexedos misTvis ukve cnobil sagnebs, is Tavisi

mexsierebidan amoarCevs monacemTa raRac struqturasmonacemTa raRac struqturasmonacemTa raRac struqturasmonacemTa raRac struqturas (saxes, romelsac avtori uwodebs

freims), im mizniT, rom masSi garkveuli detalebis cvlilebis gziT gaxados es

struqtura gamosadegi ufro farTo klasis procesebisTvis.

freimifreimifreimifreimi aris stereotipuli situaciis warmosadgeni monacemTa struqtura. TiToeul

freimTan asocirebulia sxvadasxva saxis informacia. misi erTi nawili miuTiTebs, Tu

rogor unda gamoviyenoT freimi, meore – Tu ra SeiZleba mohyves mis Sesrulebas da mesame

– ra unda movimoqmedoT, Tu es Cveni molodini ar gamarTlda. freimi SeiZleba

warmovidginoT rogorc qseli, romelic Sedgeba kvanZebisa da kavSirebisagan am kvanZebs

Soris. freimis "zeda doneebi" mkacrad gansazRvrulia, radganac Seesabamebian cnebebs,

romlebic yovelTvis sworia mocemuli SesaZlo situaciebisaTvis. SedarebiT ufro dabal

doneebze aris mravali gansakuTrebuli wvero – terminalebi anu ujredebi, romlebic

unda Seivsos damaxasiaTebeli magaliTebiT, an monacemebiT.

TiToeuli terminalis mier SeiZleba wamoyenebuli iqnas pirobebi, romlebsac unda

akmayofilebdnen misi davalebebi. martivi pirobebi, magaliTad, moTxovna, rom terminalis

davaleba iyos romelime subieqti, an garkveuli zomis sagani, ganisazRvreba markerebis

saSualebiT. ufro rTuli pirobebiT moicema mimarTebebi cnebebs Soris, romlebic

moTavsebulni arian sxvadasxva terminalur wveroebSi. semantkurad axlo freimebis jgufi


SeiZleba gavaerTianoT freimTa sistemaSifreimTa sistemaSifreimTa sistemaSifreimTa sistemaSi.

ganvixiloT umartivesi magaliTi. davuSvaT, Cven gvinda SevadginoT freimi, romlis

saSualebiTac SevZlebT codnis bazaSi aRvweroT kubi ise, rom ra poziciidanac ar unda

uyurebdes am kubs xelovnuri inteleqtualuri sistema, man SesZlos misi

sur. # 8.4. kubis gamosaxuleba da misis freimi

sur. # 8.5. kubis gamosaxuleba da freimi mobrunebis Semdeg.

punqtiriT naCvenebia uCinari waxnagebis terminalebi

amocnoba. sur. #8.4. mocemulia kubis gamosaxuleba raime konkretuli wertilidan da

Sesabamisi freimis struqturafreimis struqturafreimis struqturafreimis struqtura. davuSvaT, exla damkvirvebeli iwyebs moZraobas marjvniv,

maSin A waxnagi gaqreba da mis adgilze gamoCndeba waxnagi B, xolo B waxnagis adgilze C

waxnagi. Tu exla SevecdebiT xelaxla aRvweroT kubi, unda daviviwyoT yvelaferi, rac

vicodiT da xelaxla aRvweroT waxnagi B da E aRvweroT waxnagi C. magram, Tu Cven viciT,

rom sagani ar Secvlila, maSin SegviZlia SevinaxoT informacia B da E waxnagebis Sesaxeb

E

A B

zeda donis kvanZi “kubi”

terminalebi

E

B C

kubi kubi

A B C


aRvweroT mxolod C waxnagi. amasTan, rom ar davkargoT informacia A waxnagis Sesaxeb,

Cven SegviZlia davukavSiroT is uxilavi waxnagis terminals. maSin Cvens freims eqneba

Semdegi saxe (ix. sur. # 8.5.). SesaZlebelia gavagrZeloT aseTi rTuli struqturebis

ageba, romelsac ewodeba freimTa sistemafreimTa sistemafreimTa sistemafreimTa sistema, rodesac dakvirvebis wertilebi gvaqvs ufro

meti (sur. # 8.6. mocemulia dakvirvebis sami wertili). Sesabamisi freimebis struqtura

naCvenebia sur. # 8.7.

sur. # 8.6. kubze dakvirveba sami sxvdasxva wertilidan.

.

sur. # 8.7. freimTa sistema dakvirvebis sami wertilisaTvis.

gamartivebis mizniT suraTze naCvenebi araa E

waxnagi, romelic Cans yvela wertilidan.

mniSvnelovania mivaqcioT yuradReba situaciis freimTa sistemiT warmodgenis mTavar

Tvisebas, romelic mdgomareobs imaSi, rom sxvadasxva freimebi, romlebix Sedian erTsa da

imave sistemaSi, gamoiyeneben erTsa da imave terminalebs, romlebic Seesabamebian erTsa da

imave fizikur maxasiaTebels, miRebuls dakvirvebis sxvadasxva wertilebidan. es gvaZlevs

saSualebas mexsierebis erT wertilSi winaswar movagrovoT informacia obieqtebis ukve

cnobili Tvisebebis Sesaxeb dakvirvebis wertilidan damoukideblad. es gansakuTrebiT

momgebiania rTuli obieqtebis SemTxvevaSi, radganac maT rogorc wesi gaaCniaT bevri

E

A B

E

B

E

B C

kubi kubi kubi

D A B C


aseTi Tviseba. amis Sedegad SesaZlebelia mexsierebis ekonomia da mcirdeba agreTve aRqmis

procesi, radganac mexsierebaSi ukve gvaqvs saWiro informacia da dro ixarjeba mxolod

mis "amoRebaze" mexsierebidan.

avtoris azriT mexsierebaSi formirdeba freimTa sistema ara calkeuli obieqtebis

gamosaxulebebis, aramed Cveulebriv gamoyenebuli "ZiriTadi formebisa", romlebic

sxvadasxva kombinaciebSi warmoqmnian freimTa sistemebs axali situaciebisaTvis. aseTive

Tvisebebi axasiaTebs freimTa sistemebs, romlebic aRweren aravizualur codnas gare

samyaros Sesaxeb. SesaZlebelia freimTa sistemebis gaerTianeba ierarqiul struqturebSi,

rac sabolood mogvcems gare samyaros models. freimebi afarToeben semantikuri qselebis

SesaZleblobebs. isini gvaZleven saSualebas warmovadginoT rTuli obieqtebi ara didi

semantikuri qselis, aramed erTiani freimuli struqturis saxiT. miuxedavad amisa, rTuli

codnis bazebis organizebis problemebi aseTi midgomis dros mainc unda gadaiWras

ZiriTadad programistis intuiciisa da gamocdilebis xarjze.

15.4.15.4.15.4.15.4. konceptualuri grafebikonceptualuri grafebikonceptualuri grafebikonceptualuri grafebi. codnis bazebis SeqmnaSi Semdegi safexuri iyo qseluri

enebis Seqmna bunebrivi enis semantikis da gare samyaros modelirebisaTvis

inteleqtualur sistemebSi. Cven ganvixilavT qseluri enebis erT warmomadgenels –

konceptualur grafebskonceptualur grafebskonceptualur grafebskonceptualur grafebs. konceptualuri grafi warmoadgens sasrul, Sekrul, ormxriv

mimarTul grafs. grafis kvanZebi warmoadgenen cnebebs an konceptualur mimarTebebs.

konceptualur grafebSi rkalebis Wdeebi ar gamoiyeneba. mimarTebebi cnebebs Soris

warmoidgineba konceptualuri mimarTebebiskonceptualuri mimarTebebiskonceptualuri mimarTebebiskonceptualuri mimarTebebis kvanZebiT. imisaTvis, rom ganvasxvavoT

erTmaneTisagan cnebebi da mimarTebebi, sqemaze pirvels aRniSnaven marTkuTxedebiT, meores

ki – elifsebiT. sur. # 8.8. moyvanili konceptualuri mimarTebebi warmoadgenen

sxvadasxva n -arobis mimarTebebs. Citi frinavs aris unaruli mimarTeba, aq Citi aris

sur .# 8.8. sxvadasxva n-arobis konceptualuri mimarTebebi.

obieqti, xolo frinavs – konceptualuri mimarTeba. ZaRlis feria yavisferi aris

binaruli mimarTeba, xolo bavSvis mSoblebi arian deda da mama ki – teranuli mimarTeba.

konceptualur grafebSi cnebebis kvanZebi warmoadgenen an gare samyaroSi arsebuli

ZaRli yavisferi feri

bavSvi deda

mama

mSoblebi

Citi frena


konkretuli obieqtebis cnebebs an msjelobis dros gamoyenebul iseT abstraqtul cnebebs,

romlebic gare samyaroSi ar gvxvdeba (magaliTad patriotizmi, Ralati, siyvaruli da ase

Semdeg).

semantikuri qselebis Seqmnisas, rogorc wesi yuradRebas ar aqcevdnen iseTi

mimarTebebis gansazRvras, rogorebicaa klasi – elementi, klasi – qveklasi, ris gamoc

warmoiSva semantikuri araerTgvarovneba. magaliTad, mimarTeba egzemplarsa da klass

Soris gansxvavdeba mimarTebisagan klassa mis superklass Soris. aqedan gamomdinare

zogierTi Tviseba ekuTvnis egzemplars, xolo zogierTi ki _ klass. codnis warmodgenas

unda gaaCndes meqanizmebi am gansxvavebis aRsawerad. konceptualur grafebSi TiToeuli

cneba warmoadgens konkretuli tipis unikalur egzemplars. TiToeuli cnebis

marTkuTxedi aRiniSneba tipis WdiTtipis WdiTtipis WdiTtipis WdiT, romelic gansazRvravs am kvanZiT warmodgenil klass

an egzemplaris tips. tipis Wde da egzemplari gamoyofilia ori wertiliT. sur. # 8.9.

gviCvenebs, rom ZaRli ema yavisferia. grafi, mocemuli sur. # 8.10. gviCvenebs, rom

romeliRac araspecifirebuli, ZaRlis tipis obieqti yavisferia. konceptualuri grafebi

gvaZleven saSualebas aRvweroT agreTve konkretuli, magram usaxelo egzemplarebi.

sur. # 8.9. konceptualuri grafi, romelic gviCvenebs, rom ZaRli ema yavisferia.

sur. # 8.10. konceptualuri grafi, romelic gviCvenebs, rom romeliRac

araspecifirebuli, ZaRlis tipis obieqti yavisferia.

amisaTvis, TiToeuli egzemplaris aRsawerad monacemTa bazaSi gamoiyeneba unikaluri

deskriptori deskriptori deskriptori deskriptori (aRmweri), romelsac uwodeben markers. is warmoadgens ricxvs, romlis winac

ganTavsebulia simbolo "#". markeri saxelisagan gansxvavdeba imiT, rom is aris

unikaluri, egzemplars SeiZleba ar hqondes saerTod saxeli, SeiZleba hqondes erTi, an

ramdenime saxeli, magram mas yovelTvis aqvs zustad erTi markeri. Ees gvaZlevs

saSualebas Tavidan aviciloT semantikuri araerTmniSvneloba, kerZod rodesac gvaqvs ori

obieqti erTi da igive saxeliT, an piriqiT, erTi obieqti ramdenime saxeliT. sur. # 8.11.

moyvanilia magaliTebi, rodesac egzempliars ar gaaCnia saxeli, an aqvs erTi, an ramdenime

saxeli.

saxelisa da markeris gamoyenebis nacvlad SeiZleba gamoviyenoT ganzogadoebuli

markeri * aracspecificirebuli egzempliarebis aRsaniSnavad, Tumca es informacia xSirad

ZaRli feri

yavisferi

ZaRli: ema yavisferi feri


gamotovebulia cnebaTa WdeebTan. kvanZi, romelic mocemulia mxolod tipis WdiT ZaRli,

ekvivalenturia kvanZis ZaRli:*. konceptualuri grafebi saSualebas gvaZleven agreTve

gamoviyenoT saxelobiTi cvladebi. isini aRiniSneba "varskvlaviT" da cvladis saxeliT

(magaliTad *X, *foo). magaliTad, winadadeba "ZaRli ifxans yurs TaTiT""ZaRli ifxans yurs TaTiT""ZaRli ifxans yurs TaTiT""ZaRli ifxans yurs TaTiT" konceptualuri

grafis saSualebiT aRiwereba ase (ix. sur. # 8.12.).

sur. # 8.11. konceptualuri grafebi, romlebic gviCveneben markeris

da saxelis gamoyenebis sxvadasxva variantebs

tipebs gaaCniaT ierarqiuli struqtura. tipi “ZaRli” aris tipi “xorcismWamelebis”

qvetipi, romelic Tavis mxriv aris “ZuZumwovrebis” qvetipi da ase Semdeg. tipebis

ierarqia _ esaa nawilobrivi mowesrigeba tipebis simravleze, romelic SegviZlia

aRvniSnoT simboloTi ≤ . Tu s da t arian tipebi da t ≤ s, maSin amboben, rom t qvetipi,

xolo s _ supertipi. radganac mowesrigeba aris nawilobrivi, tips SeiZleba gaaCndes

rogorc ramdenime supertipi, aseve ramdenime qvetipi. Tu t<s da t<u, maSin amboben, rom t

aris s da u saerTo qvetipi. analogiurad ganimarteba saerTo supertipic. konceptualuri

grafebis tipebis ierarqia warmoadgens bades,bades,bades,bades, romelic aRwers mravaljeradi

ZaRli: #1123 yavisferi

ZaRli: #1123 yavisferi

ema

persona: #23456

maria

lili

feri

feri

saxeli

ana

saxeli saxeli

saxeli


sur. # 8.12. konceptualuri grafi winadadebisaTvis " " " "ZaRliZaRliZaRliZaRli ifxansifxansifxansifxans yursyursyursyurs TaTiTTaTiTTaTiTTaTiT""""

memkvidreobis sistemis zogad saxes. am badeSi tipebs SeiZleba gaaCndeT mravali mSobeli

sur. # 8.13. tipebis ierarqia

da aseve mravali Svilobili wveroebi, magram yovel wyvils tipebisa aucileblad gaaCnia

minimaluri saerTo supertipi da minimaluri saerTo qvetipi.

konceptualuri grafebis Teoria Seicavs garkveul operaciebs arsebuli grafebisagan

axali grafebis misaRebad, riTac is arsebiTad gansxvavdeba semantikuri qselebisagan. es

operaciebi saSualebas gvaZleven miviRoT axali grafebi arsebuli grafebis

specializaciis, an ganzogadebis gziT da Zalian mniSvnelovania bunebrivi enis semantikis

warmosadgenad codnis bazebSi. Ees operaciebia: kopireba, Sezkopireba, Sezkopireba, Sezkopireba, SezRudva, gaerTianebaRudva, gaerTianebaRudva, gaerTianebaRudva, gaerTianeba da

gamartivebagamartivebagamartivebagamartiveba. K

w

r

s

v

u

t

ifxans yuri agenti obieqti

nawili

ZaRli:*X

ZaRli:*X

instrumenti

TaTi nawili


kopirebis operaciakopirebis operaciakopirebis operaciakopirebis operacia saSualebas gvaZlevs g grafisagan miviRoT axali g1 grafi, romelic

warmoadgens g_s zust asls.

SezRudvis operaciiTSezRudvis operaciiTSezRudvis operaciiTSezRudvis operaciiT SegviZlia grafSi cnebis kvanZi SevcvaloT misi specializaciiT.

aq SesaZlebelia ori SemTxveva:

1. Tu cneba moniSnulia zogadi markeriT, SesaZlebelia is SevcvaloT

individualuri markeriT.

2. tipis Wde SeiZleba Seicvalos misi qvetipis WdiT, Tu is Seesabameba obieqts,

romelzedac miuTiTebs cneba.

gaerTianebis operaciiTgaerTianebis operaciiTgaerTianebis operaciiTgaerTianebis operaciiT SegviZlia movaxdinoT ori grafis integrireba erTSi. Tu maT

gaaCniaT cnebis identuri kvanZebi, maSin es kvanZi grafSi Seva erTxel. gaerTianebis

operacia warmoadgens specializaciis wess, radganac integrirebuli grafi aris naklebad

zogadi, vidre nebismieri misi komponenti.

Tu grafi Seicavs or erTnair mimarTebas, maSin SeasZlebelia amovSaloT erTerTi

maTgani Tavis rkalebTan erTad. esaa gamartivebis operaciagamartivebis operaciagamartivebis operaciagamartivebis operacia. sur. # 8.14. mocemulia am

operaciebis gamoyenebis magaliTebi. davuSvaT gvaqvs ori grafi g1 da g 2 , maSin

grafebze operaciebis saSualebiT SegviZlia miviRoT axali grafebi.

g1 :

g 2 :

g 2 -s SezRudva iqneba g 3 :

Wams Zvals

ZaRli yavisferi

yavisferi

ZaRli:”ema” zRurblze

yavisferi

agenti obieqti

feri

feri

cxoveli:”ema" zRurblze zis

zis

feri


g1 da g 3 gaerTianeba iqneba g 4 :

g 4 gamartiveba iqneba 5g :

sur. # 8.14. operaciebi konceptualur grafebze.

8.6.8.6.8.6.8.6. codnis warmodgena konceptebis saSualebiT. codnis warmodgena konceptebis saSualebiT. codnis warmodgena konceptebis saSualebiT. codnis warmodgena konceptebis saSualebiT. rodesac adamianebi msjeloben,

saubroben erTmaneTSi, an fiqroben raime problemaze, isini iyeneben cnebebs, romlebic

praqtikulad bunebaSi ar arseboben. magaliTad, Cven vxmarobT cnebas magida, magram

bunebaSi ar arsebobs raRac zogadi magida, yovelTvis arsebobs romeliRac konkretuli

magida, aseve ar arsebobs zogadad xe, an Senoba. rogor xdeba konkretul obieqtebze

dakvirvebiT am zogadi cnebebis formireba bunebriv inteleqtSi? Cven ra Tqma unda zustad

ar SegviZlia aRvweroT is procesebi, romlebic mimdinareobs adamianis Tavis tvinSi,

rodesac xdeba raime cnebis formireba, magram zogadi sqema gamoiyureba ase: adamiani

garemosTan urTierTobis procesSi akvirdeba ra erTi da igive tipis obieqtebs, aRwers

maT raRac parametrebis saSualebiT. mraval obieqtebze dakvirvebis Sedegad am

parametrebidan gamoyofs iseTebs, romlebic arsebiTia mocemuli klasis obieqtebisaTvis

da aseTnairad dafiqsirebul informacias uwodebs cnebascnebascnebascnebas. am SemTxvevaSi i mniSvnelovania,

agenti Wams obieqti

Zvali

ZaRli:”ema” zis zRurblze

feri yavisferi

agenti Wams obieqti Zvali

ZaRli:”ema” zis zRurblze

feri feri yavisferi


rom cnebis Camoyalibebis procesi ar grZeldeba usasrulod da adamians SeuZlia

mocemuli klasis sasruli elenetebis safuZvelze Camoayalibos Tavisi cneba. meore

mniSvnelovani momentia, rom am cnebis ganmsazRvrelia ara adamianis Sexeduleba ama Tu im

obieqtze, aramed swored am obieqtebis Tvisebebi. es rom ase ar iyos, adamianebs Soris

SeuZlebeli iqneboda urTierToba, radgan erTsa da imave cnebis qveS isini igulisxmebdnen

sul sxvadasxva obieqtebs. cxadia, rom gansxvaveba sxvadasxva adamianebis erTsa da imave

cnebebs Soris arsebobs, magram radganac es cnebebi asaxaven obieqturad arsebul garemos,

es gansxvaveba, rogorc wesi, ar warmoadgens gadaulaxav dabrkolebas adamianTa

urTierTobis dros.

rogor SeiZleba gavimeoroT cnebaTa formirebis principi kompiuterul sistemaSi,

raTa codna CamovayaliboT konceptiskonceptiskonceptiskonceptis (cnebis Sesabamisi, kompiuteriT gamoTvlili

artefaqti) saxiT, romelic saSualebas mogvcems ara marto kompaqturad SevinaxoT codna

kompiuterSi, aramed gamoviyenoT es codna gadawyvetilebebis misaRebad Tu raime

procesebis samarTavad.

pirvel rigSi saWiroa gvqondes Sesabamisi maTematikuri aparati, romelic saSualebas

mogvcems aRvweroT iseTi aramkafio, aramkacrad Camoyalibebuli obieqtebi, rogoricaa

cnebebi. SemovitanoT alalalal----simravlissimravlissimravlissimravlis (M ) cneba, romelSic elementis mikuTvnebis operacia

∈ Tanabrad SeiZleba ekuTvnodes rogorc ,a aseve a elements, anu am simravles ekuTvnis

Ma∈∨

, sadac a

aa {=∨

. ganuzRvrelobis es forma, romelic Cven Semogvaqvs, saSualebas

mogvcems aRvweroT is ganuzRvreloba, romelic axasiaTebs cnebebis formirebis process.

konceptis gamoTvlis procedura Sedgeba ramdenime etapisagan. pirvel rigSi unda

gamoiyos niSnebis (Tvisebebis) is simravle, romlis saSualebiTac moxdeba konkretuli

obieqtebis aRwera. mTavari principi aseTi niSnebis gamoyofis dros mdgomareobs imaSi,

rom SesaZlebeli unda iyos am niSnebis mniSvnelobaTa obieqturad dakvirveba, an Sefaseba

eqspertTa saSualebiT. amasTan mniSvneloba ara aqvs es niSnebi raodenobrivia, Tu

xarisxobrivi (anu SesaZlebelia maTi mniSvnelobebis raodenobrivad gazomva, Tu mxolod

xarisxobrivi Sefaseba). niSnebis simravlis gamoyofasTan erTad xdeba maTi mniSvnelobebis

simravleebis dadgenac. amasTan es simravleebi unda iyos diskretuli da sasruli. am

etapis Semdeg Cven gveqneba matrica nm× , sadac m aris niSnebis raodenoba, xolo

)(max ii

nn = mniSvnelobaTa maqsimaluri raodenoba. pirveli etapi mTavrdeba TiToeuli

niSnis mniSvnelobaTa binarizaciiT, anu maTi gayofiT or qvesimravled.

meore etapze unda movaxdinoT am niSnebis saSualebiT im konkretuli obieqtebis

aRwera, romelTa saSualebiTac unda gamovTvaloT koncepti. am dros yvelaze

mniSvnelovania konkretuli obieqtebis Sefaseba iyos obieqturi, anu yoveli konkretuli

obieqtisaTvis gvqondes calsaxa Sefaseba ekuTvnis, Tu ar ekuTvnis mocemuli obieqti im

cnebas, romlis konceptis gamoTvlasac Cven vapirebT. Tu Cven ar vapirebT gamovTvaloT

romelime konkretuli adamianis cnebis Sesabamisi koncepti, maSin es Sefasebebi unda iyos

miRebuli eqsperimentatorisagan damoukidebelad.


mesame etapze xdeba ukve konceptis gamoTvla. amisaTvis SeiZleba gamoviyenoT

konceptis gamoTvlis logikuri, an statistikuri meTodi. ganvixiloT es ukanaskneli.

davuSvaT, ijp iyos iA niSnis ija mniSvnelobis Sexvedris statistika im N konkretul

obieqtSi, romelTa saSualebiTac viTvliT koncepts iij

ij njmiN

aNp ,1,,1,

)(=== . amis

Semdeg TiToeuli iA niSnisaTvis SevkriboT im mniSvnelobebis sixSireebi, romlebic

gaerTianebulni arian erT qvesimravleSi. erTi simravle pirobiTad aRvniSnoT rogorc ia

da meore ki ia . gveqneba ∑=k

iki pP , sadac ajamva xdeba im mniSvnelobebis mixedviT,

romlebic gaerTianebulni arian ia qvesimravleSi da ∑=l

ili pP sadac ajamva xdeba im

mniSvnelobebis mixedviT, romlebic gaerTianebulni arian ia qvesimravleSi. ra Tqma unda,

rom adgili aqvs tolobas 1=+ ii PP . am proceduris damTavrebis Semdeg Cven miviRebT

gamosaxulebas

=

m

m

PPP

PPPP

,...,,

,...,,)(

21

21ϕ . amis Semdeg, Semogvaqvs filtraciis done, raTa

gadavideT konceptis aRweris logikur doneze. filtraciis done, anu sizustis done

damokidebulia imaze, Tu ra sizustiT gvinda gamovTvaloT koncepti. Semogvaqvs mudvivi

sidideebi ψ da ψ , ise, rom 1=+ψψ da vaxdenT filtracias Semdegi wesiT: Tu ψ≥iP

(Sesabamisad ψ≤iP ) maSin vTvliT, rom es niSani warmoadgens konceptis damaxasiaTebl,

mniSvnelovan niSans da konceptis aRweraSi is unda Sediodes iA (Sesabamisad iA )

formaSi. Tu ψ<iP (Sesabamisad ψ>iP ) , maSin es niSani aris araarsebiTi da is

konceptis aRweraSi unda Sediodes iA∨ formaSi. aseTi operaciis Semdeg Cven miviRebT

konceptis saboloo saxes:

),...,,,()( 4321 mAAAAAS∨∨

=ϕ

sadac niSnebs Soris igulisxmeba operacia ∧ . amgvarad, Cven SevZlebT raime S obieqtis

zogadi aRweridan gamovyoT is damaxasiaTebeli niSnebi, romlebic gansazRvraven am

obieqtis arss. gamoTvlili koncepti iqneba yvelaze uxeSi miaxloeba (e.w. pirveli donis

koncepti). Tu es done Cven ar dagvakmayofilebs, SesaZlebelia gamovTvaloT ufro maRali

donis koncepti. amisaTvis saWiroa ufro davazustoT niSnebi da maTi mniSvnelobebi da

filtraciis done.


1. ra upiratesoba aqvT codnaze dafuZnebul agentebs sxva agentebTan SedarebiT?

2. ra gansxvavebaa kompiuterSi monacemTa warmodgenasa da codnis warmodgenas


Soris?

3. ra principebs efuZneba semantikuri qselebi?

4. rogor xdeba cnebebis dakavSireba semantikur qselSi?

5. ra aris freimi?

6. rogor xdeba freimis Camoyalibeba?

7. rogor iqmneba freimuli sistema?

8. ra upiratesoba aqvs freimul sistemas semantikur qselTan SedarebiT?

9. ras warmoadgens konceptualuri grafi?

10. riT gansxvavdeba is semantikuri qselisa da freimebisagan?

11. CamoTvaleT konceptualur grafebze ganmartebuli operaciebi.

12. ras ewodeba koncepti?

13. ra etapebisagan Sedgeba konceptis gamoTvlis procedura?

14. moifiqreT, rogor SeiZleba gamoiyenos inteleqtualurma sistemam konceptis

saxiT Camoyalibebuli codna.

savarsavarsavarsavarjiSoebi:jiSoebi:jiSoebi:jiSoebi:

1. warmoadgineT winadadeba “vanom misca anos nayini” konceptualuri grafis

saSualebiT.

2. aageT semantikuri ierarqiuli qseli cnebisaTvis “satransporto saSualebebi”.

3. aageT freimuli struqturebi samkuTxa da oTxkuxa piramidebisaTvis.

4. CamoayalibeT, ra procedurebia saWiro, raTa gamovTvaloT cnebis - “lamazi

manqana” Sesabamisi koncepti.

lllleqcia eqcia eqcia eqcia ####9 9 9 9

amocanaTa amoxsnis Zlieri meTodamocanaTa amoxsnis Zlieri meTodamocanaTa amoxsnis Zlieri meTodamocanaTa amoxsnis Zlieri meTodebiebiebiebi

9.1. codnis inJineria. 9.1. codnis inJineria. 9.1. codnis inJineria. 9.1. codnis inJineria. rogorc ukve viciT wina leqciebidan, algoriTmebi, romlebic eZeben

amocanis amoxsnas specifikuri codnis gareSe, warmoadgenen sust algoriTmebs. am

leqciaSi Cven ganvixilavT rogor SeiZleba codnis gamoyenebiT ufro efeqturad

amovxsnaT inteleqtualuri amocanebi. codnis inJineriiscodnis inJineriiscodnis inJineriiscodnis inJineriis ZiriTadi principis Tanaxmad,

amocanaTa amomxsneli agentis SesaZleblobebs pirvel rigSi ganaszRvravs Tu ra icis man

mocemuli problemis Sesaxeb, rogoria misi informaciuli baza da mxolod Semdeg

daskvnebis gamotanis, anu Zebnis meTodebi. asea bunebrivi inteleqtis SemTxvevaSic,

adamiani – eqsperti kargad asrulebs Tavis samuSaos swored imitom, rom man bevri icis

mocemuli problemebis Sesaxeb da gaaCnia am problemebis gadaWris praqtikuli Cvevebi.

aseTi unda iyos xelovnuri agentic, man unda icodes bevri ram konkretuli problemis

sur. # 9.1. tipuri eqspertuli sistemis arqiteqtura

da gaaCndes am sferoSi problemaTa gadaWris praqtikuli Cvevebi. aseT agentebs sxvanairad

uwodeben eqspertul sistemebs. eqspertul sistemebs. eqspertul sistemebs. eqspertul sistemebs. cxadia, rom rogorc codna, aseve praqtikuli Cvevebi

eqspertul sistemaSi unda Caidos adamianis mier. eqspertuli sistemebi gamoiyeneba

sxvadasxva problemebis gadasaWrelad, praqtikulad, adamianebis moRvaweobis yvela

sferoSi. maTi ZiriTadi amocanebia: diagnostika, prognozireba, proeqtireba, dagegmva,

monitoringi da marTva.

9.2. eqspertuli sistemebis teqnologia. 9.2. eqspertuli sistemebis teqnologia. 9.2. eqspertuli sistemebis teqnologia. 9.2. eqspertuli sistemebis teqnologia. sur. # 9.1. naCvenebia tipuri eqspertuli sistemis

arqiteqtura. momxmarebeli sistemas ukavSirdeba momxmareblis interfeisis saSualebiT,

romelic SeiZleba iyos sxvadasxva saxis, momxmareblis interesebidan, monacemTa bazisa da

daskvnebis gamomtani sistemis moTxovnebis gaTvaliswinebiT. eqspertuli sistema Seicavs

momxmareblis interfeisSi SeiZleba gamoviyenoT: kiTxvebi da pasuxebi, meniu, bunebrivi ena, grafikuli aRniSvnebi

momxmarebeli

codnis bazis redaqtori

daskvnebis gamomtani manqana

ganmartebebis qvesistema

codnis zogadi baza

kerZo SemTxvevebismonacemebis

leqcia #leqcia #leqcia #leqcia #9999. . . . amocanaTa amoxsnis Zlieri meTodebiamocanaTa amoxsnis Zlieri meTodebiamocanaTa amoxsnis Zlieri meTodebiamocanaTa amoxsnis Zlieri meTodebi 91

codnis bazascodnis bazascodnis bazascodnis bazas, romelic warmoadgens sistemis ZiriTad birTvs da inaxavs codnas raime

konkretuli problemis garSemo, ganmartebebis qvesistemasganmartebebis qvesistemasganmartebebis qvesistemasganmartebebis qvesistemas da daskvnebis gamomtan maqanasdaskvnebis gamomtan maqanasdaskvnebis gamomtan maqanasdaskvnebis gamomtan maqanas.

eqspertul sistemebSi, romlebic efuZnebian wesebs, codna warmodgenilia Semdegi saxiT:

Tu…. Tu…. Tu…. Tu…. . . maSin, maSin, maSin, maSin, anu, Tu sruldeba raime piroba, maSin gamotanili iqneba Sesabamisi daskvna

(qmedeba). monacemTa baza Seicavs rogorc zogad codnas, aseve codnas kerZo SemTxvevebis

Sesaxeb. daskvnebis gamomtani manqana iyenebs bazaSi arsebul codnas da produqciuli

sistemis saSualebiT maT safuZvelze Rebulobs daskvnebs. produqciuli sistema

warmoadgens sistemas, romelic uzrunvelyofs amocanis amoxsnis procesis marTvas raime

modelis mixedviT da Sedgeba produqciuli wesebis, samuSao mexsierebisa da marTvis

ciklisagan - “gamocnoba – qmedeba“. produqciuli sistemis magaliTi Cven gvqonda pirvel

leqciaSi, rodesac vixilavdiT programa LG ----s. procedurebi, romlebsac asrulebs marTvis

cikli, gancalkevebulia produqciuli wesebisagan, rac iZleva saSualebas avagoT codnis

baza mmarTveli programis gaTvaliswinebis gareSe: SevitanoT cvlilebebi bazis raime

nawilSi ise, rom ar warmoiSvas problemebi bazis danarCen nawilSi da gamoviyenoT

sxvadsaxva eqspertul sistemebSi erTi da igive marTvis programa da interfeisi, anu clke

SevqmnaT eqspertuli sistemis garsi da Semdeg masSi sxvadasxva problemis Sesaxeb codnis

bazis CadebiT miviRoT sxvadasxva eqspertuli sistema.

ganmartebebis qvesistemaganmartebebis qvesistemaganmartebebis qvesistemaganmartebebis qvesistema saSualebas aZlevs momxmarebels miiRos sistemisagan

ganmartebebi, Tu ris safuZvelze gamoaqvs sistemas esa Tu is dakvna da darwmundes

sistemis swor funqcionirebaSi. eqspertuli sistemis Sesaqmnelad saWiroa codnis

inJineriis specialistebis, mocemuli problemis eqspertebisa da momxmarebelTa

erToblivi muSaoba. sur. #9.2. naCvenebia eqspertuli sistemis damuSavebis cikli. saidanac

kargad Cans, rom es procesi sakmaod rTuli, Sromatevadi da ZviradRirebuli procesia,

magram kargi eqspertuli sistema yovelTvis anazRaurebs masze daxarjul saxsrebs.

muSaoba iwyeba codnis inJinerisa da mocemuli problemis eqspertis mier im codnis

gansazRvriT, romelic saWiro iqneba eqspertuli sistemisaTvis. mas Semdeg, rac codnis

inJineri miiRebs warmodgenas, Tu rogor xdeba mocemuli problemis gadawyveta, is ukve

iwyebs sistemis damuSavebas, fiqrobs imaze, Tu ra saxiT warmoadginos codna sistemaSi

(magaliTad, wesebiT Tu konceptualuri grafebiT), gansazRvravs Zebnis rogor strategias

gamoiyenebs sistema (pirdapiri Tu ukuZebna), daamuSavebs interfeiss. amis safuZvelze

aigeba prototipi. amis Semdeg iwyeba am prototipis daxvewa, sanam momxmarebeli ar darCeba

kmayofili miRebuli SedegiT.

9.3. eqspertul9.3. eqspertul9.3. eqspertul9.3. eqspertuli sistemis funqcionireba.i sistemis funqcionireba.i sistemis funqcionireba.i sistemis funqcionireba. ganvixiloT wesebze dafuZnebuli eqspertuli

sistemis magaliTi. wesebze dafuZnebuli eqspertuli sistemis arqiteqtura Seicavs

amocanaTa amoxsnis produqciul sistemas. aseT SemTxvevaSi SeiZleba CavTvaloT, rom

codnis baza Sedgeba produqciuli wesebisagan. ganvixiloT avtomobilis diagnostikis

eqspertuli sistemis martivi magaliTi. davuSvaT, codnis baza Sedgeba mxolod oTxi

produqciuli wesisagan:

1. TuTuTuTu sawvavi modis ZravSi da Zravi brunavs, maSinmaSinmaSinmaSin problemas warmoadgenen

sanTlebi;

2 Tu Tu Tu Tu Zravi ar brunvs da farebic ar inTeba, maSinmaSinmaSinmaSin problemas warmoadgens


akumuliatori, an gamtarebi;

3. Tu Tu Tu Tu Zravi ar brunavs da farebi inTeba, maSin maSin maSin maSin problemas warmoadgens

startiori;

4.... Tu Tu Tu Tu avzSi sawvavi aris da sawvavi modis karburatorSi, maSin maSin maSin maSin sawvavi modis

ZravSic.

sur. # 9.2. eqspertuli sistemis damuSavebis ciklebi

sur. # 9.3. produqciuli sistemis muSaobis dasawyisi

muSa mexsiereba

problema X produqciuli wesebi

wesi #1 wesi #2 wesi #3 wesi #4

dasawyisi

miznebisa da amocanebis gansazRvra

prototipis SemuSaveba da Seqmna

sistemis testireba

sistemis analizi da naklovanebaTa gamosworeba

saWiroa koreqcia?

mzadaa sistema?

saboloo testireba

diax

ara

ara diax

sistema warmatebulia

ar varga


am wesebis safuZvelze muSa mexsierebaSi moTavsdeba maRali donis mizani -

problema X, romelic unda gamoikvlios eqspertulma sistemam. X SeiZleba iyos nebismieri

fraza, magaliTad, Tavidan es aris fraza “Zravi ar iqoqeba.” (ix. sur. # 9.3).

muSa mexsierebaSi moTavsebul frazas sistema Seusabamebs sam wess da Tu am wesebis

ganxilva iwyeba wesiT, romlis nomeric yvelaze pataraa, maSin sistema gaaqtiurebs #1

wess, amasTan X-s Seusabamebs frazas “sanTlebi” (ix. sur. # 9.4.), xolo misi

sur. # 9.4. produqciuli sistema pirveli wesis gaaqtiurebis Semdeg.

winapirobebi ki moTavsdeba muSa mexsierebaSi. pirveli wesis samarTlianobis dasadgenad

dakmayofilebuli unda iyos ori piroba: sawvavi modis ZravSi da Zravi brunavs. imisaTvis,

rom daadginos sawvavi modis Tu ara ZravSi, sistema gaaqtiurebs wess #4 (ix. sur. # 9.5).

sur. #9.5. produqciuli sistema wesi #4 gaaqtiurebis Semdeg

gadmoitans ra meoTxe wesis winapirobebs muSa mexsierebaSi, sistema aRmoaCens, rom aq

aris sami elementi, romlebic ar Seesabamebian codnis bazaSi moTavsebul arcerT wess,

muSa mexsiereba

avzSi sawvavi aris sawvavi modis karburatorSi Zravi brunavs problemaa sanTlebi

produqciuli sistema


muSa mexsiereba

sawvavi modis ZravSi Zravi brunavs problemaa sanTlebSi

produqciuli wesebi



amitom sistema SeekiTxeba momxmarebels, sruldeba Tu ara es pirobebi da Tu

momxmareblisagan is miiRebs samive elementis dadasturebas, maSin gamoitans daskvnas, rom

problemas warmoadgenen sanTlebi, Tu ar dadasturdeba Tundac erTi elementi mainc,

sistema CaTvlis rom, pirveli wesi ar Seesabameba mocemul situacias da gadava meore

wesis ganxilvaze.

sur. #9.6. mocemulia grafi, romelic aigeba sistemis muSaobis dros. patara rkali

grafze miuTiTebs, rom problemis gadasawyvetad saWiroa orive pirobis Sesruleba (anu

kvanZi grafze aris D”da” tipis). rogorc am grafidan kargad Cans, algoriTmi warmoadgens

siRrmeSi gadarCevis algoriTms. miiRebs ra informacias momxmareblisagan imis Sesaxeb,

aris Tu ara sawvavi avzSi da modis Tu ara sawvavi karburatorSi (unda sruldebodes

orive piroba erTdroulad) algoriTmi amodis zeda doneze da kvlav iTxovs informacias

“brunavs Tu ara Zravi?” dadebiTi pasuxis SemTxvevaSi sistema daaskvnis, rom problema

mdgomareobs sanTlebSi, Tu ara – gadadis meore wesze. miuxedavad imisa, rom es sistema

Zalian martivia, is kargad asaxavs Tu rogor SeiZleba sawyisi problemis dekompozicia

ufro martiv amocanebad produqciuli sistemis da da/an tipis grafebis gamoyenebiT.

aRwerili sistema warmoadgens produqciuli sistemis gamoyenebis magaliTs miznis safuZvelze, romelSic gamoiyeneba Zebna siRrmeSi, radganac sistema ar gadava meore

qvemiznis gamokvlevaze manamdis, sanam is ar moaxdens mocemuli qvemiznis srul

gamokvlevas.

sur. # 9.6. da/an da/an da/an da/an tipis grafi, romelic aigeba eqspertul

sistemaSi. problema X aq aris “Zravi ar iqoqeba”

problema X

wesi 1: problemaa sanTlebi

wesi 2: problemaa akumuliatori an gamtarebi

wesi 3: problemaa startiori

sawvavi modis ZravSi

Zravi brunavs

Zravi ar brunavs

farebi ar inTeba

Zravi ar brunavs

farebi inTeba

wesi 4: sawvavi modis ZravSi

avzSi aris sawvavi

sawvavi modis karburatorSi


9.4. 9.4. 9.4. 9.4. ganmartebebis qvesistema.ganmartebebis qvesistema.ganmartebebis qvesistema.ganmartebebis qvesistema. ra rols asrulebs eqspertul sistemaSi ganmartebebis

qvesistema? produqciuli sistema axdens Zebnas grafze, ganmartebebis qvesistema ki

Tvalyurs adevnebs am process da iyenebs miRebul informacias, raTa upasuxos

momxmareblis SekiTxvebs. rogorc wesi, eqspertuli sistemebi pasuxoben ori tipis

SekiTxvebs – “ratom?” da “rogor?”. pirveli tipis SekiTxvebi warmoiSveba, rodesac sistema

iTxovs damatebiT informacias momxmareblisagan. magaliTad, rodesac sistemam moiTxova

“aris Tu ara avzSi sawvavi?” miiRo pasuxi “diax”. Semdeg moiTxova informacia modis Tu

ara sawvavi karburatoSi?” da miiRo pasuxi “diax”. amis Semdeg is kvlav ekiTxeba

momxmarebels “brunavs Tu ara Zravi?”. nebismier etapze momxmarebeli SeiZleba

dainteresdes, Tu risTvis sWirdeba sistemas es informacia da is ekiTxeba sistemas

“ratom?”, anu risTvis sWirdeba sistemas es informacia. ganmartebebis qvesistema, romelic

Tvalyurs adevnebda am process, iZleva ganmartebas ”Tanaxmad pirveli wesisa, Tu sawvavi

modis ZravSi da Zravi brunavs, maSin problemas warmoadgenen sanTlebi”. Tu momxmarebeli

dainteresdeba, Tu rogor daadgina sistemam, rom sawvavi modis ZravSi, maSin ganmartebebis

qvesistema upasuxebs, rom “meoTxe wesis Tanaxmad, Tu sawvavi aris avzSi da sawvavi modis

karburatorSi, maSin sawvavi modis ZravSi”. amiT ganmartebebis qvesistema uzrunvelyofs

imas, rom momxmarebeli yovelTvis saqmis kursSia, Tu ras akeTebs sistema da SeuZlia

miuTiTos, an sulac Sewyvitos muSaoba, Tuki sistema uSvebs Secdomas, an moqmedebs

araswori mimarTulebiT.

9.5. monacemebze dafuZnebuli produqciuli sistema. 9.5. monacemebze dafuZnebuli produqciuli sistema. 9.5. monacemebze dafuZnebuli produqciuli sistema. 9.5. monacemebze dafuZnebuli produqciuli sistema. ganxiluli sistema warmoadgenda

produqciul sistemas, romelic dafuZnebuli iyo mizanze. exla vnaxoT, rogor SeiZleba

igive sistema muSaobdes monacemebis safuZvelze. gansxvavebiT mizanze dafuZnebuli

sistemisagan, sadac Zebna mimdinareobs siRrmeSi radganac sanam sistema ar Caatarebs erTi

qvemiznis amomwurav analizs, ar gadava meore qvemizanze, monacemTa safuZvelze muSaobisas

sistema rogorc wesi awarmoebs ganiv Zebnas. algoriTmi Zalian martivia: muSa mexsierebaSi

a) b)

sur. #9.7. monacemTa safuZvelze momuSave sistemis pirveli da meore etapebi:

a) sawyis etapi; b) sistema meore wesis pirveli winapirobis Sefasebis Semdeg.

muSa mexsiereba

produqciuli wesebi


muSa mexsiereba

produqciuli wesebi

Zravi brunavs



moTavsebuli monacemebi dardeba codnis bazaSi arsebuli wesebis pirobebs. Tu monacemebs

mivyavarT romelime wesis aqtivizaciasTan, Sedegi moTavsdeba muSa mexsierebaSi da marTva

gadaecema Semdeg wess. Cveni magaliTis SemTxvevaSi sawyis etapze muSa mexsierebaSi ar

aris araviTari informacia da sistema iwyebs wesebis winapirobebis Semowmebas, raTa

moZebnos informacia, romelsac is moiTxovs momxmareblisgan (sur. #9.7. a)). pirveli wesis

winapiroba “sawvavi modis ZravSi” ar miekuTvneba aseT informacias, amitom sistema

gadadis meore wessze da ganixilavs winapirobas “Zravi ar trialebs”, es iqneba swored is

informacia, romelic sistemam unda moiTxovos momxmareblisagan. davuSvaT, aRmoCnda, rom

es winapiroba arasworia, amitom rogorc meore, aseve mesame wesis gamoyeneba ar SeiZleba.

sistema gadava meoTxe wesis ganxilvaze da naxavs, rom am wesis orive winapiroba aris is

informacia, romelic man unda moiTxovos momxmareblisagan. amis Semdeg muSa mexsierebaSi

mas eqneba Semdegi saxis monacemebi: “sawvavi modis ZravSi”, “sawvavi modis karburatorSi”,

“sawvavi aris avzSi” da aqve moTavsdeba daskvna, romelsac sistema miiRebs meoTxe wesis

safuZvelze - “Zravi trialebs”. amis Semdeg sistema kvlav daiwyebs produqciuli wesebis

xelaxla ganxilvas. sistema aRmoaCens, rom pirveli wesis Tanaxmad da im monacemebis

safuZvelze, rac mas gaaCnia, SesaZlebelia mxolod erTaderTi daskvnis gakeTeba, rom

“problemaa sanTlebi” da daamTavrebs muSaobas.

gansxvavebiT mizanze dafuZnebuli sistemisagan, monacemebze dafuZnebul sistemaSi

Zebnas aqvs ufro arasistemuri xasiaTi. amis mizezi Zalian martivia, mizanze dafuZnebuli

sistema ZiriTad amocanas yofs ufro patara qveamocanebad da es qveamocanebis SeiZleba

daiyos kidev ufro patara qveamocanebad. amis gamo Zebna yovelTvis mimarTulia

ierarqiulad miznidan mis Semadgenelebisken. monacemebze dafuZnebul sistemaSi aseTi

mizani ar arsebobs da Zebna xorcieldeba xeze, romelic damokidebulia mxolod

produqciuli wesebis mimdevrobasa da axali informaciis gamoCenaze. amitom Zebnis

sur. # 9.8. monacemebze dafuZnebuli sistema meoTxe wesis ganxilvis Semdeg iwyebs wesebis

xelmeored ganxilvas.

muSa mexsiereba

sawvavi modis ZravSi sawvavi modis karburatorSi avzSi aris sawvavi Zravi brunavs

produqciuli wesebi



procesi ufro aramimarTuli da naklebad cxadia. aqedan gamomdinare ganmartebebis

qvesistemis muSaobac ufro SezRudulia, kerZod am sistemaSi ganmartebebis qvesistemas ar

SeuZlia upasuxos kiTxvas “ratom?” da Tu produqciuli wesebis mimdevroba zustad ar

aRiricxeba, qvesistemas aseve uWirs gasces pasuxi kiTxvas “rogor?”.

9.6. evristikebi codnis bazis agebis dros.9.6. evristikebi codnis bazis agebis dros.9.6. evristikebi codnis bazis agebis dros.9.6. evristikebi codnis bazis agebis dros. codnis bazisa da daskvnebis gamotanis

meqanizmis aseTi gayofis gamo, cxadia, rom Zebnis efeqturoba TiTqmis mTlianad

damokidebulia codnis bazaSi produqciuli wesebis struqturasastruqturasastruqturasastruqturasa da maT ierarquladierarquladierarquladierarqulad

mowesrigebaze. gansakuTrebiT mniSvnelovania, rom wesis forma, Tu Tu Tu Tu p,q da da da da r, maSin maSin maSin maSin s

miuxedavad imisa rom erTi SexedviT gvagonebs logikur gamosaxulebas, SesaZlebelia

aRqmuli iqnas rogorc amocanis amoxsnis procedurebi an bijebi: “rom miviRoT s, saWiroa

SevasruloT jer p, Semdeg q da Semdeg r qmedebebi”. codnis bazis aseTi mowesrigebis

problema Cans Cven magaliTSic. pirveli produqciuli wesi moiTxovs, rom jer

davadginoT, modis Tu ara sawvavi ZravSi da Semdeg – brunavs Tu ara Zravi. magram aseTi

rigiToba araefeqturia, radganc pirveli pirobis dadgenas sWirdeba ufro meti

gamokvleva, vidre meore pirobis.

aqedan gamomdinare sistemis efeqtianoba mTlianad damokidebulia codnis bazis

iseTnairad mowesrigebaze, rom garkveuli iyos wesebis rigiwesebis rigiwesebis rigiwesebis rigi, winapirobebis organizebawinapirobebis organizebawinapirobebis organizebawinapirobebis organizeba

wesebSi da sxvadasxva Semowmebebis fasiSemowmebebis fasiSemowmebebis fasiSemowmebebis fasi. yvela es qmedeba Tavisi SinaarsiT aris

evristikuli da asaxaven eqspertis midgomebs da mis codnas mocemuli garemos Sesaxeb.

TavisTavad cxadia, rom zogierT SemTxvevaSi isini SeiZleba iyos mcdaric. magaliTad,

Cvens SemTxvevaSi, Tu sawvavi modis ZravSi da Zravi brunavs, problema SeiZleba iyos

elqtruli naperwkalis gamanawilebel sistemaSi da ara sanTlebSi. amitom saWiroa, rom

eqspertuli sistemis codnis bazis Seqmnis dros gaTvaliswinebuli iyos sxvadasxva

eqspertebis rekomendaciebi da eqsperimentebis safuZvelze srulad daixvewos codnis baza.

Cveni magaliTi iyo martivi da is exeboda diagnostikis mxolod erT problemas “Zravi ar

iqoqeba”. magram Tu Cven movindomebT manqanis sruli diagnostikis sistemis Seqmnas,

produqciuli wesebis raodenoba gaizrdeba Zalian swrafad da aseTi principiT muSaoba,

rom Semowmdes yvela wesi, ukve aRar iqneba optimaluri, miT umetes, cxadia, rom

magaliTad, Tu manqanis damuxruWebis manZili ar gvakmayofilebs, aq araviTavi mniSvneloba

ara aqvs iqoqeba Tu ara manqana. amitom saWiro xdeba produqciuli wesebis qselur qselur qselur qselur

struqturebSistruqturebSistruqturebSistruqturebSi gaerTianeba. arsebobs Sesabamisi algoriTmebi, romlebic asruleben am

process da saSualebas gvaZleven kidev ufro gavaumjobesoT eqspertuli sistemis

muSaoba.

eqspertuli sistema aucilebeli ar aris dafuZnebuli iyo mizanze an monacemebze.

arsebeoben eqspertuli sistemebi, romlebic efuZnebian gamocdilebgamocdilebgamocdilebgamocdilebas an modelsas an modelsas an modelsas an models. modelze

dafuZnebuli eqspertuli sistema ufro xSirad gamoiyeneba iseTi problemebis

gadasaWrelad, romelTa modelebi maqsimalurad obieqturad aRiwereba da gvaqvs

xelsawyoebi, romlebis saSualebas gvaZleven zustad gavzomoT saWiro informacia. aseTi

eqspertuli sistemebis magaliTs warmoadgens NASA-s mier damuSavebuli eqspertuli

sistema, romelic gamoiyeneba kosmosuri obieqtebis Zravis samarTavad avtonomiur reJimSi.

sistema modelisa da im informaciis safuZvelze, romelic mas SeuZlia miiRos gazomvebis


safuZvelze, axdens Zravis muSaobaSi arsebuliAuwesrigobebis gamovlenas da Sesabamisad,

radganc am uwesrigobebis aRmofxvra avtonomiur reJimSi SeuZlebelia, gadayavs Zravi

funqcionirebis axal reJimSi.

sistemebi, romlebic dafuZnebulni arian gamocdilebaze (es gamocdileba ra Tqma

unda warmoadgens eqspertis gamocdilebas), problemis gadaWris dros Tavis codnis

bazaSi eZeben analogiur SemTxvevas da modelisa da am SemTxvevis safuZvelze Rebuloben

gadawyvetilebebs.

SesaZlebelia hibriduli eqspertuli sistemebishibriduli eqspertuli sistemebishibriduli eqspertuli sistemebishibriduli eqspertuli sistemebis arsebobac, romlebSic gvxvdeba

zemoTCamoTvlili midgomebis sxvadasxva kombinaciebi, rac kidev ufro efeqturs xdis

sistemis muSaobas. miRweuli warmatebebi eqspertuli sistemebis Seqmnis dargSi

adasturebs, rom es warmatebebi miiRweva ara im meqanizmebis safuZvelze, romelTa

saSualebiTac sistema gamoaqvs daskvnebi, aramed im codnis bazebis saSualebiT, romlis

sauZvelzec, xdeba daskvnebis gamotana. es kidev erTxel xazs usvavs codnis kompiuterSi

warmodgenis problemis mniSvnelobas.


1. ratomaa gayofili codnis warmodgenisa da daskvnebis gamotanis qvesistemebi?

2. ra rols asrulebs ganmartebebis qvesistema?

3. riTi gansxvavdeba erTmaneTisagan mizanze dafuZnebuli da monacemebze

dafuZnebuli eqspertuli sistemebi?

4. kidev rogor eqspertuli sistemebi arseboben?

5. ra ufro mniSvnelovania eqspertul sistemaSi, daskvnebis gamotanis qvesistema,

Tu codnis baza?

6. rogor unda iyos organizebuli codnis baza?


1. leqciaSi moyvanilia eqspertuli sistema, romelic gamoiyeneba avtomobilis

diagnostikisaTvis. vin SeiZleba iyos codnis bazis inJineri? eqsperti?

momxmarebeli?

2. CamoayalibeT kidev aTi produqciuli wesi am sistemisaTvis da aageT grafi,

romelic asaxavs kavSirebs am wesebs Soris.

3. meore savarjiSoSi gaTvaliswinebuli wesebis damatebis Semdeg gansazRvreT

Zebnis romeli principia ukeTesi am sistemisaTvis, mizanze dafuZnebuli, Tu

monacemebze dafuZnebuli?

4. SearCieT raime problemuri garemo da aageT eqspertuli sistema wina

savarjiSos Sesabamisad.

leqcia #leqcia #leqcia #leqcia #11110000

neironuli qselebi neironuli qselebi neironuli qselebi neironuli qselebi

11110000.1. neironuli qselebis arsi..1. neironuli qselebis arsi..1. neironuli qselebis arsi..1. neironuli qselebis arsi. rogorc ukve aRniSnuli iyo pirvel leqciaSi, 1943 wels u.

mak-kalokma da u. pitsma gamoaqveynes Sroma, romelSic aCvenes, rom SesaZlebelia adamianis

neironuli ujredis modelireba teqnikuri sistemis, an kompiuteris saSualebiT,

xelovnuri neironuli qselebis Seqmna da maTi saSualebiT logikuri gamoTvlebis

Sesruleba. SemovitanoT is ZirTadi terminebi, romlebic gamoiyeneba neironul qselebSi.

neironuli qselebis ZiriTadi elementia xelovnuri neironixelovnuri neironixelovnuri neironixelovnuri neironi, romlis sqemac mocemulia

sur. # 10.1. mas gaaCnia Semdegi struqtura:

sur. # 10.1. xelovnuri neironis modeli.

• Sesasvleli signalebi Sesasvleli signalebi Sesasvleli signalebi Sesasvleli signalebi ix ---- esaa monacemebi, romlebic miewodeba neirons

Sesasvlelze gare samyarodan an sxva neironebidan. Sesasvleli neironebis

diapazoni sxvadasxva modelebisaTvis SeiZleba iyos gansxvavebuli. rogorc wesi es

signalebi arian diskretuli da Rebuloben mniSvnelobebs {0,1}, {-1,1} simravleebidan

an R-dan.

• woniTi koeficientebi woniTi koeficientebi woniTi koeficientebi woniTi koeficientebi iw . woniTi koeficientebi aiReba namdvil ricxvTa

simravlidan da gansazRvraven kavSiris Zalas neironebs Soris.

• neironis aqtivaciis doneneironis aqtivaciis doneneironis aqtivaciis doneneironis aqtivaciis done. esaa sidide, romelic ganisazRvreba neironSi Semavali

signalebis Sewonili jamiT ∑ ii xw (veqtorulad WX ).

• zzzzRRRRurblovurblovurblovurblovani funqcia ani funqcia ani funqcia ani funqcia f . am funqciis daniSnulebaa aqtivaciis donis raime

zRurblTan Sedarebis gziT gamoTvalos gamosasvleli signalis mniSvneloba.

zRurblovani funqcia gansazRvravs aqtiuria Tu ara neironi.

11110000.2..2..2..2. sxvadasxva tipis neironuli qselebi. sxvadasxva tipis neironuli qselebi. sxvadasxva tipis neironuli qselebi. sxvadasxva tipis neironuli qselebi. imisaTvis, rom neironebis saSualebiT

SevasruloT seriozuli gamoTvlebi, saWiroa maTi gaerTianeba qselSi. yvelaze martiv

qsels warmoadgens neironebis jgufi, romelic gareTianebulia erT SreSi (ix. sur. # 10.2).

am suraTze neironebs warmoadgenen kvadratebi, maTSi miTiTebuli ajamvis niSniT, xolo

wreebi warmoadgenen mxolod signalebis gamanawileblebs. isini ar asruleben gamoTvlis

aranair funqcias da amitom maT ar uwodeben Sres. TiToeuli Sesasvleli signali Tavisi

∑ F (NET)

1x

2x

.

.

.

nx

(gamosasvleli)

OUT=F(NET)


sur. # 1.2. erTSriani neironuli qseli Sesabamisi woniT ukavSirdeba yvela neirons. es wonebi warmoadgenen wonebis W matricis

elementebs, romelsac aqvs m striqoni da n sveti, sadac m aris Sesasvlelebis

raodenoba, xolo n – ki neironebis ricxvi. amgvarad, N gamosasvleli, romlis

komponentebicaa neironebis OUT gamosasvlelebi, gamoiTvleba rogorc XWN =

matriculi namravli.

neironuli qseli Tavis mxriv xasiTdeba Semdegi parametrebiT:

• qselis topologiaqselis topologiaqselis topologiaqselis topologia – esaa Sabloni, romelic gansazRvravs kavSirebs calkeul

neironebs Soris

• daswavlis gamoyenebuli algoriTmidaswavlis gamoyenebuli algoriTmidaswavlis gamoyenebuli algoriTmidaswavlis gamoyenebuli algoriTmi.... neironul qselebSi SeiZleba gamoyenebuli

iyos daswavlis sxvadasxva algoriTmebi.

• kodirebis sqema.kodirebis sqema.kodirebis sqema.kodirebis sqema. gansazRvravs qselSi Semavali monacemebisa da miRebuli Sedegebis

interpretacias.

SesaZlebelia ufro rTuli, mravalSriani neironuli qselebis Sedgenac, sadac gvaqvs

ori, sami da ufro meti Sreebi. aRmoCnda, rom mravalSrian qselebs gaaCniaT ufro meti

saSualebebi, vidre erTSrian qselebs. mravalSriani qselebis Seqmnis dros yvelaze

mTavaria gaviTvaliswinoT, rom nebismieri konfiguraciis qselis Seqmnisas daculi unda

iyos Sriseburi organizacia, rac, rogorc neironuli qselebis TeoriaSi iTvleba, axdens

adamianis Tavis tvinis sxvadasxva nawilebis Sriseburi struqturebis modelirebas.

mravalSrian qselebSi erTi Sris gamosasvlelebi warmoadgenen meore Sris Sesasvlelebs.

aqedan gamomdinare, Tu gvinda, rom aseT qsels gaaCndes ufro meti gamoTvlebis unari,

saWiroa rom neironis gamaaqtivirebeli funqcia iyos arawrfivi, radganac, Tu es funqcia

iqneba wrfivi, maSin meore Sris gamosasvlelze Cven miviRebT signals

)()( 2121 WWXWXWOUT == .

∑

∑

∑

.

.

.

.

.

.

1x

2x

nx

X

leqcia #leqcia #leqcia #leqcia #10101010. . . . neironuli qselebi neironuli qselebi neironuli qselebi neironuli qselebi 101

cxadia, rom aseTive signalis miReba SegveZlo erTSriani qseliT, romlis koeficientebis

matricac iqneboda ori matricis namravli.D

11110000.3. xelovnuri neironuli qselebis swavleba..3. xelovnuri neironuli qselebis swavleba..3. xelovnuri neironuli qselebis swavleba..3. xelovnuri neironuli qselebis swavleba. yvelaze saintereso Tviseba, rac aRmoaCndaT

xelovnur neironul qselebs, aris maTi daswavlisdaswavlisdaswavlisdaswavlis unari. maTi daswavlis procesi ise

Zalian waagavs adamianis inteleqtualuri ganviTarebis process, rom erTi SexedviT

SeiZleba mogveCvenos. rom Cven marTlac Rrmad gvesmis es procesebi, magram unda

aRvniSnoT, rom xelovnuri neironuli qselebis daswavlis unari mainc aris SezRuduli

da jerjerobiT ucnobia, analogiuria Tu ara es procesebi adamianis Tavis tvinSi

mimdinare procesebisa.

daswavlis procesisdaswavlis procesisdaswavlis procesisdaswavlis procesis qveS Cven gvesmis Semdegi: mivaRwioT imas, rom Sesasvleli

signalebis raime simravlisaTvis qseli gamosasvlelze iZleodes sasurvel (an Tundac am

simravlisaTvis Sesabamis) signalebs. yoveli Sesasvleli da gamosasvleli simravle

ganixileba rogorc veqtori. daswavlis procesi xorcieldeba Sesasvleli veqtorebis

mimdevrobiTi SeyvaniT qselSi. amasTan erTdroulad xdeba garkveuli proceduris

Tanaxmad wonebis SerCeva ise, rom gamosasvlelze miviRoT sasurveli veqtori. daswavlis

procesSi wonebi TandaTanobiT Rebuloben iseT mniSvnelobebs, rom yoveli Sesasvleli

veqtori gamoimuSavebs gamosasvlel veqtors. daswavlis procesi SeiZleba

xorcieldebodes maswavleblis saSualebiT an maswavleblis gareSe.

daswavla maswavleblis saSualebiTdaswavla maswavleblis saSualebiTdaswavla maswavleblis saSualebiTdaswavla maswavleblis saSualebiT gulisxmobs, rom TiToeuli Sesasvleli

veqtorisaTvis arsebobs Sesabamisi miznis veqtori, romelic gvinda rom miviRoT

gamosasvlelze. aseT wyvils ewodeba daswavladi wyvili. rogorc wesi, qseli swavlobs

sasruli raodenobis wyvilebis saSualebiT. qsels Sesasvlelze miewodeba Sesasvleli

veqtori, gamoiTvleba gamosasvleli veqtori da xdeba misi Sedareba miznis veqtorTan.

gansxvaveba (rac warmoadgens Secdomas), ukukavSiris saSualebiT miewodeba qsels da xdeba

garkveuli algoriTmis saSualebiT wonebis Secvla ise, rom moxdes Secdomebis

minimizacia. es procedura xorcieldeba TiToeuli daswavladi wyvilisaTvis manamdis,

sanam ar miiRweva dasaSvebi done Secdomebisa mTeli dasaswavli simravlisaTvis.

miuxedavad imisa, rom daswavlis aseTi principi saSualebas iZleva gamoviyenoT

neironuli qselebi mravali praqtikuli amocanebis gadasaWrelad, mainc iTvleba, rom

aseTi midgoma arasworia, radganac SeuZlebelia warmovidginoT, rom daswavlis aseTi

meqanizmi arsebobdes adamianis Tavis tvinSi. daswavla maswavleblis gareSedaswavla maswavleblis gareSedaswavla maswavleblis gareSedaswavla maswavleblis gareSe albaT

iqneboda ufro kargi modeli Tavis tvinSi mimdinare procesebis aRsawerad. aseTi

daswavlis dros saWiro aRar aris miznis veqtori da daswavla xdeba mxolod Sesasvleli

veqtorebis saSualebiT. amasTan daswavlis mizania gadaewyos wonebi ise, rom ori,

sakmarisad axlos mdgomi Sesasvleli veqtorisaTvis gamosasvleli veqtori iyos erTi da

igive. daswavlis procesi am SemTxvevaSi gamoyofs dasaswavli simravlis statistikur

maxasiaTeblebs da ajgufebs msgavs veqtorebs erT klasSi. mocemuli klasis veqtoris

miwodeba Sesasvlelze mogvcems garkveul veqtors gamosasvleze, magram sanam ar

damTavrdeba daswavla, SeuZlebelia vicodeT, ra saxis iqneba es veqtori.

11110000.4. .4. .4. .4. erTerTerTerTSriani Sriani Sriani Sriani perceptroni. perceptroni. perceptroni. perceptroni. pirveli neironuli qseli, romelsac SeeZlo aRqma

(percepcia) da garkveuli reaqciis formireba am aRqmaze iyo f. rozenblatis perceptroni. perceptroni. perceptroni. perceptroni.


avtori Tvlida rom es iyo Tavis tvinis muSaobis modeli. f. rozenblati am models,

romelic Seiqmna kornelis saaviacio laboratoriaSi MARK-1 saxeliT, uwodebda samSrian

perceptrons, magram dRevandeli terminologiiT is warmoadgens erTSrian neironul

qsels. perceptronis Semavali cvladebi ( ix ) Rebuloben mxolod or mniSvnelobas -1 an

1, xolo wonebi – mniSvnelobebs namdvil ricxvTa simravlidan. aqtivaciis done

gamoiTvleba rogorc Semavali monacemebis Sewonili jami ∑ ii wx . perceptronis

gamomavali mniSvneloba gamoiTvleba mkacri zRurbluri funqciis saSualebiT: Tu

aqtivaciis done metia an toli zRurblur mniSvnelobaze, perceptronis gamosasvleli

tolia 1-s, winaaRmdeg SemTxvevaSi -1-s. amgvarad perceptronis gamomavali mniSvnelobebi

gamoiTvleba Semdegnairad: XW = 1, Tu ∑ ≥ twx ii da XW = 1− , Tu ∑ < twx ii .

perceptronis wonebis regulirebisaTvis gamoiyeneba swavlebis martivi algoriTmi

maswavlebliT, anu perceptrons Sesasvlelze miewodeba dasaswavli wyvilis pirveli

elementi, perceptroni gamoTvlis gamosasvlel veqtors da amis Semdeg mas uCveneben Tu

ra Sedegi unda mieRo. perceptronis wonebs cvlian iseTnairad, rom Semcirdes Secdomebi

mis gamosasvlelze. am dros gamoiyeneba Semdegi wesi: vTqvaT c aris swavlebis siCqaris

mudmivi koeficienti, xolod d – gamosasvlelis mosalodneli mniSvneloba. Semavali

veqtoris i -uri komponentis woniTi koeficientis koreqtireba xdeba Semdegi formuliT:

∑−=∆ iiii xwxsigndcw ))((

sadac ∑ )( ii wxsign aris perceptronis gamomavali mniSvneloba, romelic tolia +1, an -1.

sxvaoba sasurvel da realur gamomaval mniSvnelobebs Soris SeiZleba iyos 0, 2 an -2.

Sesabamisad Semavali veqtoris yoveli komponentebisaTvis daswavlis algoriTmi asrulebs

Semdeg moqmedebebs:

• Tu sasurveli da realuri gamosasvleli veqtorebi erTmaneTs emTxveva, wonebi ar

icvleba;

• Tu realuri gamosasvleli veqtoris mniSvnelobaa -1, xolo sasurvelis ki 1, maSin

i -uri Sesasvlelis woniTi koeficienti izrdeba icx2 -iT;

• Tu realuri gamosasvleli veqtoris mniSvnelobaa 1, xolo sasurvelis ki -1, maSin

i -uri Sesasvlelis woniTi koeficienti mcirdeba icx2 -iT.

daswavlis am meTods uwodeben deltadeltadeltadelta----wess.wess.wess.wess.

rogorc ukve vnaxeT, qselis Semavali monacemebi warmoadgenen n ganzomilebian

veqtors da gansazRvraven n ganzomilebian sivrces, amitom klasifikaciis swavlebis

amocana daiyvaneba am sivrceSi hipersibrtyeebis saSualebiT sxvadasxva klasis wertilebis

raime jgufebad gancalkavebis amocanaze.

f. rozenblatma daamtkica Teorema perceptronis daswavladobis daswavladobis daswavladobis daswavladobis Sesaxeb, romlis

Tanaxmadac perceptrons SeuZlia iswavlos yvelaferi, risi warmodgenac mas SeuZlia. am

damtkicebis qveS igulisxmeba, rom daswavlis procesi aris sasrulo. aq mTavaria

gavarCioT Tu ra gansxvavebaa warmodgenasa warmodgenasa warmodgenasa warmodgenasa da daswavlasdaswavlasdaswavlasdaswavlas Soris. warmodgenis cnebis qveS

igulisxmeba perceptonis unari moaxdinos garkveuli funqciis modelireba, daswavla ki

leqcia #leqcia #leqcia #leqcia #10101010. . . . neironuli qselebi neironuli qselebi neironuli qselebi neironuli qselebi 103

niSnavs qselis wonebis regulirebis iseTi sistematuri proceduris arsebobas, romelic

uzrunvelyofs am funqciis realizacias.

11110000....5555 ra ar SeuZlia erTSrian perceptrons. ra ar SeuZlia erTSrian perceptrons. ra ar SeuZlia erTSrian perceptrons. ra ar SeuZlia erTSrian perceptrons. rogorc vnaxeT, perceptrons SeuZlia

yvelafris daswavla, risi warmodgenac SesaZlebelia perceptronSi. samwuxarod, rogorc

mogvianebiT (1969 wels) m. minskma da s. peipertma aCvenes, arsebobs Zalian bevri martivi

funqciebi, romelTa warmodgena perceptrons ar SeuZlia. ganvixiloT erTerTi Zalian

martivi funqcia - “gamomricxavi an” funqcia anu operacia XOR. es logikuri funqcia “an “

funqciisagan gansxvavadeba imiT, rom Rebulobs mniSvnelobas noli maSin, rodesac

cvladebs aqvT erTnairi mniSvnelobebi. ganvixiloT perceptroni ori SesasvleliT 1x Nda

2x da ori woniTi koeficientiT 1w da 2w da zRurbliT t . perceptronis muSaobis

principis Tanaxmad, Cven miviRebT Semdeg utolebebs:

w1*1+ w2*1 < t (WeSmaritobis cxrilis pirvel striqonidan)

w1*1+ 0 > t (WeSmaritobis cxrilis meore striqonidan)

0+ w2*1 >t (WeSmaritobis cxrilis mesame striqonidan)

0+0<t (WeSmaritebis cxrilis bolo striqonidan).

bolo utolobidan gamodis rom zRurbli aris dadebiTi.

utolobaTa am sistemas amonaxsni ar gaaCnia, riTac mtkicdeba rom perceptrons ar

SeuZliaT gadawyvitos “gamomricxavi an” – is problema.

“gamomricxavi an” amocanis amoxsnis SeuZlebloba perceptronisaTvis aixsneba imiT,

rom ori klasi, romlebic unda ganacalkeos qselma, ar warmoadgenen wrfivad gayofad

klasebs, anu Tu 1x da 2x warmoadgenen X veqtoris koordinatebs, sibrtyeze SeuZlebelia

iseTi wrfis gatareba, romelic erTmaneTisagan gamoyofs wertilTa Semdeg simravleebs:

{(0,0), (1,1)} da {(1,0), (0,1)}. (ix. sur. #10.3)

sur. #10.3. “gamomricxavi an” – is problema, sibrtyeze

SeuZleblia iseTi wrfis gatareba, romelic

gayofs erTmaneTisagan TeTr da Sav wertilebs


1. ras warmoadgens xelovnuri neironi da ra funqciebis ganxorcieleba SeuZlia mas?


2. ganmarteT terminebi: Sesasvleli signalebi, woniTi koeficienti, neironis

aqtivaciis done, zRurblovani funqcia.

3. rogor sistemas ewodeba erTSriani neironuli qseli?

4. ra gansakuTrebuli Tviseba aRmoaCndaT neironul qselebs?

5. ras niSnavs daswavla maswavlebliT? maswavleblis gareSe?

6. ra aris preceptoni?

7. CamoayalibeT Tqveni sityvebiT saxeTa klasifikaciis amocana.


1. aageT mak kalokisa da pitsis neironi, romelic gamoiTvlis logikuri implikaciis

funqcias.

2. programulad moaxdineT iseTi xelovnuri neironebis modelireba, romlebic

Seasruleben elementarul logikur funqciebs.

lllleqcia # 1eqcia # 1eqcia # 1eqcia # 11111....

neironuli qselebi (gagrZeleba)neironuli qselebi (gagrZeleba)neironuli qselebi (gagrZeleba)neironuli qselebi (gagrZeleba)

11111111.1. perceptronis gamoyeneba saxeTa klasifikaciis amocanisaTvis. .1. perceptronis gamoyeneba saxeTa klasifikaciis amocanisaTvis. .1. perceptronis gamoyeneba saxeTa klasifikaciis amocanisaTvis. .1. perceptronis gamoyeneba saxeTa klasifikaciis amocanisaTvis. saxeTa klasifikaciis

amocana umartivesi SemTxvevisaTvis SeiZleba aRvweroT Semdegnairad: davuSvaT, mocemuli

gvaqvs obieqtebis erToblioba, romlebic gvinda gavyoT or klasad. magaliTad, gvinda

ganvasxvaoT erTmaneTisagan samkuTxedebi da oTxkuTxedebi. imisaTvis, rom SesaZlebeli

iyos neironul qsels (perceptrons) vaswavloT am ori klasis erTmaneTisagan garCeva,

pirvel rigSi saWiroa gvqondes Semfasebeli funqcia, romelic mogvcems saSualebas

mivakuTvnoT es obieqtebi ama Tu im klass. klasifikatoris mier gamovlenili monacemTa

yoveli jgufi SeiZleba warmodgenili iyos raime ares saSualebiT mravalganzomilebian

sivrceSi. yoveli iR klass Seesabameba am aresTan kuTvnilebis xarisxis ganmsazRvrelikuTvnilebis xarisxis ganmsazRvrelikuTvnilebis xarisxis ganmsazRvrelikuTvnilebis xarisxis ganmsazRvreli

ig diskriminantuli funqcia. yvela aseT ig diskriminantul funqciebs Soris

maqsimaluri mniSvneloba iR aresaTvis aqvs iseT ig funqcias, romlisTvisac sruldeba

piroba: )()( xgxg ji > yoveli nj <<1 . yvelaze martiv SemTxvevaSi am funqciis

mniSvnelobebi SeiZleba iyos {-1,1} simravle, anu obieqti ekuTvnis mocemul simravles (1)

da obieqti ar ekuTvis mocemul simravles (-1). ufro mniSvnelovani SemTxvevaa, rodesac

diskriminantuli funqcia warmoadgens mikuTvnebis Sefasebas ares raime centraluri

wertilidan manZilis safuZvelze. aseT SemTxvevaSi klasifikacias uwodeben klasifikacias klasifikacias klasifikacias klasifikacias

minimaluri manZiliT.minimaluri manZiliT.minimaluri manZiliT.minimaluri manZiliT. Tu ori iR da jR klasebi warmoadgenen mosazRvre klasebs, maSin

arsebobs sazRvari, romlisTvisac 0)()( =− xgxg ji . ganvixiloT magaliTi, davuSvaT,

simravle, romlis safuZvelzec unda vaswavloT perceptrons saxeTa gamocnoba

warmoadgens simravles, romelic mocemulia Semdegi cxriliT:

1x 2x )(NETf

1,0 1,0 1 9,4 6,4 -1 2,5 2,1 1 8,0 7,7 -1 0,5 2,2 1 7,9 8,4 -1 7,0 7,0 -1 2,8 0,8 1 1,2 3,0 1 7,8 6,1 -1

cxrilis pirveli ori sveti Seicavs monacemTa veqtorebs, romlebic gamoiyenebian qselis

swavlebisaTvis. mesame svetSi warmodgenilia klasifikaciis mosalodneli Sedegebi +1 an -

1, romlebic gamoiyenebian qselis swavlebisaTvis.

am monacemebisaTvis sur. # 11.1 moyvanilia maTi ganlageba sibrtyeze da maT Soris

wrfe, romelic warmoadgens sazRvars am or simravles Soris. Tu SesaZlebelia klasebis


wrfivad gayofa, rogorc es xdeba sur. # 11.1., maSin orive klasis diskriminantuli

funqciebi )(xgi da )(xg j warmoadgenen wrfes. radganac wrfe aris iseTi wertilebis

erToblioba, romelic romlebic Tanabari manZilebiT arian daSorebuli ori fiqsirebuli

wertilidan, gamodis, )(xgi da )(xg j funqciebi warmoadgenen TiToeuli ares dekartuli

centridan minimaluri manZilis funqciebs.

sur. # 12.1. monacemebis ganlageba sibrtyeze.

wrfivi gamyofi funqcia SeiZleba gamovTvaloT perceptronis saSualebiT romelic

mocemulia sur. #11.2. igi Seicavs or Cveulebriv Sesavals da erT zRurblur Sesavals

mudmivi mniSvnelobiT 1. perceptroni asrulebs gamoTvlebs Semdegi formuliT:

)1()( 32211 wxwxwfNETf ++=

sadac )()( xsignxf = .Tu 1)( +=xf , maSin x ekuTvnis erT klass da Tu 1)( −=xf , maSin

igi ekuTvnis sxva klass. aseT gardaqmnas ewodeba wyvetil-wrfivi bipolaruli

zRurbluri funqcia.

sur. # 11.2. perceptroni, romelic gamoiyeneba saxeTa klasifikaciisaTvis.

zRurbluri Sesasvleli emsaxureba zRurbluri funqciis gadaadgilebas

vertikaluri RerZis gaswvriv. am gadaadgilebis sidide ganisazRvreba swavlebis procesSi

∑ F (NET)

1x

2x

3x (gamosasvleli)

OUT=F(NET)

zRurbli

leqcia #leqcia #leqcia #leqcia #11111111. . . . neironuli neironuli neironuli neironuli qselebi (gagrZeleba)qselebi (gagrZeleba)qselebi (gagrZeleba)qselebi (gagrZeleba) 107

3w woniTi koeficientis daxmarebiT. daviwyoT perceptronis swavleba. amisaTvis

SevarCioT wonebis sawyisi mniSvnelobebi SemTxveviTad, magaliTad [0,75; 0,5; -0,6]. imisaTvis,

rom gavarCioT, romeli monacemebisTvis viTvliT funqciis mniSvnelobas, davumatoT

funqcias zeda indeqsi nNETf )( daviwyoT cxrilis pirveli striqonidan.

1)65,0()16,015,0175,0()( 1 ==⋅−⋅+⋅= ffNETf

radgan funqciis mniSvneloba miviReT erTis toli da is emTxveva cxrilis mniSvnelobas,

amitom woniTi koeficientebis cvlileba ar aris saWiro. Sesabamisad meore wyvilisTvisac

gamoviyenebT igive woniT koeficientebs.

1)65,9()16,04,65,04,975,0()( 2 ==⋅−⋅+⋅= ffNETf

mocemuli wyvilisaTvis gamosasvleze unda migveRo -1, amitom saWiroa woniTi

koeficientebis Secvla zemoTmoyvanili wesis Tanaxmad

11111 )))sgn((( −−−−− −+= ttTtttt XXWdcWW

sadac c aris daswavlis mudmivi koeficienti, x da w -Sesavlis da woniTi

koeficientebis veqtorebi t – swavlebis iteraciis nomeri, T - transponirebis simbolo,

1−td mosalodneli Sedegi )1( −t dros momentSi (am SemTxvevaSi 2=t ). 2=t mniSvnelobis

dros qselis gamosasvleli tolia 1-is, nacvlad -1-isa, amitom Semdegi wyvilisaTvis

woniTi koeficientebi Seicvleba da miviRebT

−−−

=

−

−=−−+=

1

06,2

01,3

1

4,6

4,9

4,0

6,0

5,0

75,0

)11(2,0 223 XWW

axla saWiroa gamovTvaloT qselis gamomavali mniSvnelobebi swavlebis mesame

magaliTisaTvis agebuli wonebis gaTvaliswinebiT miviRebT, rom .1)( 3 −=NETf

es mniSvneloba isev ar emTxveva mosalodnel gamosasvlels. Semdegi iteraciis dros

kvlav moxdeba wonebis ganaxleba igive formuliT. perceptronis qsels swavlebis aTi

iteraciis Semdeg formirdeba wrfivi gayofadoba, romelic mocemulia sur. #10.4.

daaxloebiT swavlebis 500 bijis Semdeg woniTi koeficientebis veqtori miiRebs

mniSvnelobas: [-1,3; -1,1; 10,9]. Cven gvainteresebs ori klasis wrfivi gayofa. )(xgi da )(xg j

diskriminantuli funqciebis terminebSi gamyofi zedapiri warmoadgens wertilTa

simravles, romelTaTvisac 0)()( =− xgxg ji , e.i. aqtivaciis done tolia 0-is. qselis

funqcionirebis gantoleba SeiZleba CavweroT wonebis terminebiT, Semdegi saxiT:

32211 wxwxwnet ++=

Sesabamisad or klass Soris wrfivi gamyofi zedapiri ganisazRvreba wrfivi gantolebiT:.

.09.10)1,1(3,1 21 =+−+− xx

11111111....2222. delta . delta . delta . delta ––––wwwwesis ganzogadeba. esis ganzogadeba. esis ganzogadeba. esis ganzogadeba. imisaTvis, rom ganvazogadoT perceptronis idea da avagoT

daswavlis ufro daxvewili algoriTmebi, saWiroa SevcvaloT misi zRurblovani funqcia

da gavxadoT is ufro moqnili da uwyveti funqcia, romelic saSualebas mogvcems ufro


zustad gamovTvaloT wonebi. erTerT aseT funqcias warmoadgens sigmoiduri funqcia,

romelmac Tavisi saxeli miiRo laTinur S-Tan msgavsebis gamo.

sur. # 11.3 aqtivaciuri fuqciebi: a) wyvetil-wrfivi bipolaruli zRurbluri funqcia;

b) sigmoiduri unipolaruli zRurblovani funqcia; g) waZruli sigoiduri

sxvadasxva simrudis funqcia. rac ufro didia parametris mniSvneloba, miT

ufro axlosaa funqciis aproqsimacia wyvetil-wrfiv funqciasTan G

tipuri sigmoiduri aqtivaciuri funqcia anu logistikuli funqcia moicema

gantolebiT: )1(1)( neteNETf ⋅−+= λ sadac ∑= ii wxNET . aq λ aris simrudis

(amozneqilobis parametri), romelic gamoiyeneba sigmoiduri wiris formis agebisaTvis. λ – s didi mniSvnelobebisTvis sigmoidas forma uaxlovdeba Cveulebriv wyvetil-wrfiv

zRurblur funqcias, romlis mniSvnelobebi moTavsebulia {0,1} diapazonSi, xolo

simrudis parametris im mniSvnelobebisaTvis romlebic axlos arian 1-Tan, sigmoiduri

wiri hgavs swor xazs. zRurbluri funqciis arguments warmoadgens neironis aqtivaciis

done, xolo misi mniSvnelobaa neironis gamosasvleli. sigmoiduri aqtivaciuri funqcia

aris uwyveti rac, iZleva qselis gamosasvlelze Secdomebis ufro zustad Sefasebis

saSualebas. Cveulebrivi zRurbluri funqciis msgavsad, sigmoiduri aqtivaciuri funqcia

f(x) 1 x -1

f(x) 1 0 x

a) b)

f(x) 1 didi λ

patara λ 0 x

g)


asaxavs gansazRvris aris wertilebs (0,1) intervalSi moTavsebuli mniSvnelobebSi. Tumca

unda iTqvas isic, rom Cveulebrivi zRurbluri funqciisgan gansxvavebiT sigmoidas

SeuZlia miiRos mniSvnelobebi mTeli intervalidan. e.i. is uzrunvelyofs klasikuri

zRurbluri funqciis uwyvet aproqsimacias. λ parametri gansazRvravs gadasvlis simrudes. zRurblis Sewonili mniSvneloba gadaadgilebs funqciis grafiks abscisaTa

RerZis gaswvriv.

sur. 11.4 Secdomis organzomilebiani sibrtye.

c konstanta gansazRvravs daswavlis bijis zomas.

uwyveti aqtivaciuri funqciebis mqone qselebis gamoCenam istoriulad ganapiroba

Secdomebis koreqciaze dafuZnebuli swavlebis axali midgomebi. magaliTad, vidrou-hofis

daswavlis wesi gvTavazobs saSualo kvadratuli Secdomebis minimizacias gamomaval

mniSvnelobasa da qselis aqtivaciis dones Soris imis miuxedavad Tu rogori saxe aqvs

aqtivaciur funqcias, magram uwyveti aqtivaciuri funqciebis mqone qselebisaTvis

swavlebis yvelaze mniSvnelovan wess warmoadgens deltadeltadeltadelta----wesiwesiwesiwesi. intiuciurad delta-wesi

efuZneba iseT cnebas, rogoricaa Secdomis zedapiriSecdomis zedapiriSecdomis zedapiriSecdomis zedapiri (sur. #11.4), romelic monacemTa mTel

nakadisaTvis jamur Secdomas gansazRvravs rogorc funqcias damokidebuls qselis

wonebze. wonebis yoveli SesaZlo konfiguracia gansazRvravs Secdomis zedapiris

wertils. gvaqvs ra wonebis garkveuli konfiguracia, swavlebis algoriTmis saSualebiT

SeiZleba vipovoT am zedapirze mimarTuleba, romlis gaswvrivac yvelaze swrafad xdeba

Secdomis funqciis Semcireba. am midgomas ewodeba swavleba gradientuli daSvebis gradientuli daSvebis gradientuli daSvebis gradientuli daSvebis

meTodiTmeTodiTmeTodiTmeTodiT, radganac gradienti gansazRvravs zedapiris daxrilobas mis yovel wertilSi.

deltadeltadeltadelta----wesiwesiwesiwesi gvTavazobs uwyveti da diferencirebadi aqtivaciuri funqciis

gamoyenebas. es Tvisebebi gaaCnia zemod ganxilur logistikur funqcias. delta-wess

qselis i -uri kvanZis j -uri woniTi koeficientis regulirebisaTvis aqvs Semdegi saxe:

Secdomis zedapiri

lokaluri minimumi

W axali mniSvneloba

W Zveli mniSvneloba

E

W

c


jiii xnetfOdc )()( ′−

sadac c aris swavlebis siCqarisswavlebis siCqarisswavlebis siCqarisswavlebis siCqaris mudmivi koeficienti mudmivi koeficienti mudmivi koeficienti mudmivi koeficienti, id da iO O i -uri neironis

mosalodneli da realuri gamosasvlelebi, f ′ i -uri kvanZis aqtivaciuri funqciis

warmoebuli, xolo jx i -uri kvanZis j -uri Sesasvlelis mniSvneloba. vaCvenoT Tu saidan

gamodis es formula. qselis gamosasvlelze saSualokvadratuli Secdoma proporciulia

yoveli kvanZisaTvis Secdomebis kvadratebis jamisa da gamoiTvleba formuliT

∑ −=i

ii OdE 2)(21

sadac id aris neironis gamosasvlels mosalodneli mniSvneloba, xolo iO –misi

realuri mniSvneloba. ajamvis dros xdeba Secdomebis kvadratSi ayvana, imisaTvis, rom

dadebiTma da uaryofiTma Secdomebma ar moaxdinon erTmaneTis kompensireba.

ganvixiloT SemTxveva, roca qseli Sedgeba neironis erTaderTi (gamosasvleli)

Srisagan. Tavdapirvelad aucilebelia ganvsazRvroT qselis yovel gamosasvlel neironze

Secdomis cvlilebis siCqare. amisaTvis unda aviRoT kerZo warmoebuli, romelic

gansazRvravs veqtoruli cvlilebis siCqares, misi erT-erTi cvladis mixedviT. zogadi

Secdomis kerZo warmoebuli gamomavali Sris yoveli i -uri neironisaTvis iqneba

)()(21

)(21 2

iii

ii

i

iii

i

OdO

Od

O

Od

O

E −−=∂

−∂=

∂

−∂=

∂∂ ∑

.

aseTi gamartiveba SesaZlebelia imitom, rom gansaxilveli qseli Seicavs neironebis

mxolod erT gamomaval Sres da aqedan gamomdinare Secdoma erTerTi kvanZis

gamosasvlelze ver moaxdens gavlenas sxva neironebze. ganvsazRvroT Secdomis cvlilebis

siCqare i -uri kvanZis yoveli kw woniTi koeficientisaTvis. amisaTvis gamovTvaloT

Secdomis funqciis kerZo warmoebuli yoveli kvanZisaTvis, kw woniTi koeficientebis

mixedviT, romelsac mivyavarT am kvanZamde.

k

i

ik w

O

O

E

w

E

∂∂

⋅∂∂=

∂∂

anu k

iii

k w

OOd

w

E

∂∂

−−=∂∂

)( .

ganvixiloT am gamosaxulebis marjvena mxare, sadac gamoiTvleba i -uri neironis realuri

gamomavalis kerZo warmoebuli kavSirebis im woniTi koeficientebis mixedviT, romlebsac

mivyavarT am neironTan. neironis gamosasvleli mniSvneloba woniTi koeficientebis

saSualebiT gamoisaxeba Semdegi saxiT:

)( iii XWfO = , sadac iii netXW =

radgan f am SemTxvevaSi uwyveti funqciaa, SeiZleba gamovTvaloT misi warmoebuli.

)( ikk

i netfxw

O ′⋅=∂∂

maSin kiiik

xnetfOdw

E)()( ′−−=

∂∂

Secdomis minimizaciisaTvis aucilebelia SevcvaloT wonis mniSvneloba antigradientis

mimarTulebiT, saidanac miviRebT, rom


kiiikiiik

k xnetfOdcxnetfOdcw

Ecw )()(])()([ ′−=′−−−=

∂∂−=∆

unda aRiniSnos, rom iseve rogorc lokaluri pikis Zebnis algoriTmi, delta

wessac ar SeuZlia gaarCios lokaluri minimumi globalurisagan, rac iwvevs am wesis

aramdgradobas. delta wesis efeqturobaze arsebiT gavlenas axdens agreTve swavlebis

siCqaris c koeficienti. (ix. sur. #11.4.). am koeficientis mniSvneloba gansazRvravs

swavlebis yovel bijze wonebis cvlilebis sidides. rac ufro didia c , miT ufro Cqara

midis wona optimalur mniSvnelobamde. Tumca Tu c koeficienti Zalian didia, algoriTmi

SeiZleba gascdes eqtremumis wertils an daiwyos rxeva mis irgvliv. swavlebis siCqaris

koeficientis mcire mniSvnelobebi saSualebas iZlevian aRmovfxraT es problema, magram es

iwvevs swavlebis procesis Senelebas.

sakontrolosakontrolosakontrolosakontrolo kiTxvebi: kiTxvebi: kiTxvebi: kiTxvebi:

8. ras warmoadgens xelovnuri neironi da ra funqciebis ganxorcieleba SeuZlia mas?

9. ganmarteT terminebi: Sesasvleli signalebi, woniTi koeficienti, neironis

aqtivaciis done, zRurblovani funqcia.

10. rogor sistemas ewodeba erTSriani neironuli qseli?

11. ra gansakuTrebuli Tviseba aRmoaCndaT neironul qselebs?

12. ras niSnavs daswavla maswavlebliT? maswavleblis gareSe?

13. ra aris preceptoni?

14. CamoayalibeT Tqveni sityvebiT saxeTa klasifikaciis amocana. 15. rogori tipis SeiZleba iyos zRurblovani funqcia? 16. ras warmoadgens ganzogadoebuli delta wesi? 17. ra ar SeuZlia erTSrian perceptons?


1. aageT neironis sqema, romelic gamoiTvlis logikur funqcias “implikacia”. 2. leqciaSi ganxiluli magaliTisaTvis gamoiyeneT ganzogadoebuli delta wesi da

gansazRvreT rogori saxe eqneba gamyof wrfes.

leqcia #leqcia #leqcia #leqcia # 11112222

mravalSriani neironuli qselebimravalSriani neironuli qselebimravalSriani neironuli qselebimravalSriani neironuli qselebi

11112222....1111.... mravalSriani perceptronebi. mravalSriani perceptronebi. mravalSriani perceptronebi. mravalSriani perceptronebi. wrfivi gayofadobis problemis gamovlenis Semdeg aSkara

gaxda, rom erTSriani perceptronebi am problemis gadasawyvetad ver gamodgeboda. amitom

gaCnda idea mravalSrianimravalSrianimravalSrianimravalSriani perceptronebis. ra SesaZleblobebi emateba perceptrons, Tu is

Seicavs erT Sreze met Sres? ganvixiloT orSriani perceptroni, romelic Sedgeba sami

sur. # 12.1. orSriani perceptroni, romelsac SeuZlia

“gamomricxavi an” operaciis ganxorcieleba.

neironisagan ix. sur. #12.1). aq pirvel SreSi ganlagebulia ori neironi, romlebic axdenen

“da” da “an” logikuri operaciebis ganxorcielebas, xolo meore Sris erTaderTi

elementi asrulebs “ gamomricxavi an” operacias. es magaliTi gviCvenebs, rom

mravalSriani perceptronebis saSualebiT SesaZlebelia ufro rTuli procesebis

modelireba da saxeTa klasifikaciis ufro saintereso SemTxvevebis gadaWra.

11112222.2..2..2..2. pirdapiri gavrcelebis neironuli qselpirdapiri gavrcelebis neironuli qselpirdapiri gavrcelebis neironuli qselpirdapiri gavrcelebis neironuli qselebi. ebi. ebi. ebi. neironul qsels, romelSic arsebobs

ramdenime Sre da d Sris yvela elementi iRebs Sesasvlel signalebs )1( −d Sris yvela

neironisagan da gadascems gamosasvlel signalebs )1( +d Sris yvela elements, uwodeben

pirdapiri gavrcelebispirdapiri gavrcelebispirdapiri gavrcelebispirdapiri gavrcelebis neironul qselebs gafarToebuli delta wesigafarToebuli delta wesigafarToebuli delta wesigafarToebuli delta wesi warmoadgens

daswavlis algoriTms aseTi qselebisaTvis.

signalis mravalSriani damuSavebis dros, Secdoma qselis gamosasvlelze SeiZleba

gamowveuli iyos mis SigniT mimdinare rTuli procesebis Sedegad. amitom qselis

gamosasvlel SreSi Secdomis wyaro unda gaanalizdes kompleqsurad. Secdomis Secdomis Secdomis Secdomis

ukugavrcelebis meTodiukugavrcelebis meTodiukugavrcelebis meTodiukugavrcelebis meTodi, romelsac exla Cven ganvixilavT, uzrunvelyofs wonebis agebas

mravalSriani neironuli qselis struqturis gaTvaliswinebiT.

am midgomis Tanaxmad, Secdoma qselis gamosasvlelze vrceldeba ukumimarTulebiT

dafarul Sreebisaken. dafaruli dafaruli dafaruli dafaruli ewodeba yvela Sres, romlebic moTavsebulni arian

Sesasvlelsa da gamosasvlel Sres Soris. swavlebis delta-wesiT analizisas ar aris

rTuli imis SeniSvna, rom mTeli informacia, romelic aucilebelia neironis wonebis

modifikaciisaTvis, garda TviT Secdomis sididisa, ekuTvnis mxolod am neirons.

gamosasvleli Sris neironebisaTvis Secdomis sidide gamoiTvleba ubralod, rogorc

sxvaoba mosalodneli da rTul gamosasvlel mniSvnelobebs Soris. dafaruli Sreebis

da

an

2221 11 xx +− ),( 21 xxXOR

1x

2x

21x

22x

leqcia #leqcia #leqcia #leqcia #11112222. . . . mravalSriani neironuli mravalSriani neironuli mravalSriani neironuli mravalSriani neironuli qselebi qselebi qselebi qselebi 113

sur. # 12.2. Secdomis ukugavrceleba dafarul Srian neironul qselSi

kvanZebisaTvis ki Secdomis gansazRvra mniSvnelovnad ufro rTulia. ukugavrcelebis

meTodis gamoyenebis dros aqtivaciur funqciad rogorc wesi irCeven logistikur

funqcias: )1(1)( neteNETf ⋅−+= λ sadac ∑= ii wxNET .

am funqciis gamoyeneba ganpirobebulia sami mizeziT:

1. igi ekuTvnis sigmoiduri funqciebis klass.

2. radgan funqcia uwyvetia, amitom misi warmoebuli arsebobs yovel wertilSi.

3. vinaidan warmoebulis maqsimaluri mniSvneloba Seesabameba funqciis yvelaze ufro

swrafi cvlilebis segments, amitom udidesi Secdoma Seesabameba im kvnaZebs,

romlebisTvisac aqtivaciis done yvelaze naklebad aris gansazRvruli da bolos, am

funqciis warmoebuli advilad gamoiTvleba TviT am funqciis saSualebiT:

))).(1()(())1(1()( NETfNETfeNETf net −⋅=′+=′ − λλ

11112222.3. Secdomis ukugavrcelebis meTodi. .3. Secdomis ukugavrcelebis meTodi. .3. Secdomis ukugavrcelebis meTodi. .3. Secdomis ukugavrcelebis meTodi. ukugavrcelebis meTodi warmoadgens delta-wesis

ganzogadoebas. am SemTxvevaSic gamoiyeneba wina leqciebSi aRwerili gradientuli

daSvebis meTodi. dafaruli Sris kvanZebisaTvis Secdoma gamoiTvleba gamomavali Sris

Secdomis safuZvelze. k da i neironebs Soris kavSiris kiw woniTi koeficientis

cvlileba Secdomebis ukugavrcelebis meTodis gamoyenebis SemTxvevaSi gamoiTvleba

formulebiT:

kiiiiki xOOOdcw )1()( −−−=∆ λ

Sesasvleli Sris kvanZebisaTvis da

gamosasvleli Sre

dafaruli Sre

Sesasvleli Sre

informaciis pirdapiri gavrceleba qselSi

Secdomis ukugavrceleba


∑ −−−∆j

kijjiiki xwdeltaOcOw )()1(λ

dafaruli Sreebis kvanZebisaTvis.

meore formulaSi j aris im Semdegi Sris kvanZis indeqsi, sadamdec vrceldeba signali i -

uri neironidan da

).1()( iiiij

j OOOdnet

Edelta −−=

∂∂−=

gamovTvaloT am funqciis warmoebuli. jer aviRoT pirveli formulis warmoebuli. is Cven

ukve gvqonda, rodesac viTvlidiT delta wess.

kiiik

xnetfOdw

E)()( ′−−=

∂∂

rogorc ukve vnaxeT,

))(1)(()( netfnetfnetf −=′ λ .

gavixsenoT, rom ii Onetf =)( , miviRebT

kiiiiik

xOdOOdw

E)()( −−−=

∂∂ λ

radgan Secdomis minimizaciisaTvis wonebi unda icvlebodes gradientis sawinaaRmdego

mimarTulebiT, maSin i -uri neironisaTvis woniTi koeficientis cvlilebis gamoTvlisas es

warmoebuli unda gavamravloT c− -ze:

kiiiik xOOOdcw )1()( −−−=∆

gamoviyvanoT dafaruli SreebisaTvis wonebis agebis formula. simartivisaTvis dasawyisSi

davuSvaT, rom qseli Seicavs mxolod erT dafarul Sres. aviRoT erTi i -uri neironi

dafaruli Sridan da gavaanalizoT misi wvlili saerTo SecdomaSi qselis

gamosasvlelze. amisaTvis ganvixiloT i -uri neironis wvlili gamomavali Sris j -uri

sur. #12.3. i -uri neironis ∑∑∑∑ ⋅⋅⋅⋅−−−− ijj wdeltaa mTliani wvliliSecdomaSi qselis

gamosasvlelze, romelic miiReba mxedvelobaSi kiw woniTi koeficientis agebisas.

1 2 j

1 2 i

1 2 k

kiw


neironis gamosasvlelze arsebul SecdomaSi, xolo Semdeg SevkriboT es wvlilebi

gamomavali Sris yvela elementisaTvis da bolos gaviTvaliswinoT i -ur neironTan

kavSiris k -uri woniTi koeficientis mTliani Secdoma. es situacia aRwerilia sur. # 12.3.

jer ganvixiloT qselis Secdomis kerZo warmoebuli dafaruli Sris SecdomaSi i -uri

neironis gamosasvlelis mixedviT, amisaTvis SegviZlia visargebloT igiveobiT:

i

j

ji O

net

net

E

O

E

∂∂

⋅∂

∂=∂∂

am damokidebulebis marjvena mxaris pirveli mamravli, aRebuli sawinaaRmdego niSniT,

iqneba jdelta . maSin gveqneba, rom

i

jj

i O

netdelta

O

E

∂∂

⋅−=∂∂

.

gavixsenoT, rom jnet gamosasvleli Sris j -uri neironis aqtivaciis done gamoiTvleba

rogorc dafaruli Sris woniTi koeficientebisa da gamosasvlelebis namravlis jami

∑=i

ijj Ownet

radgan kerZo warmoebuli gamoiTvleba jamis mxolod erTi koponentis – i da j

neironebs Soris kavSiriT iji

j wO

net=

∂∂

, sadac ijw aris dafaruli Sris i -ur neironsa da

gamomaval Sris j -ur neirons Soris kavSiris wona. Tu CavsvaT am Sedegs Secdomis

warmoebuls formulaSi miviRebT:

ijji

wdeltaO

E −=∂∂

.

avjamoT es gamosaxuleba i -uri neironis yvela kavSirebiT gamosasvlel SresTan:

∑−=∂∂

jijj

i

wdeltaO

E.

es toloba gansazRvravs qselis gamosasvlelze Secdomis damokidebulebas dafaruli

Sris i -uri neironis gamosasvlelze. ganvsazRvroT exla idelta mniSvneloba – qselis

Secdomis damokidebuleba dafaruli Sris i -uri neironis aqtivaciis doneze.. es mogvcems

saSualebas, miviRoT qselis Secdomis damokidebuleba i -uri kvanZis Semavali kavSirebis

woniT koeficientebze. kvlav visargebloT igiveobiT

i

i

iii net

O

O

E

net

Edelta

∂∂

⋅∂∂=

∂∂=−

radgan gamoiyeneba logistikuri funqcia, miviRebT

∑−−=−j

ijjiii wdeltaOOdelta )1(λ .


SevafasoT exla qselis gamosasvlelze Secdomis damokidebuleba dafaruli Sris i -

uri neironis Sesasvleli kavSirebis wonebze. ganvixiloT kavSiris k -uri woniTi

koeficienti kiw i -uri kvanZiT. gveqneba

kiki

ii

ki

i

iki

xdeltaw

netdelta

w

net

net

E

w

E −=∂∂

⋅−=∂∂

⋅∂∂=

∂∂

sadac kx aris i -uri neironis k -uri Sesasvleli. Tu CavsvamT am damokidebulebas idelta –

s gamosaxulebaSi, miviRebT:

∑ −−=∂∂

jkjii

ki

xdeltaOOw

E)()1( .

radgan Secdomis minimizaciisaTvis aucilebelia wonis Secvla antigradientis

mimarTulebiT, maSin wonis ageba sruldeba Semdegi formuliT:

∑−=∆j

kijjiiki xwdeltaOcOw )()1(λ .

qselebSi, romlebic Seicaven ramdenime dafarul Sres, Secdomis gavrcelebis es

procedura gamoiyeneba rekursiulad n -uri dafarul Sridan )1( −n dafarul Srisaken..

miuxedavad imisa, rom Secdomis ukugavrcelebis meTodi iZleva mravalSriani qselebis

swavlebis problemis gadawyvetis saSualebas, mas gaaCnia igive nakli, rac delta wess.

radgan igi dafuZnebulia eqstremumis Zebnis meTodze, amitom is SeiZleba ikribebodes

lokaluri minimumisken da amasTan gamosaTvlelad arc ise martivia, gansakuTrebiT

qselebisaTvis Secdomis rTuli zedapiriT.

11112222.4. .4. .4. .4. Secdomis ukugavrcelebis meTodis gamoyenebis magaliTi: sistema Secdomis ukugavrcelebis meTodis gamoyenebis magaliTi: sistema Secdomis ukugavrcelebis meTodis gamoyenebis magaliTi: sistema Secdomis ukugavrcelebis meTodis gamoyenebis magaliTi: sistema NETtalk. sistema

NETtalk aris swavlebis rTuli problemis neiroqseluri amoxsnis saintereso magaliTi.

sistema swavlobs inglisuri teqstis warmoTqmas.

NETtalk sistema swavlobs teqstis striqonis kiTxvas da abrunebs fonemas Sesabamisi

maxviliT striqonis yoveli asosaTvis. fonema aris enaSi bgeris bazuri erTeuli, xolo

maxvili – am bgeris fardobiTi simZlavre. radgan yoveli asos warmoTqma damokidebulia

konteqstze da mis garemomcvel asoebze, amitom NETtalk sistema muSaobs fanjarasTan,

romelic Seicavs Svid simbolos. am fanjaraSi teqstis gadaadgilebis dros, NETtalk

sistema yoveli asosaTvis abrunebs wyvils “fonema-maxvili”.

NETtalk sistemis arqiteqtura mocemulia sur. #12.4. qseli Sedgeba neironebis sami

Srisagan. Semavali kvanZebi Seesabamebian teqsturi fanjris Svid simbolos. fanjaraSi

yoveli pozicia warmodgenilia 29 Semavali neironiT, maT Soris TiTo alfabetis yoveli

asosaTvis da sami punqtuaciis niSnebisa da probelebisaTvis. aso yovel poziciaSi

aaqtiurebs Sesabamis neirons. gamomavali Sris kvanZebi adamianisaTvis damaxasiaTebeli

artikulaciis 21 Tvisebis daxmarebiT, warmoadgenen fonemebs. darCenili 5 neironis

saSualebiT xdeba maxvilisa da marcvlebis sazRvrebis kodireba. NETtalk qseli Seicavs 80

dafarul neirons, 26 gamomavl kvanZs da 18629 kavSirs.


sistema NETtalk -is swavlebis dros mas waredgineba 7 simboliani fanjara da igi

cdilobs warmoTqvas Sua aso. warmoTqmulis koreqtulTan Sedarebis Semdeg, sistemis

wonebi aigeba Secdomis ukugavrcelebis meTodiT.

es magaliTi warmoadgens neironul qselebis mravali saintereso Tvisebis

ilustracias, romelTa nawilic asaxavs adamianuri swavlebis bunebas. magaliTad,

dasawyisSi rodesac koreqtuli pasuxebis procentuli Sefardeba mcirea, swavlebis

sur. # 12.4. NETtalk sistemis qselis topologia.

procedura midis sakmarisad swrafad da TandaTanobiT neldeba swori pasuxebs wilis

gazrdis gamo. ise, rogorc adamiani, qselic rac ufro meti sityvis warmoTqmas iswavlis,

miT ufro uadvildeba ucnobi sityvebis gamoTqma. eqsperimentebma, romlebSic woniTi

koeficientebi icvlebodnen SemTxveviTad, aCvena, rom qseli mdgradia struqturis

dazianebisadmi. gamokvlevebma aCvenes dazianebuli qselis xelaxali swavlebis maRali

efeqturoba.

mravalSriani qselebis kidev erTi saintereso aspeqtia dafaruli Sreebis roli.

swavlebis nebismierma algoriTmma unda Seasrulos ganzogadeba sagnobrivi aris

wertilebis ucnob qselebze. dafaruli Sreebi TamaSoben mniSvnelovan rols qselisaTvis

am ganzogadebis realizaciaSi. bevri qselis msgavsad, romlebic axoricieleben swavlebis

ukugavrcelebis meTodiT NETtalk sistemis dafaruli Sre Seicavs ufro mcire raodenobis

neirons, vidre Semavali Sre. es niSnavs, rom im informaciis kodirebisaTvis, romelsac

Seicaven dasaswavli saxeebi, dafarul SreebSi gamoiyeneba mcire raodenobis neironebi,

e.i. es Sre realizacias ukeTebs abstraqciis romeliRac formas. aseT SekumSul kodirebas

mivyavarT iqamde, rom sxvadasxva Semaval saxeebs dafarul SreSi aqvT erTni da igive

warmodgenebi. swored es niSnavs, rom xdeba saxeTa ganzogadoeba.

80 dafaruli neironia

26 gamosasvleli neironi

7×29 Sesasvleli


NETtalk sistemis swavleba mimdinareobs sakmarisad efeqturad, Tumca amisTvis

moiTxoveba didi raodenobis saswavlo magaliTebi, agreTve swavlebis iteraciis

mravaljeradi gameoreba erTi da igive saswavlo monacemebze.

11112222.5..5..5..5. birTvuli manqanebi. birTvuli manqanebi. birTvuli manqanebi. birTvuli manqanebi. Cven ganvixileT erTSriani da mravalSriani neironuli qselebi

da vnaxeT, rom erTSriani qselebi saSualebas gvaZleven gamoviyenoT martivi da efeqturi

daswavlis algoriTmi, magram gaaCniaT SezRuduli SesaZleblobebi, radganac swavlis

procesSi SeuZliaT daadginon mxolod wrfivi sazRvrebi. mravalSrian qselebs gaaCniaT

ufro meti SesaZleblobebi, radganac maT SeuZliaT warmoadginon arawrfivi funqciebi,

magram maTi daswavlis algoriTmi xdeba Zalian rTuli imis gamo, rom Cndeba didi

raodenobis lokaluri minimumebi da Zalian izrdeba wonebis koeficentebis sivrcis

ganzomileba. ganvixiloT SedarebiT axali mimarTuleba daswavlis algoriTmebisa,

romlebic efuZneba mxardamWeri veqtorebis manqanebis,mxardamWeri veqtorebis manqanebis,mxardamWeri veqtorebis manqanebis,mxardamWeri veqtorebis manqanebis, anu sxvanairad birTvuli manqanebisbirTvuli manqanebisbirTvuli manqanebisbirTvuli manqanebis

gamoyenebas. es manqanebi saSualebas gvaZleven gamoviyenoT erTSriani da mravalSriani

qselebis saukeTeso Tvisebebi. ganvixiloT aseTi manqanebis ZiriTadi idea magaliTze.

sur. # 12.5. Sesasvlelebis organzomilebiani sivrce

davuSvaT, mocemuli gvaqvs Sesasvlelebis organzomilebiani sivrce, romelic

ganisazRvreba ),( 21 xxX = veqtoriT da romelSic wertilebi, romlebic ekuTvnian im

klass, romlis gamoyofac Cven gvinda, moTavsebulia wris SigniT )1( +=y , xolo

uaryofiTi wertilebi ki – wris gareT )1( −=y . cxadia, rom am SemTxvevaSi funqcia,

romelic moaxdens am wertilebis gayofas, ver iqneba wrfivi da saWiroa gamoviyenoT

mravalSriani qseli, magram Cven moviqceT sxvanairad. gamovsaxoT Sesasvleli monacemebi

raime gamoTvliTi maxasiaTeblebis saSualebiT, anu yoveli Sesasvleli X veqtori

asaxulia veqtorze )(XF , kerZod, Cveni magaliTisaTvis SeiZleba gamoviyenoT sami

veqtori 213222

211 ,, xxfxfxf === . sur. # 12.6. naCvenebia igive wertilebi axal,

samganzomilebian sivrceSi, romlis ganzomilebebi warmoadgenen Zveli ganzomilebebis

1,5 1 0,5 0 -0,5 -1 -1.5

-1,5 -1, -0,5 0 0,5 1 1,5


kombinaciebs. aSkaraa, rom am sivrceSi wertilebi isea ganlagebuli, rom SesaZlebelia

maTi gayofa 1−n ganzomilebiani sibrtyiT.

aseTi midgoma marTlac sakmaod zogadia, rac ufro metganzomilebian sivrceSi

avsaxavT wertilebs, miT ufro advili iqneba maTi wrfivad gamijvna. am SemTxvevaSi

gamoyenebuli iyo samganzomilebiani sivrce, zogadad ki, Tu gvaqvs NN wertili, SeiZleba

yovelTvis vipovoT RerZebis iseTi veqtoruli gardaqmna, rom movaxdinoT maTi wrfivad

gayofa N-1 ganzomilebian sivrceSi, magram problemas warmoadgens aseTi gamyofis ageba.

sur. # 12.6. igive wertilebi axal koordinatebSi.


1. rogor muSaobs orSriani qseli, romelic axdens “gamomricxavi an” operaciis

modelirebas?

2. rogoria mravalSriani qselebis struqtura?

3. ra gansxvavebaa delta wessa da SecdomaTa ukugavrcelebis meTods Soris?

4. ra aris SecdomaTa ukugavrcelebis meTodis nakli?

5. ratom gamoiyeneba am meTodSi logistikuri funqcia?

6. ras warmoadgens birTvuli manqana?

7. riTi sjobia birTvuli manqana mravalSrian neironul qsels?

8. ra aris rTuli birTvuli manqanis praqtikulad gamoyenebis dros?


1. moaxdineT pirdapiri gavrcelebis qselis kompiuteruli modelireba da gamoiyeneT

is XOR operaciis realizaciisaTvis. moaxdineT am operaciis sxvadasxva qselebiT

realizacia.

212 xx

3 2 1 0 -1 -2 -3

0

0,5

1

1,5

2 21x

22x


2. pirdapiri gavrcelebis qselis saSualebiT gadawyviteTYamoxseniT xelnaweri

cifrebis gamocnobis amocana. amisaTvis aiReT bade 64 ×××× da moaxdineT masze

cifrebis proecireba. Tu cigris nawili moxvdeba ujraSi, miakuTvneT mas erTis

toli mniSvneloba, Tu ara – maSin mniSvneloba noli.aseT ocdaoTxelementiani

veqtori SeiZleba gamoiyenoT qselis Sesasvlel veqtorad.

.

leqcia leqcia leqcia leqcia #1#1#1#13333.... genetikuri algoriTmebigenetikuri algoriTmebigenetikuri algoriTmebigenetikuri algoriTmebi

11113333.1.1.1.1 evolucia.evolucia.evolucia.evolucia. wina leqciebSi ganvixileT xelovnuri neironuli qselebis gamoyeneba

manqanuri daswavlis problemis gadasWrelad, magram neironuli qselebi ar warmoadgenen

erTaderT biologiur prototips, romlebic gamoiyeneba manqanuri daswavlis

algoriTmebis SemuSavebisaTvis. am leqciaSi Cven ganvixilavT daswavlis algoriTmebs,

romlebic dafuZnebuli arian biologiuri evoluciis principebze: populaciis Zlieri

personis gadarCena misi ganviTarebis procesSi. populaciis uZlieresi warmomadgenlis

arCevis roli naTlad vlindeba rogorc saxeTa evoluciis, aseve socialur procesebSi. am

procesebis formalizebas cdiloben ujredovani avtomatebis Teoriis, genetikuri

algoriTmebis, genetikuri programirebis, emerjentuli gamoTvlebis sxva formebis

daxmarebiT.

daswavlis emerjenemerjenemerjenemerjenttttululululiiii, anu gamovlinebadi modelebi (Emergent model) axdenen

adaptaciis yvelaze ufro eleganturi da Zlieri formis – mcenareuli da cxoveluri

samyaros cocxali formebis evoluciisevoluciisevoluciisevoluciis imitacias. Tavisi bunebiT evolucia Zalian

martivi procesia. garemos zemoqmedebis Sesabamisad, TandaTanobiT, populiaciis yvelaze

ufro Zlier warmomadgenlebSi zogierTi Tvisebebis ubralo cvlilebebisa da SedarebiT

warumatebeli egzemplarebis gamoxSirvis Sedegad izrdeba populiaciis adaptaciis unari

da gamomJRavndeba gansxvaveba populaciis sxvadasxva warmomadgenelebs Soris. evoluciis

safuZvlebSi mimdinare procesebis simartive uzrunvelyofs maT sakmarisad sayovelTao

damkvidrebas. biologiuri evoluciis procesSi axali saxeobebi iqmnebian genomis yvelaze

ufro xelsayreli cvlilebebis SerCevis xarjze. analogiurad kulturuli evoluciis

procesSi, socialurad damuSavebuli da modificirebuli informaciis erTeulis

gadacemisas formirdeba codna. genetikuri algoriTmebi da sxva formaluri evoluciuri

analogebi ganapirobeben amocanis ufro zust amoxsnaszust amoxsnaszust amoxsnaszust amoxsnas amocanis amomxsnel kandidat

populaciebze garkveuli operaciebis saSualebiT.

amocanis amoxsnis genetikuri algoriTmi Sedgeba samsamsamsamiiii stadi stadi stadi stadiisaganisaganisaganisagan, romelTagan

pirvelia calkeuli potenciuri amoxsnebispotenciuri amoxsnebispotenciuri amoxsnebispotenciuri amoxsnebis warmodgena specialuri formiT, romelic

mosaxerxebelia cvlilebebis da SerCevis evoluciuri operaciebis Sesasruleblad. ufro

xSirad esaa Cveulebriv bituri (orobiTi) striqonebi. meore stadiaze xdeba Sejvarebis daSejvarebis daSejvarebis daSejvarebis da

mutaciismutaciismutaciismutaciis realizacia, romelic damaxsiaTebelia cocxali biologiuri formebisaTvis. am

operaciebis gamoyenebis Semdeg miiReba axali Taoba TavianTi mSoblebis rekombinirebuli

TvisebebiT. bolo mesame stadiaze romelime SerSerSerSerCevis kritriumis Cevis kritriumis Cevis kritriumis Cevis kritriumis safuZvelze moxdeba

saukeTesoebis, anu mocemuli problemis amoxsnis yvelaze ufro zustad Sesatyvisi

amoxsnebis amorCeva. es egzemplarebi amoirCeva gasamravleblad, anu potenciuri amoxsnebis

axali Taobis formirebisaTvis. sabolood romeliRac Taoba gaxdeba sawyis amocanis

amonaxsni. genetikur algoriTmebSi SeiZleba gamoyenebuli iyos ufro rTuli

warmodgenebic.

11113333.2.2.2.2.... genetikuri algoriTmebi genetikuri algoriTmebi genetikuri algoriTmebi genetikuri algoriTmebis zogadi saxes zogadi saxes zogadi saxes zogadi saxe. . . . rogorc ukve iTqva, neironuli qselebis

msgavsad, genetikuri algoriTmebi efuZnebian biologiuri prototipebis Tvisebas. am


SemTxvevaSi daswavla ganixileba, rogorc konkurencia amocanis amoxsnis rolis

evolucioner kandidatebis populaciis SigniT. yoveli amoxsnis Sefaseba xdeba SerCevis

kriteriumis Tanaxmad. Sefasebis Sedegebis mixedviT ganisazRvreba, miiRebs Tu ara

monawileobas mocemuli egzemplari amoxsnebis Semdeg TaobaSi. Semdeg, biologiuri

kvlavwarmoqmnis procesSi genotipis transformaciebis analogiuri operaciebis

gamoyenebiT miiReba amoxsna - kandidatebis axali Taoba.

vTqvaT )(tP aris tix amonaxsn – kandidatebis Taoba drois raRac t momentSi

},...,,{)( 21tn

tt xxxtP = ,

maSin zogadi saxiT genetikuri algoriTmi SeiZleba warmovadginoT Semdegnairad:

procedure genetic algorithm; begin

mivaniWoT t:=0;

moaxdine )(tP populaciis inicireba;

while ar aris miRweuli damTavrebis piroba;

begin

gamovTale xarisxis kriteriumis mniSvneloba )(tP populaciis yoveli

wevrisaTvis;

xarisxis kriteriumis mniSvnelobis safuZvelze avirCioT )(tP – dan saWiro

raodenobis wevrebi;

SevqmnaT Semdegi Taoba genetikuri operaciebis daxmarebiT;

xarisxis kriteriumis mniSvnelobis gaTvaliswinebiT SevcvaloT )(tP

populaciis egzemplarebi maTi STamomavlebiT;

mianiWe 1+= tt ;

end;

end;

es algoriTmi asaxavs genetikuri swavlebis ZiriTad principebs. misi konkretuli

realizaciebi SeiZleba gansxvavdebodnen amocanebis mixedviT. personebis ra procentuli

Tanafardoba gadarCeba Semdeg TaobaSi? ramdeni egzemplari Rebulobs monawileobas

SejvarebaSi? ra sixSiriT da vis mimarT gamoiyenebian genetikuri operatorebi?

“ )(tP populaciis egzemplarebis Secvlis” procedura SeiZleba Sesruldes

umartivesi gziT, Tu SevcvliT susti kandidatebis fiqsirebul procentul Tanafardobas.

ufro rTuli midgoma mdgomareobs populaciis dalagebaSi xarisxis kriteriumis mixedviT

da egzemplarebis amogdebaSi albaTobebis gaTvaliswinebiT, romelic xarisxis

kriteriumis mniSvnelobis ukuproporciulia. miuxedavad imisa, rom am SemTxvevaSi

populaciis saukeTeso egzemplaris amogdebis albaToba Zalian mcirea, es mainc

SesaZlebelia. aseTi midgomis upiratesoba mdgomareobs zogierTi “susti” egzemplaris

SenarCunebis SesaZleblobaSi, romlebmac SemdegSi SeiZleba Seitanon TavianTi wvlili

ufro zusti amoxsnis miRebaSi. Secvlis aseTi algoriTmi cnobilia sxvadasxva saxeliT,

leqcia #1leqcia #1leqcia #1leqcia #13333. genetikuri algoriTmebi. genetikuri algoriTmebi. genetikuri algoriTmebi. genetikuri algoriTmebi 123

maT Soris rogorc montemontemontemonte----karlos meTodikarlos meTodikarlos meTodikarlos meTodi, an xarisxis kriteriumisxarisxis kriteriumisxarisxis kriteriumisxarisxis kriteriumis proporciulad arCevis proporciulad arCevis proporciulad arCevis proporciulad arCevis

algoriTmialgoriTmialgoriTmialgoriTmi.

davuSvaT, rom saWiroa genetikuri algoriTmis damxarebiT viswavloT striqonebis

klasificireba, romlebic Sedgebian erTianebisa da nulebisagan. aseT amocanaSi bituri

striqonebis populaciis aRwera SeiZleba Sablonis daxmrebiT, romelic Sedgeba 1-s 0-s da

# simboloebisagan, sadac. # - simbolo SeiZleba Seesabamebodes rogorc erTians aseve

nuls. Sesabamisad Sabloni 1##00##1 warmoadgens yvela rvabitian striqons, romelic

iwyeba da mTavrdeba erTianiT da SuaSi Seicavs or 0-s miyolebiT.

genetikuri algoriTmis muSaobis dros xdeba )0(P Pkandidatebis populaciis

inicirieba raime saxiT. rogorc wesi es xdeba SemTxveviTi ricxvebis generatoris

daxmarebiT. amonaxsn-kandidatebis SefasebisaTvis Semoitaneba xarisxis kriteriumi )( tixf ,

romelic gansazRvravs drois t momentSi yoveli kandidatis Sesabamisobis zomas.

klasifikaciis amocanebis dros kandidatebis Sesabamisobis zomas warmoadgens dasaswavli

magaliTebis simravleSi swori pasuxebis procentuli Tanafardoba. xarisxis aseTi

kriteriumis dros yovel amonaxsn – kandidats Seesabameba mniSvneloba.

),()( tPmxf ti

sadac ),( tPm aris xarisxis kriteriumis saSualo mniSvneloba populaciis yvela

wevrisaTvis. Cveulebriv Sesabamisobis zoma damokidebulia droze, amitom xarisxis

kriteriumi SeiZleba iyos an )( tixf , an funqcia, damokidebuliamocanis amoxsnis stadiaze.

yoveli kandidatis analizis Semdeg airCeva wyvilebi rekombinaciisaTvis. am dros

gamoiyeneba genetikuri operatorebigenetikuri operatorebigenetikuri operatorebigenetikuri operatorebi, romelTa Sesrulebis Sedegad miiReba axali

amonaxsnebi mSoblebis Tvisebebis kombinirebis gziT. iseve, rogorc es xdeba evoluciis

bunebriv procesSi, reproduqtiul procesSi monawileobis xarisxi yoveli

kandidatisaTvis ganisazRvreba xarisxis kriteriumis mniSvnelobiT: xarisxis kriteriumis

ufro maRali mniSvnelobis mqonde kandidatebi monawileoben kvlav warmoqmnis procesSi

ufro didi albaTobiT. rogorc ukve iyo aRniSnuli, amorCeva xorcieldeba albaTuri

kanonebis safuZvelze, rodesac populaciis sust wevrebs aqvT kvlav warmoqmnis mcire

albaToba, Tumca es SesaZlebloba gamoricxuli ar aris. zogierTi usustesi egzemplaris

gadarCenas didi mniSvneloba aqvs populaciis ganviTarebisaTvis, imitom rom isini

SeiZleba Seicavdnen amoxsnis zogierT mniSvnelovan komponents, magaliTad bituri

striqonis garkveul fragments, romelic ar gaaCniaT sxva kandidatebs da romelic

SeiZleba gamoyenebuli iqnas kvlavwarmoqmnis dros.

arsebobs STamomavlebis miRebis mravali genetikuri operatori, romlebic inarCuneben

mSoblebis Tvisebebs. maT Soris yvelaze ufro tipuria SejvarebaSejvarebaSejvarebaSejvareba. Sejvarebis dros ori

amonaxsn-kandidati iyofa ramdenime nawilad, es nawilebi icvleba erTmaneTSi da am

operaciis Sedegad miiReba ori axali kandidati (ix. sur. # 13.1). rogorc am suraTidan

Cans, striqonebi iyofa ori tol nawilad, ris Semdegac formirdeba ori STamomavali,

romlebic Seicaven orive mSobelis TiTo fragments. amonaxsn-kandidatebi SeiZleba gaiyon

nebismier wertilSi da nebismieri raodenobis nawilebad. gayofis wertlebis adgili da


maTi raodenoba SeiZleba icvlebodes nebismierad ara marto sxvadasxva amocanebisaTvis,

aramed TviT amocanis amoxsnis procesSic.

sur. # 13.1. Sejvarebis operaciis gamoyeneba ori rvabitiani striqonisaTvis

simbolo # aRniSnavs “ nebismier mniSvnelobas”.

davuSvaT, rom miznobriv klass warmoadgens yvela im striqonebis nakrebi, romlebic

iwyebian da mTavrdebian erTianebiT. sur. # 13.1. mocemuli orive mSobeli striqoni

sakmarisad kargad ergebian am amocanis amoxsnas, magram maTi pirveli STamomavali ufro

zustad Seesabameba xarisxis kriteriums vidre romelime mSobeli. magram misi “Zma”

gacilebiT cudia nebismier Tavis mSobleze, amitom es egzemplari albaT gamoiricxeba

erT-erT uaxloes TaobaSi.

meore mniSvnelovani genetikuri operatoria mutacia.mutacia.mutacia.mutacia.. es operacia SemTxveviTad

amoirCevs kandidats da aseve SemTxveviTad Seucvlis mas zogierT Tvisebas. magaliTad,

mutacia iqneba SablonSi bitis SemTxveviTad amorCeva da misi mniSvnelobis 1-ianis 0-iT an

#-iT Secvla. mutaciis operaciis arsi mdgomareobs amoxsnis zogierTi iseTi

mniSvnelovani komponentis warmoqmnis SesazLeblobaSi, romelic ar iyo sawyis

populaciaSi. Tu zemoT ganxilul magaliTSi sawyis populaciis arcerTi wevri ar

Seicavs 1-s pirvel poziciaSi, maSin Sejvarebis procesSi ar SeiZleba am Tvisebis mqonde

STamomavlis miReba. pirveli bitis mniSvnelobis Secvla SeiZleba mxolod mutaciis

Sedegad.

genetikuri algoriTmis muSaoba grZeldeba manam, sanam ar iqneba miRweuli misi

damTavrebis piroba, magaliTad, erTi an ramdenime kandidatisaTvis xarisxis kriteriumis

mniSvneloba ar gadaaWarbebs raime zRurbls. ganvixiloT amocanis warmodgenisa da

xarisxis kriteriumebis SerCevis problemebi konkretul magaliTebze.

11113333.3. genetikuri a.3. genetikuri a.3. genetikuri a.3. genetikuri algoriTmis gamoyenebalgoriTmis gamoyenebalgoriTmis gamoyenebalgoriTmis gamoyeneba normalur konunqciur formaSi aRwerili normalur konunqciur formaSi aRwerili normalur konunqciur formaSi aRwerili normalur konunqciur formaSi aRwerili

problemisaTvisproblemisaTvisproblemisaTvisproblemisaTvis.... normalur konunqciur formaSi (nkfnkfnkfnkf) aRwera niSnavs gamosaxulebas,

romelic Sedgeba erTaneTTan “da” )(∧ operaciiT dakavSirebuli operatorebis

mimdevrobisagan. amasTan TiToeuli operatori unda Sedgebodes an erTi asosagan, an

Semavali bituri striqonebi 1 1 # 0 1 0 1 # # 1 1 0 # 0 # 1 1 1 # 0 # 0 # 1 # 1 1 0 1 0 1 # miRebuli bituri striqonebi


ramdenime asosagan, romlebic erTmaneTTan dakavSirebulia “an” )(∨ operaciiT. magaliTad,

gamosaxuleba

)()()()()( fecbaedcbecaca ∨¬∧∨¬∨∧¬∨∨∨¬∧¬∨∨¬∧∨¬

warmoadgens nkfnkfnkfnkf, romelic Sedgeba xuTi operatorisagan, sadac TiToeuli operatori

warmoadgens ramdenime literalis dizunqcias. warmodgenawarmodgenawarmodgenawarmodgena nkfnkfnkfnkf-Si niSnavs, rom yvela

literalisaTvis (Cvens SemTxvevaSi – eqvsi) arsebobs logikuri mniSvnelobebi 0 (mcdari)

an 1 (WeSmariti) iseTi, rom nkfnkfnkfnkf Rebulobs mniSvnelobas 1. magaliTad, Tu literalebi c

da f Rebuloben mniSvnelobebs 1, maSin nkfnkfnkfnkf-c Rebulobs mniSvnelobas 1. aqedan mtkicdeba,

rom es nkfnkfnkfnkf warmodgenadia.

imisaTvis rom aRvweroT monacemebi am amocanisaTvis, dagvWirdeba eqvsbitiani

striqonebi, sadac TiToeuli biti Seesabameba fedcba ,,,,, literalebis mniSvnelobebs.

ase magaliTad 1 0 1 0 1 0 striqoni niSnavs, rom literalebi eca ,, Rebuloben

mniSvnelobas 1 da literalebi fdb ,, - ki mniSvnelobas 0.

genetikuri operaciebis Sesrulebis Sedeged unda miviRoT STamomavloba,

romlisTvisac nkf nkf nkf nkf Rebulobs mniSvnelobas 1. es imas niSnavs, rom genetikuri operaciebis

Sedegad unda miviRoT axali striqoni, romelic SeiZleba ganxiluli iyos rogorc

amocanis amoxsnis kandidati. am SemTxvevaSi SesaZlebelia gamoyenebuli iyos rogorc

Sejvarebis, aseve mutaciis operaciebi, radganac maTi gamoyenebis Sedegad kvlav miiReba

eqvsbitiani striqonebi. aseve SeiZleba gamoviyenoT inversirebisinversirebisinversirebisinversirebis da gacvlis gacvlis gacvlis gacvlis operaciebi.

pirvelis arsi mdgomareobs striqonSi bitebis mimdevrobis Secvla Sebrunebulze, xolo

meoresi ki – nebismieri ori bitisaTvis adgilebis gacvlaSi. am TvalsazrisiT amocanis

striqonebis saxiT warmodgena yvelaze mosaxerxebelia.

SedarebiT rTulia xarisxis kriteriumebis amorCeva, radganac amoxsna warmoadgens

iseT striqons, romlisTvisac nkf nkf nkf nkf Rebulobs mniSvnelobas erTians da erTi SexedviT

rTulia viwinaswarmetyveloT ramdenime striqonidan romeli ufro axlos dgas

amoxsnasTan. magram, Tu gaviTvaliswinebT, rom nkfnkfnkfnkf Rebulobs mniSvnelobas erTs mxolod

maSin, rodesac xuTive gamosaxuleba Rebulobs mniSvnelobas erTs, Cven SegviZlia

movaxdinoT amocanis dekompozicia da xarisxis kriteriumebad aviRoT iseTi bituri

striqonebi, romlebic uzrunvelyofen rac SeiZleba meti gamosaxulebebisaTvis erTianis

miniWebas. kerZod, SegviZlia SevadginoT aseTi cxrili:

1 1 0 0 1 0 – 1

0 1 0 0 1 0 – 2

0 1 0 0 1 1 – 3

1 0 1 0 1 1 – 5

anu pirveli striqoni uzrunvelyofs erTi gamosaxulebis erTTan tolobas da misi

reitingia erTi, meore striqoni uzrunvelyofs ori gamosaxulebis erTTan tolobas da

misi reitingia ori, mesame striqoni uzrunvelyofs sami gamosaxulebis erTTan tolobas

da misi reitingia sami. bolo striqoni warmoadgens faqtobrivad amoxsnas, radganc is

uzrunvelyofs xuTive gamosaxulebis erTTan tolobas.


am aRweris Semdeg SesaZlebelia gamoviyenoT genetikuri algoriTmi am amocanis

amosaxsnelad. yvelaze mniSvnelovani aseT midgomaSi aris is, rom algoriTmi

erTdroulad muSaobs amoxsnaTa mTel populiaciasTan, anu faqtobrivad Zebna xdeba

paralelur reJimSi. amas emateba isic, rom SesaZlebelia amocanis dekompozicia da

algoriTms SeuZlia imuSaos TiToeuli gamosaxulebis amoxsnaze cal-calke.

11113333.4. genetikuri algoriTmis gamoyeneba komivoiaJeris amocanisaTvis. .4. genetikuri algoriTmis gamoyeneba komivoiaJeris amocanisaTvis. .4. genetikuri algoriTmis gamoyeneba komivoiaJeris amocanisaTvis. .4. genetikuri algoriTmis gamoyeneba komivoiaJeris amocanisaTvis. komivoiaJeris amocana

– es aris testuri amocanis klasikuri magaliTi xelovnuri inteleqtis meTodebisaTvis

da zogadad kompiuteruli mecnierebisaTvis. Cven es amocana vaxseneT gadrCevis

algoriTmebTan dakavSirebiT (ix. sav. #1, leqcia #4). CamovayaliboT amocana zogadi

saxiT:

komivoiaJers moeTxoveba moinaxulos N qalaqi. svlis marSrutze qalaqebis yoveli

wyvilisaTvis dadgenilia fasi (magaliTad manZili). moiTxoveba moiZebnos minimaluri

fasis gza, romelic iwyeba romelime qalaqidan da romelic uzrunvelyofs danarCeni

qalaqebis naxvas zustad erTjer da gamgzavrebis centrSi dabrunebas.

komivoiaJeris amocana farTod gamoiyeneba praqtikaSi, maT Soris igi uzrunvelyofs iseTi

amocanebis amoxsnas, rogorebicaa eleqtronuli sqemebis gaxsnis problema, rentgenuli

kristalografiis da didi integraluri sqemebis warmoebisas marSrutizaciis amocanebis

gadaWra. zogierT am amocanebSi damatebiT moiTxoveba, rom moiZebnos minimaluri fasis

mqone gza. did interess warmoadgens komivoiaJeris klasis amocanebis analizi maTi

realizaciis efeqtianobis TvalsazrisiT. ra ufro iafi dagvijdeba, davxarjoT ramdenime

saaTi mZlavri kompiuteris gamoyenebiT suboptimaluri amoxsnis misaRebad, Tu gamoviyenoT

naklebad Zlieri kopiuteri, romelic ramdenime wuTSi mogvcems araoptimalur, magram

savsebiT misaReb amoxsnas? komivoiaJeris amocana – es aris saintereso da rTuli (NP

sirTulis) problema, romelic exeba Zebnis strategiis realizaciis mraval aspeqtebs.

imisaTvis, rom gamoviyenoT genetikuri algoriTmi am amocanis amosaxsnelad, pirvel

rigSi unda avirCioT warmodgena qalaqebis monaxulebis marSrutisaTvis, agreTve

SeavarCioT gamosayenebeli genetikuri operatorebi. rac Seexeba xarisxis kriteriumis

arCevas, is Zalian martivia am SemTxvevaSi. saWiroa mxolod gzis sigrZis Sefaseba. amis

Semdeg marSrutebi SeiZleba davalagoT sigrZis mixedviT – rac moklea, miT ukeTesi.

vcadoT marSrutis warmodgena bituri striqonebis saSualebiT. davuSvaT aucilebelia

9 qalaqis 1,2,...,9 monaxuleba. gza SegviZlia warmovadginoT 9 mTeli ricxvisagan

Sedgenili dalagebuli siiT. yoveli qalaqis rigiTi nomeri warmovadginoT oTxbitiani

striqoniT: 0001, 0010,...,1001. am dros gamosaxuleba

0001 0010 0011 0100 0101 0110 0111 1000 1001

warmoadgens qalaqebis monaxulebis mimdevrobas maTi rigiTi nomris zrdis mixedviT. am

gamosaxulebaSi hari (probeli) gamoyenebulia mxolod aRqmis simartivisaTvis. romeli

genetikuri operatorebi SeiZleba gamoviyenoT ase warmodgenili amocanisaTvis?

Sejvarebis operacia calsaxad ar gamodgeba, radgan mis Sedegad miRebuli striqoni ar

warmoadgens iseT gzas, romlis drosac yoveli qalaqis monaxuleba SesaZlebeli iqneba

mxolod erTjer. marTlac, Sejvarebis dros zogierTi qalaqi amovardeba mimdevrobidan,

xolo sxvebi Segxvdeba masSi orjer. ra SeiZleba iTqvas mutaciaze? davuSvaT, rom meqvse


qalaqis aRvniSvnaSi 0110 marcxena ganapira wevri icvleba 1-iT, maSin miRebuli ricxvi 1110

Sesabamisi iqneba 14 rigiTi nomris, romelic ar Sedis qalaqebis dasaSvebs CamonaTvalSi.

gzis gamosaxulebaSi qalaqebis invertireba mocemul SemTxvevaSi warmoadgens erTaderT

dasaSveb operacias, magram sakmarisi iqneba Tu ara es operacia, ucnobia.

komivoiaJeris amocana SeiZleba amoixsnas sxvanairadac: uari vTqvaT bitur

warmodgenaze da mivaniWoT qalaqebs Cveulebrivi rigiTi nomrebi: 1,2,..,9. am qalaqebs Soris

gza warmoadgens cxra cifrisgan Semdgar romeliRac mimdevrobas, xolo Sesabamisi

genetikuri operatorebi mogvcemen axali gzis formirebis saSualebas. am SemTxvevaSi

mutacia, rogorc marSrutSi ori qalaqis SemTxveviTi gacvla, iqneba dasaSvebi operacia,

magram Sejvareba isev usargebloa. marSrutis fragmentebis Secvla imave gzis sxva

fragmentebiT an nebismieri operatori, romelic ucvlis adgilebs marSrutSi qalaqebis

nomrebs (amogdebis, damatebis an dublirebis gareSe), aRmoCndeba sakmarisad efeqturi,

magram aseTi midgomebis dros SeuZlebelia mSoblebis saukeTeso Tvisebebis SeTavseba

STamomavalSi, radgan amisaTvis moiTxoveba misi formireba ori mSoblis safuZvelze.

damuSavebuli iqna sxvadasxva saxis Sejvarebis operatorebi, romlebic icileben am

probelmebs da iZlevian mosanaxulebeli qalaqebis dalagebul siasTan muSaobis

saSualebas. erTerTi aseTi operatoria dalagebuli Sejvarebis dalagebuli Sejvarebis dalagebuli Sejvarebis dalagebuli Sejvarebis operatori.

dalagebuli Sejvarebis procesSi STamomavlis ageba xdeba erT-erTi mSoblis gzaSi

qalaqebis qvemimdevrobis arCevis saSualebiT. masSi agreTve SenarCunebulia meore

mSoblis qalaqebis fardobiTi rigi. dasawyisSi amoirCeva aRniSnuli kveTis ori wertili

(aRiniSneba “I” simboloTi), romlebic SemTxveviTad dgebian TiToeuli mSoblis erTsa da

igive poziciebSi. kveTis wertilebis adgilmdebareoba airCeva SemTxveviTad, Tumca

mSoblebidan TiToeulisaTvis es wertilebi emTxveva erTmaneTs. magaliTad, Tu ori

mSoblisTvis p1 da p2 kveTis wertilebi ganlagebuli arian mesame da meSvide qalaqebis

Semdeg

p1 = (192 I 4657 I 83),

p2 = (459 I 1876 I 23),

maSin ori STamomavali c1 da c2 miiReba Semdegnairad. pirvel rigSi yoveli

STamomavlisaTvis kopirdeba wyvetis wertilebs Soris moTavsebuli mSoblebis striqonis

fragmneti:

c1 = (xxx I 4657 I xx),

c2 = (xxx I 1876 I xx).

(daakvirdiT mSoblebis da STamomamvlebis indeqsebs, c1-iT aRniSnuli STamomavali,

romelSic gadadis p1-is kveTebs Soris moTavsebuli fragmenti). amis Semdeg p2 mSoblis

striqoni gardaiqmneba Semdegnairad: striqoni iwyeba meore kveTis Sedeg darCenili

fragmentiT da Semdeg gagrZeldeba Cveulebrivad, miiReba striqoni:

234591876234591876234591876234591876

radganac qalaqebi 4,6,5 da 7 ukve Sedian pirveli STamomavlis SemadgenlobaSi, amitom

amovyriT maT striqonidan da miiReba Semoklebuli striqoni 2,3,9,1,8, romelic Caismeba c1-

Si, p2-Si arsebuli rigis SenarCunebiT da gveqneba:

c1 = (239 I 4657 I 18).


analogiurad miiReba meore STamomavalic c2 = (392I1876I45).

amgvarad dalagebuli Sejvarebis dros gzis fragmentebi erTi mSoblidan (p1) gadaecema

STamomavals (c1), am dros qalaqebis monaxulebis rigi mas gadaecema meore (p2)

mSoblisagan. aseTi midgoma eyrdnoba intuiciur varauds imis Sesaxeb, rom qalaqebis

monaxulebis rigi mniSvnelovan rols TamaSobs umoklesi gzis moZebnaSi. amitom xdeba

STamomavlebisaTvis qalaqebis monaxulebis rigis Sesaxeb infromaciis Senaxva.

dalagebuli Sejvarebis algoriTmi iZleva yvela qalaqis erTjer monaxulebis

garantias. am operaciis Sedegze mutaciis gamoyeneba unda moxdes Zalian frTxilad.

rogorc zemoT ukve iyo aRniSnuli, mutaciis operacia daiyvaneba erTi marSrutis

CarCoebSi ori qalaqis adgilis gacvlaze anu invertirebaze. mocemul SemTxvevaSi ubralo

invertireba (qalaqebis monaxulebis rigis martivi Secvla) miuRebelia, radgan am dros ar

xdeba axali gzis formireba. magram, Tu erTi marSrutis CarCoebSi avirCevT raime

fragments da movaxdenT mis invertirebas maSin aman SeiZleba mogvces kargi Sedegi.

magaliTad aviRoT gza:

c1 = (239 I 4657 I 18)

da movaxdinoT misi Suanawilis invertireba. STamomavali miiRebs saxes:

c1 = (239 I 7564 I 18).

SeiZleba SemovitanoT mutaciis kidev erTi operatori, romelic mdgomareobs SemdegSi:

SemTxveviTad avirCioT romelime qalaqi da gadavadgiloT igi marSrutis SemTxveviTad

arCeul adgilze. aseTi operatori SeiZleba gamoviyenoT gzis fragmentisTvisac,

magaliTad, avirCioT sami qalaqisgan Semdgari fragmenti da movaTavsoT igi axal,

SemTxveviTad arCeul adgilze.

gansxvavebiT nkf-is amocanisagan am magaliTSi ufro rTuli iyo rogorc warmodgenis,

aseve operatorebis gansazRvra, rac kidev erTxel gviCvenebs, rom genetikuri

algoriTmisTvis damaxasiaTebel codnis warmodgenis, operatorebis arCevis da xarisxis

kriteriumis gansazRvris problemebi warmoadgens erTerT yvelaze mTavar problemas

genetikuri algoriTmebisaTvis. arCeuli warmodgena unda iyos iseTi, rom SesaZlebeli

iyos genetikuri operatorebis gamoyeneba. zogjer bunebrivia bituri warmodgena (rogorc

es iyo pirvel magaliTSi). am SemTxvevaSi potencialuri amonaxsnebis misaRebad saWiroa

pirdapir gamoviyenoT iseTi tradiciuli genetikuri operatorebi, rogoricaa Sejvareba da

mutacia. magram komivoiaJeris amocanaSi sruliad sxva situaciaa. pirvel rigSi, misTvis

ar gamodgeba bituri warmodgena. meorec, mutaciis da Sejvarebis operaciebis

gansazRvrisas yoveli STamomavlisTvis aucilebelia Tvali mivadevnoT saWiro Tvisebebis

Sesrulebas (maSrutSi yvela qalaqis arseboba da TiToeulis mxolod erTjer naxva).

bolos, genetikuri operaciebis realizaciisas arsebiTi informacia unda gadaeces Semdeg

Taobas. komivoiaJeris amocanaSi gadamwyvetia marSrutSi qalaqebis Tanmimdevroba, amitom

STamomavlebs unda gadaeceT am informaciis fargmentebi. imisaTvis, rom uzrunvelvyoT

Tvisebebis aseTi memkvidreoba, aucilebelia TiToeuli amocanisaTvis cal-calke

Sesabamisi saxiT avirCioT monacemebis warmodgenis xerxi da genetikuri operatorebi.


cxrili 13.1.

ricxvi orobiT sistemaSi greis kodi

0000 0000

0001 0001

0010 0011

0011 0010

0100 0110

0101 0111

0110 0101

0111 0100

1000 1100

1001 1101

1010 1111

1011 1110

1100 1010

1101 1011

1110 1001

1111 1000

ganvixiloT monacemebis warmodgenis problemis erTi aspeqti, romelic cnobilia,

rogorc warmodgenis “bunebrivobis” problema. amisaTvis ganvixiloT Zalian martivi,

magaliTi. ganvixiloT 6,7,8 da 9 ricxvebis garCevadobis amocana. bunebrivi, anu aTobiTi

warmodgena, romelic uzrunvelyofs monacemebis daxarisxebas, aris Cveulebrivi aRwera

mTeli ricxvebiT, radganac aT cifrs Soris yoveli Semdegi 1-iT metia winaze. orobiT

aRweraze gadasvlis Semdeg es bunebrivoba qreba. ganvixiloT 6,7,8 da 9 ricxvebis orobiTi

warmodgena:

0110 01110 1000 1001

SevniSnoT, rom ricxvebi 6 da 7, agreTve 8 da 9 gansxvavdebian marTlac erTmaneTisgan

erTi bitiT. magram 7 da 8 ricxvebs saerTo araferi aqvT. warmodgenis am Tvisebam

SeiZleba gamoiwvios didi problemebi im amocanebis amoxsnis dros, romlebSic moiTxoveba

am saxeebis sistematizacia. araerTgvarovani warmodgenis problemis mosaxsnelad,

genetikuri algoriTmebis TeoriaSi farTod gamoiyeneba greis kodigreis kodigreis kodigreis kodi. greis kodi, romelsac

oficialurad ewodeba refleqsuri orobiTi kodi, refleqsuri orobiTi kodi, refleqsuri orobiTi kodi, refleqsuri orobiTi kodi, warmoadgens numeraciis orobiT

sistemas, romelSic ori mezobeli mniSvneloba gnsxvavdeba mxolod erT orobiT TanrigSi.

magaliTad, orobiT sistemaSi warmodgenili pirveli Teqvsmeti ricxvisaTvis greis kods

aqvs saxe (ix. cxrili 14.1). SevniSnoT, rom aq yoveli ricxvi gansxvavdeba Tavisi

mezoblisgan zustad erTi bitiT. Cveulebrivi orobiTi warmodgenis magivrad greis kodis

gamoyenebis dros mdgomareobebs Soris gadasvlebi, genetikuri operatorebis

Sesrulebisas, warmoadgenen ufro bunebrivs.


genetikuri algoriTmebis mniSvnelovan upiratesobas warmoadgens Zebnis paraleluri paraleluri paraleluri paraleluri

bunebabunebabunebabuneba. es algoriTmebi axdenen eqstremumis Zebnis erT-erTi mZlavri formis realizacias,

romelic mdgomareobs erTdroulad ramdenime amonaxs-kandidatebis mxardaWeraSi.

a) b)

sur. # 13.2. genetikuri algoriTmi, rogorc eqstremumis paraleluri Zebna

a) Zebnis sawyisi sivrce b) Zebnis sivrce n Taobis Semdeg

sur. # 13.2. naCvneebia, rogor ikribeba amonaxsnebis simravle eqstremumis

wertilisaken Zebnis sivrceSi. am suraTze horizontaluri RerZze aRebulia SesaZlo

wertilebi amonaxsnTa simravleSi, xolo vertilakurze am amoxsnaTa xarisxi. wertilebi

wirebze arian mimdinare populaciis amonaxsn-kandidatebis wevrebi, romlebic miRebuli

arian genetikuri algoriTmis muSaobis Sedegad. dasawyisSi amonaxsnebi Tanabrad

nawildebodnen Zebnis sivrceSi. ramdenime iteraciis Semdeg isini jgufdebian areebSi,

romlebic Seesabamebian amoxsnebis ufro maRla xarisxs.

genetikuri algoriTmis, rogorc eqstremumis Zebnis algoriTmis aRweris dros,

aracxadad igulisxmeba gadadgileba xarisxis kriteriumiT gansazRvruli zedapiris

gaswvriv. am zedapirze arseboben Tavisi maRlobebi da dablobebi, agreTve lokaluri

maqsimumebi da minimumebi. am sivrcis uwyvetobis darRveva aris konkretuli amocanisTvis

warmodgenis da genetikuri operatorebis arCevis Sedegi. magaliTad, uwyvetobis aseT

garRveva SeiZleba gamowveuli iyos araswori kodirebiT, maT Soris greis kodis ar

gamoyenebiT. avRniSnoT agreTve, rom genetikuri algoriTmebi, eqstremumis Zebnis “xarbi”

algoriTmebisagan gansxvavebiT (leqcia#5), maSinve ar agdeben araperspeqtiul amoxsnebs.

genetikuri operatorebis realizaciis dros cudi amonaxsnebic ki SeiZleba darCnen

populaciaSi da Seitanon TavianTi wvlili amoxsnebis Semdegi Taobebis formirebaSi.

mdgomareobaTa sivrceSi evristikuli Zebna gansxvavdeba genetikuri algoriTmebisagan

kidev erTi momentiT. evristikuli Zebnis dros yovel bijze xdeba mimdinare da miznobriv

mdgomareobebs Soris gansxvavebebis analizi. aseT informaciis gaTvaliswineba xdeba

magaliTad A* algoriTmSi (leqcia #5), rac moiTxovs im qmedebaTa Sefasebas, romelic

saWiroa mimdinare mdgomareobidan miznobrivSi gadasvlisaTvis. genetikuri algoriTmis

amoxsnis xarisxi

Zebnis sivrce Zebnis sivrce

amoxsnis xarisxi


muSaobisaTvis aseTi Zalisxmeva saWiro ar aris. ubralod potencialuri amoxsnebis

yoveli Taoba fasdeba raRac xarisxis kriteriumis daxmarebiT. agreTve ar moiTxoveba

Semdgomi mdgomareobebis mkacri sistematizacia, romelic saWiroa mdgomareobebis

sivrceSi Zebnis dros. ubralod formirdeba amonaxsn-knadidatebis Taoba, romelTagan

TiToeuls SeuZlia Seitanos Tavisi wvlili axal SesaZlo amonaxsnis miRebaSi

paraleluri Zebnis procesis dros.

genetikuri algoriTmebis efeqturobis mniSvnelovan wyaros warmoadgens

evoluciuri operatorebis aracxadi paralelizmiaracxadi paralelizmiaracxadi paralelizmiaracxadi paralelizmi. mdgomareobebis sivrceSi Zebnisgan

gansxvavebiT, mocemul SemTxvevaSi operaciebi sruldebian paralelurad potencialuri

amonaxsnebis mTeli ojaxisaTvis. susti amoxsnebis reproduqtiuli Tvisebebis SezRudviT,

genetikur algoriTmebs mivyavarT aramarto am amoxsnis, aramed mTeli misi STamomavlebis

amogdebamde. magaliTad, Tu algoriTmis muSaobis procesSi moxda 101#0##1 striqonis

gadagdeba, maSin mas aRar SeuZlia dabados 101#_ _ _ _ saxis striqoni. Tu mSobeli

amonaxsni ar Seesabameba xarisxis kriteriums, maSin algoriTmis muSaobis procesSi ar

moxdeba misi arc erTi potencialuri STamomavlis ganxilva.


1. ra biologiuri prototipi udevs safuZvlad genetikur algoriTmebs?

2. ras warmoadgens evoluciis procesi?

3. ris saSualebas iZlevian genetikuri algoriTmebi?

4. ra stadiebisagan Sedgeba genetikuri algoriTmi?

5. CamoayalibeT zogadi genetikuri algoriTmi.

6. CamoTvaleT genetikuri operaciebi.

7. ra gansxvavebaa genetikuri operaciebis TvalsazrisiT nkf nkf nkf nkf da komivoiaJeris

amocanebs Soris?

8. ra aris greis kodi da risTvis iyeneben mas?

9. raSi mdgomareobs genetikuri algoriTmebis mniSvnelovani upiratesoba?

10. ra gansxvavebaa evristikuli Zebnis algoriTmebsa da genetikur algoriTmebs

Soris?

11. ras niSnavs aracxadi paralelizmi?


1. dawereT genetikuri algoriTmi nkf nkf nkf nkf amocanis amosaxsnelad.

2. aRwereT rukis gaferadebis amocana (leqcia #6) ise, rom SesaZlebeli iyos

genetikuri algoriTmis gamoyeneba da dawereT Sesabamisi programa.

leqcia #14leqcia #14leqcia #14leqcia #14

genetikuri algoriTmebis gamoyeneba klasifikaciis genetikuri algoriTmebis gamoyeneba klasifikaciis genetikuri algoriTmebis gamoyeneba klasifikaciis genetikuri algoriTmebis gamoyeneba klasifikaciis

amocanebisaTvisamocanebisaTvisamocanebisaTvisamocanebisaTvis

14.1. warmodgenis tipebi genetikur algoriTmebSi. 14.1. warmodgenis tipebi genetikur algoriTmebSi. 14.1. warmodgenis tipebi genetikur algoriTmebSi. 14.1. warmodgenis tipebi genetikur algoriTmebSi. genetikuri algoriTmebi sul ufro

xSirad gamoiyeneba maTematikuri modelirebisa da gamoyenebiTi amocanebis amosaxsnelad,

amitom TavisTavad cxadia, rom gaizarda interesi maTi Teoriuli safuZvlebisadmi. pirvel

rigSi mniSvnelovani gaxda im amocanebis tipebis daxasiaTeba, romlebisTvisac genetikuri

algoriTmebi muSaoben ufro efeqturad. aseve arsebiTia imis dadgena, Tu ra pirobebSi

moqmedeben genetikuri algoriTmebi ufro efeqturad, vidre Zebnis sxva inteleqtualuri

meTodebi.

Cven nkfnkfnkfnkf-is magaliTze vnaxeT, rom zogierTi amocanebi kargad aRiwereba bituri

striqonebis doneze. bituri striqonebiT aRweris Sablons uwodeben sqemassqemassqemassqemas. magaliTad,

10##01 sqema warmoadgens eqvsbitiani striqonebis ojaxs, romlebic iwyebian 10 fragmentiT

da mTavrdebian 01 simboloebiT. radgan centraluri fragmenti ## aRwers oTx SesaZlo

kombinacias 00, 01, 10, 11, amitom mTeli sqema warmoadgens oTx bitur striqons, romlebic

Sedgebian 1 da 0 simboloebisgan. tradiciulad iTvleba, rom yoveli sqema aRwers

hipersibrtyes. genetikuri algoriTmebis tradiciuli Teoriis centralur moments

warmoadgens mtkicebuleba imis Sesaxeb, rom msgavsi sqemebi warmoadgenen amoxsnebis

ojaxebis samSeneblo blokebssamSeneblo blokebssamSeneblo blokebssamSeneblo blokebs. Sejvarebis da mutaciis genetikuri operatorebi operireben

aseT sqemebTan potenciuri amonaxsnebis Zebnis procesSi. am operaciebis aRwera xdeba

sqemebis Sesaxeb Teoremis saSualebiT, romlis Tanaxmadac, warmoebadobis gazrdisaTvis

raime garemoSi, adapturma sistemam unda moaxdinos sqemebis saSualebiT formalizebuli

zogierTi struqturuli Tvisebis identificireba, Semowmeba da realizacia.

am sqemebis analizianalizianalizianalizi gulisxmobs, rom xarisxis kriteriumisxarisxis kriteriumisxarisxis kriteriumisxarisxis kriteriumis arCevis algoriTmi arCevis algoriTmi arCevis algoriTmi arCevis algoriTmi

daiyvaneba Zebnis sivrceSi im qvesimravleebis Zebnaze, romlebic yvelaze ukeT

akmayofileben mocemul kriteriums. Sesabamisad, es qvesimravleebi aRiwerebian sqemebiT,

romlebisTvisac xarisxis kriteriumis mniSvneloba saSualoze maRalia. Sejvarebis

genetikuri operatoris Sesrulebis dros, xarisxis maRali maCveneblis mqone samSeneblo

blokebi grovdebian erTad da axdenen “gaumjobesebuli” striqonebis formirebas.

mutaciebi iZlevian imis garantias, rom genetikuri Taviseburebebi ar daikargeba Zebnis

procesSi, anu es operatorebi uzrunvelyofen Zebnis zedapiris axal midamoebSiZebnis zedapiris axal midamoebSiZebnis zedapiris axal midamoebSiZebnis zedapiris axal midamoebSi

gadasvlas. amgvarad, genetikuri algoriTmebi SeiZleba ganvixiloT, rogorc Zebnis

procesis raime ganzogadeba mniSvnelovani genetikuri Tvisebebis SenarCunebiT. dReisaTvis

ukve cnobilia, rom am analizis Sedegebianalizis Sedegebianalizis Sedegebianalizis Sedegebi SeiZleba gavavrceloT warmodgenis ufro

maRali donismaRali donismaRali donismaRali donis, rTul, arabitur arabitur arabitur arabitur sqemebzec.

14.2. 14.2. 14.2. 14.2. klasifikaciis sistemebi. klasifikaciis sistemebi. klasifikaciis sistemebi. klasifikaciis sistemebi. pirveli genetikuri algoriTmebi TiTqmis mTlianad

bazirdebodnen dabaldonian warmodgenebze, kerZod, bitur striqonebze (0,1,#). imis garda,

rom bituri striqonebi warmoadgenen bunebriv warmodgenebs genetikuri operatorebis

leqcia # 14. genetikuri algoriTmebis gamoyeneba klasifikaciis amocanebisaTvisleqcia # 14. genetikuri algoriTmebis gamoyeneba klasifikaciis amocanebisaTvisleqcia # 14. genetikuri algoriTmebis gamoyeneba klasifikaciis amocanebisaTvisleqcia # 14. genetikuri algoriTmebis gamoyeneba klasifikaciis amocanebisaTvis 133

realizaciisTvis, isini uzrunvelyofen genetikuri algoriTmebisaTvis iseTive maRal

warmoebadobas, rogorc sxva arasimboluri midgomebi, maT Soris neiroqseluri midgomac.

magram arseboben amocanebi, magaliTad, komivoiaJeris problema, romlebisTvisac

bunebrivia kodireba warmodgenebis ufro maRal doneze. Cven exla ganvixilavT genetikuri

algoriTmebis gamoyenebis magaliTs klasifikaciis amocanebis gadasaWrelad.

klasifikaciis sistemebSi gamoiyeneba genetikuri swavleba logikuri daskvnebis gamotanis

wesebisadmi. klasifikaciis sistema Seicavs daskvnebis gamotanis sistemis standartul

elementebs (sur. #14.1.): daskvnebis gamotanis wesebi (klasifikatorebi), samuSao mexsiereba,

Semavali gadamwodebi (an dekoderebi) da gamomavali elementebi (efeqtorebi).

sur. #14.1 klasifikaciis sitemis urTierTqmedeba garemosTan

klasifikaciis sistemis ganmasxvavebeli Tviseburebasganmasxvavebeli Tviseburebasganmasxvavebeli Tviseburebasganmasxvavebeli Tviseburebas warmodgens konfliqtis

mogvarebisadmi konkurentuli midgomakonkurentuli midgomakonkurentuli midgomakonkurentuli midgoma, swavlebisadmi genetikuri algoriTmis gamoyeneba

da algoriTmi “saxanZri jaWvi” swavlebis procesSi waxalisebebis da sasjelebis

ganawilebisaTvis. gare garemosTan ukukavSiri iZleva saSualebas Sefasdes klasifikator-

kandidatebis xarisxi, rac aucilebelia genetikuri swavlebisaTvis.

amocanis amoxsnis dros klasfikatori muSaobs rogorc logikuri daskvnebis

gamotanis tradiciuli sistema. klasifikaciis sistemis deteqtors garedan miewodeba

garemo

dekoderi Semaval SetyobinebaTa sia

muSa mexsierebis Sida Setyobinebebi

gamomaval SetyobinebaTa sia efeqtori

genetikuri operatorebi wesebis Sesacvlelad

produqciuli mexsierebis klasifikaciis wesebi

dekoderi kreditebis ganawileba “saxanZro jaWvis” principiT

Sesasvle-li

gamosasvleli

ukukavSiri


Setyobineba, magaliTad informacia moTamaSis mier svlis gakeTebis Sesaxeb. es xdomileba

kodirdeba da moTavsdeba daskvnebis gamotanis sistemis samuSao mexsierebis Sida

Setyobinebebis siaSi rogorc saxe. daskvnebis gamotanis sistemis Cveulebrivi muSaobis

dros, es Setyobinebebi monacemebis safuZvelze Seesabamebian klasfikaciis wesebis

pirobebs. “ufro metad aqtiuri klasifikatoris” arCeva xorcieldeba auqcionis sqemiTauqcionis sqemiTauqcionis sqemiTauqcionis sqemiT,

romelSic SemoTavazebuli fasi – es aris funqcia, romelic damokidebulia am

klasifikatoris xarisxis kriteriumis akumulirebul mniSvnelobasa da Semaval stimulsa

da klasfikatoris pirobas Soris Sesabamisobis doneze. es Setyobinebebi daematebian

Sesabamisobis yvelaze ufro maRali donis mqone klasifikatorebis samuSao mexsierebas.

daskvnebis gamotanis sistemis muSaobis procesSi, Setyobinebebi ganaxlebuli siidan

SeiZleba efeqtorebis saSualebiT gadaeces garemos an maT SeiZleba gaaqtiuron

klasfikaciis axali wesebi.

klasifikaciis sistemebi axdenen waxalisebiTwaxalisebiTwaxalisebiTwaxalisebiT swavlebis swavlebis swavlebis swavlebis erT-erTi formis

realizacias, anu imis da mixedviT, swori iyo Tu ara maTi gadawyvetileba, xdeba sistemis

waxaliseba, an dasja. xarisxis kriteriumis mniSvnelobiT gansazRvruli an

maswavleblisgan mosuli informaciis safuZvelze, ddddaswavlaswavlaswavlaswavladiadiadiadi sistema sistema sistema sistema iTvlis wesebi-

kandidatebis populaciisaTvis xarisxis kriteriumis mniSvnelobas da agebs axal

populacias genetikuri swavlebis variantebidan erT-erTis daxmarebiT. klasfikaciis

sistemebis swavleba xdeba ori xerxiT. pirveli xerxi mdgomareobs waxalisebis sistemis

gamoyenebaSi, romelic klasifikaciis wesebis xarisxis zomas agebs sasargeblo wesebis

gaZlierebis da araswori qmedebebis Sesustebis xarjze. kreditebis ganawilebis

algoriTmi gadascems jildoebis da jarimebis nawils im klasifikaciis yovel wevrs,

romlebmac miiRes monawileoba saboloo wesis formirebaSi. sxvadasxva jildoebis aseTi

ganawileba urTierTmoqmed klasifikatorebs Soris, xSirad realizdeba “saxanZro jaWvis”

algoriTmis daxmarebiT. es algoriTmi moxsnis kreditebis da jarimebis ganawilebis

problemas im sistemebisaTvis, romelTa gamosasvleli warmoadgens wesebis nakadis

mimdevrobiTi gamoyenebis Sedegs. rogor gavanawiloT jarimebi am jaWvis wesebs Soris

gamosasvlelze Secdomis SemTxvevaSi? jaWvis romeli wesi warmoadgens Secdomis wyaros:

bolo Tu erT-erTi winamdebareebidan? “saxanZro jaWvis” algoriTmi saSualebas gvaZlevs

gavanawiloT kreditebi da jarimebi am mimdevrobis wesebs Soris imis mixedviT, Tu ra

wvlili miuZRvis TiToeul wess saboloo amoxsnaSi. es algoriTmi analogiuria wina

leqciebSi ganxiluli SecdomaTa ukugavrcelebis algoriTmisa.

swavlebis meore forma dakavSirebulia TviT wesebis modifikaciasTan, Sejvarebis

da mutaciis tipis genetikuri operatorebis safuZvelze. aseTi midgomebis dros

gadarCebian saukeTeso wesebi, xolo maTi kombinaciebis Sedegad formirdeba axali

klasifikatorebi.

klasifikaciis yoveli wesi Sedgeba sami komponentisagan da muSaobs rogorc

daskvnebis gamotanis Cveulebrivi sistema: raRac pirobis safuZvelze mowmdeba monacemebis

Sesabamisoba samuSao mexsierebis SigTavsTan. swavlebis procesSi genetikur operatorebs

SeuZliaT moaxdinon rogorc pirobebis ise gamotanis wesebis moqmedebis modifikacia.

meore komponents, wesi – moqmedeba, SeuZlia Secvalos SetyobinebaTa Sida sia


produqciuli mexsierebaSi. da bolos yovel wess Seesabameba xarisxis zoma. rogorc ukve

iyo aRniSnuli, es parametri icvleba wesis, rogorc warmatebuli ise warumatebel,

gamoyenebis dros. Tavidan es zoma mieniWeba yvela wess genetikuri operatoris

saSualebiT maTi Seqmnis dros. magaliTad, xarisxis zomad SeiZleba iyos ori mSoblis

xarisxis saSualo mniSvneloba.

vaCvenoT martiv magaliTze klasifikaciis sistemis am komponentebis urTierTqmedeba.

davuSvaT, obieqtebis nakrebi, romelTa klasifikaciasac vaxdenT, aRiwereba eqvsi

parametriT (pirobebiT 621 ,...,, ccc ). davuSvaT, agreTve, rom am parametrebidan TiToeuli

iRebs 5 sxvadasxva mniSvnelobas. zogadobis daurRvevlad SeiZleba yvela atributis

dasaSvebi mniSvnelobis aRwera mTeli ricxvebiT {1,2,3,4,5}. vTqvaT daskvnebis gamotanis

wesebis Tanaxmad es obieqtebi iyofian 4 klasad: A1,A2,A3,A4. amgvarad, yoveli klasfikatori

SeiZleba avRwerod Semdegi TanafardobiT:

iAcccccc →),,,,,( 654321 , sadac 4,1=i (1)

sadac TiToeuli ic piroba iRebs mniSvnelobas Sesabamisi parametris {1,2,..,5}

mniSvnelobaTa diapazonidan. rogorc wesi, pirobas agreTve SeiZleba Seesabamebodes

yoveli parametris nebismieri # mniSvneloba (analogiuria konceptebis gamoTvlis

meTodisa, sadac parametrma SeiZleba miiRos nebismieri MmniSvneloba). (1) gamosaxulebis

marjvena mxare iA aRniSnavs A1,A2,A3,A4 klasebidan erT-erTs. 14.1 cxrilSi moyvanilia

klasifikatorebis nakrebi. yuradReba miaqcieT imas, rom gansxvavebuli pirobebis ramdenime

Sabloni SeiZleba Seesabamebodes erT klas, rogorc 1 da 2 wesSi, an ori erTnairi

Sabloni SeiZleba Seesabamebodes sxvadasxva klass.

rogorc ukve aRvniSneT, klasifikaciis sistema dafuZnebulia logikuri gamotanis

wesebze. moyvanil magaliTSi gamoyenebuli klasifikaciis wesebis erTaderTi

ganmasxvavebeli Tviseba aris pirobebis warmosadgenad cifrebiT da # simboloTi

Sedgenili striqonebis gamoyeneba. pirobebis aseTi warmodgena uzrunvelyofs genetikuri

algoriTmebis gamoyenebas logikuri gamotanis wesebSi. vnaxoT, rogor xdeba genetikuri

daswavlis gamoyeneba klasifikaciis sistemebSi.

piroba(parametri) moqmedeba(klasi) wesis nomeri

cxrili 11.2. pirobebis nakrebi sxvadasxva klasebisaTvis.


simartivisaTvis ganvixiloT sistemis swavleba mxolod 1A klasisaTvis. mivaniWoT

Sablonebs (striqonebs) 1 an 0 imis da mixedviT, Seesabamebian isini 1A klass, Tu ara.

SevniSnoT, rom aseTi gamartiveba ar zRudavs msjelobis zogadobas, radgan es

gamoTvlebi SeiZleba gavavrceloT ramdenime klasis swavlebis SemTxvevaze. amisaTvis

sakmarisia SemovitanoT veqtori, romelic Seesabameba konkretul pirobiT Sablons.

magaliTad klasifikatori 14.1. cxrilidan SeiZleba avRweroT aseTi saxiT:

(1###1#) � (1000),

(2##3##) � (1000),

(1#####) � (0100),

(##43##) � (0110).

Aam magaliTSi bolo striqoni Seesabameba klasifikaciis wesebs A2 da A3

klasebisaTvis da ara A1 an A4. Tu SevcvliT 0 an 1 klasebis aseTi veqtoruli

warmodgenebiT, maSin SeiZleba SevafasoT klasfikaciisaTvis wesebis efeqturobaklasfikaciisaTvis wesebis efeqturobaklasfikaciisaTvis wesebis efeqturobaklasfikaciisaTvis wesebis efeqturoba ramdenime

klasze.

klasifikaciis koreqtulobis gansazRvrisaTvis gamoviyenoT 14.1 cxrilSi mocemuli

wesebi. kerZod, ganvixiloT isini, rogorc maswavlebeli klasifikaciis sistemaSi wesebis

xarisxis SefasebisaTvis. rogorc umravles swavlebis genetikur sistemebSi, SemTxveviTad

avirCioT wesebis sawyisi populacia. pirobis yovel Sablons SevusabamoT xarisxisxarisxisxarisxisxarisxis an

Zalis Zalis Zalis Zalis parametri (namdvili ricxvi [0,0; 1,0] diapazonidan). Zalis am s parametrs

gamovTvliT yoveli mSoblis wesis xarisxis safuZvelze wina istoriis gaTvaliswinebiT.

wesebis daxmarebiT swavlebis yovel ciklSi SevecadoT Sesasvlelebis klasificirebas da

klasifikaciis xarisxis Semowmebas xarisxis zomisxarisxis zomisxarisxis zomisxarisxis zomis,,,, anu maswavleblis daxmarebiT. vTqvaT,

romelime bijze miRebulia klasifikaciis wesebis rolze kandidatebis Semdegi populacia,

romlis yoveli elementisaTvis 1 aRniSnavs klasifikaciis koreqtul Sedegs, xolo 0

uTiTebs araswor Sedegze.

(###21#) � 1 s=0.6,

(##3##5) � 0 s=0.5,

(21####) � 1 s=0.4,

(#4###2) � 0 s=0.23.

davuSvaT, garemodan Semovida axali Setyobineba (1 4 3 2 1 5), da maswavlebelma (14.1

cxrilidan pirveli wesis safuZvelze) moaxdina am veqtoris klasificireba, rogorc

dadebiTi magaliTi A1 klasisaTvis. vnaxoT ra moxdeba am saxis gadacemisas muSa

mexsierebaSi, misi klasifikaciis cdis dros 4 wess-kandidatis daxmarebiT. es saxe

Seesabameba 1 da 2 wesebs. saTanado wesebs Soris konfliqtis mogvareba xdeba

konkurenciis safuZvelze. Cvens magaliTSi yoveli wesis Sesabamisobis xarisxiSesabamisobis xarisxiSesabamisobis xarisxiSesabamisobis xarisxi

gamoiTvleba rogorc yoveli parametris Sesabamisobis xarisxebis da mocemuli wesis

xarisxis zomis namravlebis jami. ganusazRvrel parametrs # Seesabameba 0.5, xolo

parametris zusti Sesabamisobis SemTxvevaSi mas mieniWeba xarisxi 1,0. normirebisaTvis

miRebuli mniSvneloba iyofa Semavali veqtoris sigrZeze. radgan pirveli klasifikatori

mocemuli Semavali veqtorisaTvis iZleva or zust Sesatyvis da 4 ganusazRvrel


parametrs, amitom Semaval veqtorTan misi Sesabamisobis saerTo xarisxi iqneba

4,06)6,0)125,04(( =⋅⋅+⋅ . meore klasifikatorisTvis aseve aris ori zusti Sesatyvisi da

4 ganusazRvreli parametri, amitom misi Sesabamisobis xarisxi Seadgens 33,0 . Cvens

magaliTSi konkurenciis principiT imarjvebs Sesabamisobis maqsimaluri xarisxismaqsimaluri xarisxismaqsimaluri xarisxismaqsimaluri xarisxis mqone

klasifikatori, magram ufro rTul amocanebSi albaT sasurvelia raime zRurblis

gaTvaliswineba.

amgvarad gaimarjva pirvelma wesma, romlis Sesabamisadac warmodgenili saxe

miekuTvneba A1 klass. radgan es moqmedeba aris koreqtuli, amitom pirveli wesis xarisxis

zoma izrdeba da iRebs 1-Tan miaxloebul axal mniSvnelobas. Tu am wesis Sesrulebis

Sedegi iqneboda arakoreqtuli, maSin xarisxis zoma Semcirdeboda. Tu Sedegis

miRebisaTvis sistemaSi mravaljer sruldeboda wesebis raime nakrebi, maSin waxalisebis

gansazRvruli nawili unda miiRos am Sedegis miRebaSi monawile yvela wesma. xarisxis

zomis gadaTvlis zusti proceduris gansazRvra damokidebulia sistemaze da SeiZleba

aRmoCndes Zalian rTuli. is SeiZleba aigos “saxanZro jaWvis” algoriTmis an kreditebis

ganawilebis sxva meTodis safuZvelze.

wes-kandidatebis xarisxis zomis gamoTvlis Semdeg swavlebis algoriTmSi

gamoiyenebian genetikuri operatorebi wesebis Semdegi Taobis SeqmnisaTvis. Tavdapirvelad

SerCevis principiT amoirCeva xarisxis kriteriumis ufro maRali mniSvnelobis mqone

wesebis simravle. es amorCeva efuZneba xarisxis zomis mniSvnelobaze, magram man SeiZleba

gaiTvaliswinos damatebiTi SemTxveviTi sidideebic. SemTxveviTobis elementi

uzrunvelyofs xarisxis cudi maCveneblis mqone wesebis amorCevis SesaZleblobas,

romlebsac, zogadi Seusabamobis miuxedavad, SeuZliaT Semoitanon sasargeblo elementebi

amocanis amoxsnaSi. davuSvaT, ganxilul magaliTSi Semdgomi muSaobisaTvis arCeulia

klasfikaciis pirveli ori wesi.

meoTxe da mexuTe elementebs Soris Sejvarebis wertilis SemTxveviT arCevis Semdeg

(###2 I 1#) � 1 s=0.6,

(##3# I #5) � 0 s=0.5,

miviRebT STamomavlebs

(##3# I 1#) � 0 s=0.53,

(###2 I #5) � 1 s=0.57.

TiToeuli STamomavlis xarisxis sazomixarisxis sazomixarisxis sazomixarisxis sazomi aris maTi mSoblebis xarisxis maCveneblebis

SeSeSeSewonili funqcia.wonili funqcia.wonili funqcia.wonili funqcia. woniTi koeficientebi ganisazRvrebian Sejvarebis wertilis

adgilmdgomareobiT. pirvelma STamomavalma miiRo 6,0 xarisxis zomis mqone

klasifikatorisgan 31 informacia da 5,0 xarisxis zomis mqone klasifikatorisgan 32

informacia. amitom misi xarisxis zoma Seadgens

53,0)5,032()6.031( =⋅+⋅ .

analogiuri msjelobiT miviRebT, rom meore STamomavlis xarisxis zoma tolia 57,0 .

wesis Sesrulebis Sedegi (0 an 1 mniSvneloba) ganisazRvreba imis da mixedviT, Tu ramdeni

parametri Seesabameba mocemul wess. klasifikaciis tipur sistemebSi es ori axali wesi,


maT mSoblebTan erTad, Sedis klasifikatorTa im nakrebSi, romlebTanac muSaobs sistema

Semdeg etapze.

SeiZleba ganvsazRvroT mutaciis operatoric. martivi mutacia mdgomareobs

parametris yoveli mniSvnelobis dasaSvebi diapazonidan nebismieri mniSvnelobiT

SecvlaSi. magaliTad, 5 SeiZleba SevcvaloT 1,2,3,4 an # mniSvnelobiT. rogorc miTiTebuli

iyo genetikuri algoriTmis aRweris dros, mutaciis operatorebi mowodebulni arian

Seitanon SemTxveviTobis elementi klasifikatoris ZebnaSi, maSin, rodesac Sejvareba

saSualebas iZleva SevinaxoT STamomavlebSi maTi mSoblebis Sablonebidan monacemebis

warmatebuli fragmentebi.

ganxiluli magaliTi sakmarisad martivia da mowodebulia mxolod klasifikaciis

sistemebis ZiriTadi komponentebis muSaobis ilustrirebisaTvis. realur sistemebSi

SeiZleba Sewyvilebulad imuSaos ramdenime wesma da yvela maTgans SeuZlia gadasces

Tavisi Sedegebi muSa mexsierebas. xSirad klasifikatorebidan erT-erTis aSkara

dominirebis Tavidan acilebis mizniT amoxsnis procesSi gamoiyeneba e.w. dabegvris sqemadabegvris sqemadabegvris sqemadabegvris sqema,

romlis drosac aseTi klasifikatoris xarisxis zoma yovel warmatebul bijze ramdenadme

mcirdeba. aq ar aris aRwerili agreTve “saxanZro jaWvis” algoriTmi, romelic axdens

amocanis warmatebiT amoxsnaSi da garemosTvis Setyobinebebis gadacemaSi monawile wesebis

sxvadasxva xarisxiT waxalisebas. amis garda, rogorc wesi, genetikuri operatorebi

klasifikatorebis transformaciisaTvis ar gamoiyenebian algoriTmis muSaobis yovel

bijze. Cveulebriv arsebobs raRac zogadi parametri, romelic ganisazRvreba yoveli

amocanis specifikaciis gaTvaliswinebiT, kerZod, garemosTan ukukavSiris analizis

safuZvelze da romlis safuZvelzec miiReba gadawyvetileba genetikuri operatorebis

gamoyenebis aucileblobis Sesaxeb.

14.3.14.3.14.3.14.3. programireba genetikuri operatorebis gamoyenebiTprogramireba genetikuri operatorebis gamoyenebiTprogramireba genetikuri operatorebis gamoyenebiTprogramireba genetikuri operatorebis gamoyenebiT.... ganvixiloT genetikuri

operaciebis gamoyeneba ufro rTuli SemTxvevebisaTvis, kerZod, maTi gamoyeneba

kompiuteruli programebisadmi. am dros genetikuri programirebisgenetikuri programirebisgenetikuri programirebisgenetikuri programirebis principebi gamoiyeneba

kompiuteruli programis ierarqiulad organizebuli fragmentebze. programis xarisxiprogramis xarisxiprogramis xarisxiprogramis xarisxi

ganisazRvreba misi unariT amoxsnas garkveuli klasis amocana, xolo programis

modifikaciamodifikaciamodifikaciamodifikacia xdeba programis qvexeebisadmi Sejvarebis da mutaciis gamoyenebiT. genetikuri

programirebis dros Zebna mimdinareobs sxvadasxva sirTulis da zomis kompiuteruli

programebis sivrceSi. faqtobrivad Zebnis sivrce – es aris, amocanis sagnobrivi aris

Sesabamisi simboloebis mimdevrobebisgan da funqciebis gamoZaxebebisgan Sedgenili,

kompiuteruli programebis yvela SesaZlo simravle. iseve, rogorc genetikuri daswavleba,

aseTi Zebna Seicavs SemTxveviTobis elements, is bevrjer sruldeba “brmad”, magram,

ramdenadac gasakvirvi ar unda iyos, aris sakmarisad efeqturi.

genetikuri programirebis dros Tavdapirvelad inicializirdeba SemTxveviTad SemTxveviTad SemTxveviTad SemTxveviTad

generirebuli programebis populaciagenerirebuli programebis populaciagenerirebuli programebis populaciagenerirebuli programebis populacia, romlebic Sedgenili arian Sesabamisi programuli

fragmentebisagan. amocanis sagnobriv areze damokidebulebis mixedviT es fragmentebi

SeiZleba Seicavdnen standartul ariTmetikul operaciebs, maTematikur da logikur

funqciebs da agreTve specifikur funqciebs mocemuli sagnobrivi arisaTvis. programuli


komponentebis ricxvSi Sedian standartuli tipis monacemebi: logikuri, mTeli ricxviTi,

mcocavmZimiani, veqtorul simboluri an mravalmniSvnelobiani.

inicializaciis Semdeg generirdeba populacia aTasamde kompiuteruli programidan.

yoveli axali programa iqmneba genetikuri operatorebis gamoyenebiT. kompiuteruli

programebis SeqmnisaTvis aucileblad unda moxdes Sejvarebis, mutaciis da sxva

kvlavwarmoebis uzrunvelmyofi operatorebis adaptacia. yoveli axali programis xarisxi

ganisazRvreba misi unariT amoxsnas amocana konkretuli sagnobrivi aridan. TviT xarisxis

kriteriumic formirdeba sagnobrivi aris gaTvliswinebiT. xarisxis kriteriumis maRali

mniSvnelobis mqone programebi gadarCebian da miiReben monawileobas programebis Semdegi

Taobis formirebaSi.

amgvarad, genetikuri programirebagenetikuri programirebagenetikuri programirebagenetikuri programireba Seicavs Semdeg eqvs komponents, romelTagan

mravali gvagonebs genetikuri algoriTmebis Semadgenel nawilebs:

1. struqturebis nakrebi, romlebic eqvemdebarebian transformacias genetikuri

operatorebis daxmarebiT.

2. sawyisi struqturebis nakrebi, romlebic Seesabamebian sagnobriv ares.

3. xarisxis zoma am struqturebis Sesafaseblad, romelic airCeva sagnobrivi

aris gaTvaliswinebiT.

4. genetikuri operatorebis nakrebi struqturebis transformaciisaTvis.

5. yoveli Taobis elementebis parametrebis da mdgomareobebis aRwera.

6. gaCerebis pirobebis nakrebi.

genetikur programirebaSi operaciebi sruldeba ierarqiulad organizebul programul

modulebze. programuli enebis komponentebis warmodgenis ZiriTad saSualebas

warmoadgens ena LISP-i. programuli fragmentebi warmodgineba rogorc simboluri

gamosaxulebebi LISP-Si, s-gamosaxulebebi.

genetikuri operatorebi operireben s-gamosaxulebebTan. kerZod, isini asaxaven s-

gamosaxulebebis xismagvar struqturebs (programis fragmentebi LISP enaze) axal xeebSi

(sxva programebi LISP enaze)..

genetikuri programireba iZleva sasargeblo programebis agebis saSualebas im sawyisi

monacemebis da predikatebis safuZvelze, romlebic aRweren amocanis sagnobriv ares.

amocanebis romelime simravlis amoxsnisaTvis daniSnuli programebis TaobisaTvis

gansazRvris aris mocemisas, aucilebelia Tavdapirvelad gavaanalizoT TviT amoxsna da

Semadgeneli elementebis SesaZlo saboloo mniSvnelobebi, agreTve funqciebi, romlebic

aucilebelia am saboloo mniSvnelobebis misaRebad.

imisaTvis, rom movaxdinoT genetikuri operatorebis daxmarebiT modificirebuli

struqturebis inicializacia, aucilebelia SevqmnaT ori simravle: funqciebis F

simravle da saboloo mniSvnelobebis T simravle, romlebic aucilebelia mocemuli

sagnobrivi arisaTvis. F F simravle SeiZleba Sedgebodes martivi operaciebisagan {+, -, *,

/} an Seicavdes ufro rTul funqciebs, rogoricaa )cos(),sin( xx da matriculi operaciebi.

T simravle SeiZleba Seicavdes mTeli an namdvil ricxvebs, matricebs an ufro rTuli


gamosaxulebebs. simboloebis simravle T unda iyos Caketili F F simravlis funqciebis

mimarT.

am simravleebis Seqmnis Semdeg xdeba sawyisi “programebis” generireba F Fda T

simravleebidan elementebis SemTxveviTad amorCevis gziT. T simravlidan elementis

amorCevis Sedegad, Cven miviRebT gadagvarebul xes, romelic Sedgeba erTi elementisgan.

amitom, ufro sainteresoa situacia, rodesac Tavdapirvelad amoirCeva elementi F F -dan,

vTqvaT operacia “+”. am SemTxvevaSi miiReba xis sawyisi kvanZi ori potencialuri

STamomavliT. davuSvaT, amis Semdeg pirveli STamomavlis rolSi inicializatori

amoirCevs F F simravlidan gamravlebis “*” operacias, xolo meore STamomavlis rolSi ki

- T simravlidan saboloo mniSvnelobas 6. Semdegi SemTxveviTad amorCeuli elementebi

SeiZleba gaxdnen saboloo mniSvneloba 8 da “+” funqcia F -dan. davuSvaT procedura

mTavrdeba T simravlidan 5 da 7 mniSvnelobebis amorCeviT.

aseTi saxiT SemTxveviTad generirebuli programa warmodgenilia sur. #14.2. sur.

#14.2. a) naCvenebia xe, “+” operaciis pirveli arCevis Semdeg, sur. #14.2. b) mocemulia xe 6-

is toli saboloo mniSvnelobis arCevis Semdeg, xolo sur. #14.2 g) ki – naCvenebia

saboloo programa.

genetikuri programirebis procesis inicializaciisaTvis formirdeba msgavsi

programebis mTeli Taoba. am populaciis ganzomilebis kontrolisaTvis SeiZleba

gamoviyenoT SezRudvebi, magaliTad programebis maqsimaluri siRrmis SezRudvamaqsimaluri siRrmis SezRudvamaqsimaluri siRrmis SezRudvamaqsimaluri siRrmis SezRudva. arsebobs

aseTi SezRudvebis da agreTve sawyisi populaciebis generirebis sxvadasxva meTodebi,

romlebic SeiZleba gamoviyenoT genetikuri programirebis procesis inicializaciisaTvis.

aqamde ganvixilavdiT warmodgenis sakiTxebs (s-gamosaxulebebi da xiseburi

struqturebi), romlebic aucilebelia programebis evoluciis procesebis

generirebisaTvis. imisaTvis, rom vmarToT programaTa populaciebi, saWiroa ganvsazRvroT

xarisxis kriteriumebi. xarisxis kriteriumis arCeva damokidebulia konkretul amocanaze

da Cveulebriv daiyvaneba im amocanebis nakrebis gansazRvrze, romlebic unda amoxsnas

a) b) g)

sur. #14.2 sawyisi programis SemTxveviTi generacia.

wreebiT aRniSnuli kvanZebi Seesabamebian funqciebs


evolucionirebadma programam. TviTon xarisxis kriteriumi – es aris funqcia, romelic

iTvlis mocemuli programiT amocanis amoxsnis efeqturobas. xarisxis wrfivi kriteriumixarisxis wrfivi kriteriumixarisxis wrfivi kriteriumixarisxis wrfivi kriteriumi

iTvaliswinebs programis Sesrulebis Sedegsa da realur amoxsnas Soris gansxvavebas.

maSasadame, xarisxis wrfivi kriteriumi SeiZleba ganvixiloT rogorc Secdomebis jami

amocanebis nakrebis dros. SesaZloa agreTve xarisxis sxva kriteriumebi. xarisxis

normalizebuli kriteriumi gulisxmobs xarisxis saerTo kriteriumis gayofas yvela

SesaZlo Secdomis raodenobaze. maSasadame, xarisxis normalizebuli kriteriumi SeiZleba

icvlebodes 0-dan 1-mde diapazonSi. normalizaciis upiratesoba vlindeba programebis

didi populaciis muSaobis dros. xarisxis zoma iTvaliswinebs programis zomas,

magaliTad, SeiZleba waxalisdes mcire zomis kompaqturi programebis Seqmna.

genetikuri operatorebi programebis sivrceSi Seicaven rogorc TviT xis gardaqmnas,

ise sxvadasxva xeebs Soris fragmentebis gacvlas. ganvixiloT ori ZiriTadi genetikuri

operacia, romlebmac miiRes kvlavwarmoebiskvlavwarmoebiskvlavwarmoebiskvlavwarmoebis da SejvarebisSejvarebisSejvarebisSejvarebis saxelwodeba. kvlavwarmoeba

aris mimdinare Taobis programebis amorCeva da maTi kopireba (cvlilebebis gareSe)

Semdegi Taobis populaciaSi. Sejvareba gulisxmobs ori arsebuli programis qvexeebis

gacvlas. davuSvaT arsebobs sur. # 14.3 warmodgenili ori mSobeli programa, a) da

b)BBromlebSic “I” simboloTi naCvenebia Sejvarebis wertilebi. Svilobili xeebi,

romlebic miiRebian Sejvarebis Sedegad, gamosaxuli arian sur. # 14.4. Sejvareba SeiZleba

gamoviyenoT agreTve erTi mSobeli xis gardaqmnisaTvis misi ori qvexis adgilebis

gacvlis gziT. Sejvarebis wertilis SemTxveviTad arCevis dros orma identurma mSobelma

xem SeiZleba mogvces sxvadasxva STamomavali. Sejvarebis wertili agreTve SeiZleba iyos

programis Zireuli kvanZi.

cnobilia programebis xeebis mravali naklebad gavrcelebuli da naklebad

sasargeblo genetikuri gardaqmnebi. maT miekuTvneba mutaciamutaciamutaciamutacia, romlis drosac programis

struqturaSi ubralod Seitanebian SemTxveviTi cvlilebebi (magaliTad, saboloo

mniSvnelobis Secvla sxva mniSvnelobiT an qvexiT). gadagadagadagadanacvlebanacvlebanacvlebanacvleba, romelic striqonebis

a) b)

sur. #14.3. ori programa, romlebic eqvemdebarebian Sejvarebas SemTxveviTad SerCeul wertilSi.

a) b)

nax. 11.6. Svilobili programebi, romlebic miiRebian Sejvarebis Sedegad.


investirebis analogiuria. es operaciac sruldeba calkeuli programebisTvis da

mdgomareobs saboloo simboloebis an qvexeebis adgilebis gacvlaSi.

programebis mimdinare Sevseba asaxavs amoxsnis mdgomareobas. ar arseboben

specialuri meTodebi, romlebic mogvcemdnen saSualebas gaviTvaliswinoT xarisxis

kriteriumiT gansazRvruli zedapiris reliefi evoluciuri procesis dros.. am

TvlsazrisiT genetikuri programireba gvagonebs eqstremumis Zebnis “xarb” algoriTms,

romelic ganvixileT Zebnis informirebuli algoriTmebis ganxilvis dros. genetikuri

programireba aris evoluciis bunebrivi procesis msgavsi, radgan programebis

transformacia SeiZleba Sesruldes uwyvetad. miuxedavad amisa drois da gamoTvliTi

resursebis SezRuduloba Txoulobs gaCerebis pirobebis mocemas. aseTi pirobebi

Cveulebriv damokidebuli arian xarisxis kriteriumis mniSvnelobaze da moxmarebul

gamoTvliT resursebze.

radgan genetikuri programireba aris kompiuteruli programebis generirebis meTodi,

amitom is SeiZleba mivakuTnoT avtomaturi programebis sferos. fragmentuli informaciis

safuZvelze kompiuteruli programebis avtomaturi Seqmnis problemaze mkvlevarebi

muSaoben xelovnuri inteleqtis ganviTarebis dawyebidan. genetikuri programireba

SeiZleba ganvixiloT, rogorc erT-erTi saSualeba gamokvlevebis am mniSvnelovan

sferoSi.


1. ras ewodeba sqema?

2. raSi mdgomareobs sqemebis analizi?

3. ra elementebs Seicavs klasifikaciis sistema?

4. ra mizniT gamoiyeneba klasifikaciis sistemaSi genetikuri operaciebi?

5. ras niSnavs swavla “waxalisebiT”?

6. risi analogia “saxanZro jaWvis” algoriTmi?

7. rogor gamoiTvleba xarisxis zoma, romelic Seesabameba maklasificirebel

wess?

8. rogor gamoiTvleba maklasificirebeli wesis Sesabamisobis xarisxi?

9. ras niSnavs genetikuri programirebia?

10. rogor ganisazRvreba programis xarisxi?

11. ra komponentebs Seicavs genetikuri programireba?

12. rogor xdeba sawyisi “programebis generireba?

13. raSi mdgomareobs xarisxis wrfivi kriteriumi?

14. ra ZiriTadi genetikuri operaciebi gamoiyeneba genetikur programirebaSi?

15. ratomaa naklebad sasargeblo mutaciis operaciis gamoyeneba genetikur

programirebaSi?



1. aageT genetikuri algoriTmi nkf-is amocanis amosaxsnelad.

2. leqciaSi ganxiluli iyo genetikuri operaciebis gamoyeneba nkfnkfnkfnkf-is

amocanisaTvis. daadgineT, raSi mdgomareobs im dizunqciebis raodenobis roli,

romlebic gansazRvraven nkfnkfnkfnkf-is agebas? SeiZleba Tu ara am amocanisaTvis sxva

xarisxis zomis arCeva?

3. moifiqreT warmodgena komivoiaJeris amocanisaTvis, damatebiTi genetikuri

operaciebi da xarisxis zoma.

4. aageT algoriTmi komivoiaJeris amocanis amosaxsnelad.

silabusi “xelovnur inteleqtSi”silabusi “xelovnur inteleqtSi”silabusi “xelovnur inteleqtSi”silabusi “xelovnur inteleqtSi”

saswavlo kursis dasaxeleba

xelovnuri inteleqti

saswavlo kursis kodi saswavlo kursis statusi zust da sabunebismetyvelo

mecnierebaTa fakulteti(kompiuterul mecnierebaTa departamenti; swavlis safexuri bakalavriati; savaldebulo

saswavlo kursis xangrZlivoba erTi semestri ECTS 5 krediti(45 sakontaqto saaTi; 80

damoukidebeli muSaobis saaTi) leqtori asocirebuli profesori zurab

qoClaZe, tel. 224712 (b).

saswavlo kursis mizani

1. gaacnos studentebs kompiuteruli mecnierebebis erT erTi dargi - xelovnuri inteleqti. 2. Seaswavlos studentebs Tanamedrove inteleqtualur agentebis ideaze damyarebuli midgoma xelovnuri inteleqtisadmi. 3. misces safuZvliani da Rrma codna xelovnuri inteleqtis or ZiriTad mimarTulebaSi - problemaTa gadaWra da codnis warmodgena.

saswavlo kursis Seswavlis winapirobebi studenti unda flobdes diskretuli maTematikis, logikis da algoriTmebis Teoriis ZiriTad cnebebs. SeeZlos programireba romelime enaze.

saswavlo kursis formati leqcia 1 akad. saaTi, seminari 1 akad. saaTi praqtikuli mecadineoba 1 akad. saaTi (1+1+1).

saswavlo kursis Sinaarsi

1. leqcia 1.leqcia 1.leqcia 1.leqcia 1. xelovnuri inteleqtis warmoSoba da ganviTareba.

[1, leq.1,2] [2, gv. 34 –71] 2. leqcia 2.leqcia 2.leqcia 2.leqcia 2. inteleqtualuri agentebis Teoria [1, leq.3,4,5] [2, gv. 75 –104]

3. leqcia leqcia leqcia leqcia 3.3.3.3. agentebi, romlebic problemebs wyveten Zebnis saSualebiT.

4. leqcia 4.leqcia 4.leqcia 4.leqcia 4. Zebnis arainformirebuli algoriTmebi

5. leqcia 5.leqcia 5.leqcia 5.leqcia 5. Zebnis informirebuli algoriTmebi

6. leqcia 6.leqcia 6.leqcia 6.leqcia 6. amocanebi SezRudvaTa dakmayofilebaze

7. leqcia 7.leqcia 7.leqcia 7.leqcia 7. Zebna winaaRmdegobis SemTxvevaSi

8. leqcileqcileqcileqcia 8.a 8.a 8.a 8. codnis kompiuterul sistemebSi warmodgenis problema.

9. leqcia 9.leqcia 9.leqcia 9.leqcia 9. amocanaTa amoxsnis Zlieri meTodebi

145

10. leqcia 10leqcia 10leqcia 10leqcia 10----11.11.11.11. neironuli qselebi 11. leqcia 12.leqcia 12.leqcia 12.leqcia 12. mravalSriani neironuli qselebi

12. leqcia 13.leqcia 13.leqcia 13.leqcia 13. genetikuri algoriTmebi

13. leqcia 14.leqcia 14.leqcia 14.leqcia 14. genetikuri algoriTmebis gamoyeneba klasifikaciis amocanebisaTvis

seminarebze unda moxdes leqciaze wakiTxuli masalis gaRrmaveba da studentebisaTvis gaurkveveli sakiTxebis dazusteba. praqtikul mecadineobebze studentebma unda Seasrulon garkveuli savarjiSoebi. amasTan, yvela studentma semestris ganmavlobaSi unda daweros ori programa Seswavlili algoriTmebis safuZvelze.

Sefaseba daswreba 10 koloqviumebSi monawileoba 30 seminarze muSaoba 10 praqtikulze muSaoba 20 saboloo gamocda 30 saboloo Sefaseba 100

savaldebulo literatura 1.YleqciaTa kursi.YYYYYYY YYYYYYYYYY A2. Стюарт Р. Норвиг П. Искусственный интеллект Москва, Санкт-Петербург, Киев 2006

damatebiTi literatura da sxva saswavlo masala

1. Джордж Ф. Люгер Искусственный интеллект Москва, Санкт-Петербург, Киев 2003

swavlis Sedegi saswavlo kursis gavlis Semdeg students unda SeeZlos Seswavlili algoriTmebisa da midgomebis gamoyeneba praqtikuli amocanebis gadasaWrelad.

Documents

leqciaTa kursi saganSileqciaTa kursi saganSi · PDF file4 leqciaTa kursi xelovnur inteleqtSi leqciaTa kursi xelovnur inteleqtSi is gamoiyenebs ra mTel Tavis gamocdilebas, rac mas gaaCnia