Tic tac toe using Ant colony optimization

8/9/2019 Tic tac toe using Ant colony optimization

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ContentsContents

+ntroduction,eed o classicationMaze -roblemsEisting solution a--roachesClassication scheme

Pro-osed algorithmsCom-arati/e anal!sisConclusion


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+ntroduction+ntroduction

Maze -roblems "# Commonl! kno0n as boardgames

Maze -roblems "# concerned b! both scientic

communit! and non technical users.

1ell suited to test heuristic and metaheuristica--roaches.

PSO based a--roaches are no0ada!s beinga--lied on to /arious -roblem domains.


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,eed o classication,eed o classication

Classication o an! -roblem domain makes thetask o nding the solution more eas! andefcient.

Maze -roblems constitutes a 0ide -roblemdomain 0ith a large number o -roblems l!ing init.

Most o the maze -roblems are similar in some

characteristics 0ith a e0 modications.

,o -ro-er taonom! -resent or the maze-roblems.


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Maze -roblemsMaze -roblems

%) 2night tour

3) ic ac oe

') ,#4ueen

() Sudoku

5) 6ight 7u-

8) 9at in a Maze

:) ,# -uzzle

;) Slither# link


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Classication schemeClassication scheme

%. =ased u-on 0inning condition "#%. >ied

3. ?!namic

3. =ased u-on initial boardconguration "#%. Em-t!

3. >illed

'. =ased u-on state o board $b@0solution)

%. >ied

3. ?!namic


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ClassicationClassication

SchemeScheme$$Contd..Contd..)) =ased u-on the abo/e classicationscheme total o ; classes are ormedbut not all the ; classes eists at-resent. he a--licable classes are "#

%. Class A$em-t! ed ed)

3. Class =$lled ed d!namic)

'. Class C$lled d!namic d!namic)

(. Class ?$lled d!namic ed)


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Eisting a--roachesEisting a--roaches

Ant colony based algorithm for Knights tour

+nitialize the chessboard 0ith a small amount o-heromone on each cell in our e-eriment it is

ro0colkB%.

>or each c!cle E/a-orate -heromones

>or each starting s4uare start an ant

Select net mo/e based on -robabilit! calculation. he-robabilit! is calculated as ProbkB $ro0 col k )@D$ro0colk)

the cell 0ith highest -robabilit! is calculated.

Mo/e to ne0 s4uare i tour com-lete sa/e it else go toste- (.

U-date the -heromone matri based u-on the tourormed.


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ContdFContdF

Backtracking based algorithm for Knightstour

Select the start s4uare

Make the start s4uare as the current s4uare9e-eat ste-s ( to 8 until current B destination

Create a list o all -ossible mo/es rom thiss4uare.

Select the net s4uare b! the 0arndoGHsheuristic.

Make it current s4uare


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Genetic algorithm based algorithm for lightup.

%) Ienerate initial -o-ulation

3) E/aluate the tness o each indi/idual in the-o-ulation

') Select best#ranking indi/iduals to re-roduce.

() Create ne0 generation through crosso/er and

mutation e/aluate the indi/idual tness.5) Until $terminating condition) re-eat ste- $ii) to

$i/)

8) 9eturn best chromosome


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Ant colon! based algorithm or light u-

%) >or iteration rom % to maJiteration re-eat ste-s 3 to


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Algorithms Pro-osedAlgorithms Pro-osed

1-Ant based Algorithm for Tic Tac Toe1) Initialization of Goal matrix, adjacency graph. Distribute some

initial pheromone on each node e.g. 0.1 and maing the status as

unused.

!) "ae the first random mo#e.

$) %ccording to opponent&s mo#e the ant tae a tour of length $.

') (rom the tours found deposit pheromone on each edge of those

tours hich lies in the inning set.

*) +he next mo#e by the algorithm ill be on the node ha#ing the

highest pheromone #alue.) -epeat the steps $* until the game ins or dra.


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Algorithm -ro-osed$Algorithm -ro-osed$contdF)contdF)

ACO based Algorithm for Rat in a Mae%) >irst the adacenc! matri is constructed or the gra-h ?ene

source and destination.

3) +nitialize the ant mo/ement rom the start node 0ith number oants let n the destination or the ants is not ed the! 0ill sto-their tour 0hen their 0ill be no -ossible mo/e rom their -osition.

') +nitialize the -heromone matri.

() Calculate the -robabilit! matri b! the gi/en ormulae"

ProbLL! BPheroLL!Q$%@adLL!)@ D niB% $-heroLiLQadLiL)

5) he -aths o all n ants are stored and the -ath 0ith the endnode as the destination node 0ith the shortest node countis considered as the result.

8) he edges o the resultant -ath 0ill recei/e the -heromone/alue and as -heromone increases the -robabilit! oselecting this -ath 0ill also increase.


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Com-arison >or 2nightHsCom-arison >or 2nightHs

tourtourOrder/Technique Execution time for

Backtracking (sec)

Execution time for

AO (sec)

/ x / 0.0$ approx. 0.0$1 approx.

1 x 1 !./ approx. 1. sec approx

!' x !' $.1 approx. 1.* approx.


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Com-arison or 9at in aCom-arison or 9at in a

mazemaze BacktrackingEas! (in "sec) #ifficult(in "sec)

AO

Eas! (in "sec) #ifficult(in "sec)

$ x $ $02approx) $2approx) $02approx) $!2approx)

1% x 1% '02approx) '2approx) $2approx) $/2approx)

&' x &' **2approx) '2approx) *02approx) *12approx)


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Com-arison or 6ight u-Com-arison or 6ight u--roblem-roblem

ie Time taken b! AO(in sec)

Time taken b!*enetic algorithm (in

sec)

10 x 10 0.0* approx. approx.

1* x 1* *.! approx. !0 approx.

!* x !* !0. approx. 1!0 approx.


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Com-arati/e anal!sis or icCom-arati/e anal!sis or icac oeac oeAlgo.

!e"el

#ecision $ree Based#ra%&'(

)in&'(

ACO Based#ra%&'(

)in&'(

Eas! 3& ;& 5


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Com-arison or SudokuCom-arison or Sudoku

Technique Accurac! A+g, Time(in sec)

imulated Annealing 0.' '0.!0

*enetic algorithm 0.1$ *.*

!brid 0.' .


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Com-arison or ,#4ueenCom-arison or ,#4ueenL3&L3&

* A"erage number of +tness function&in ,-runs( A $GA

; (


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ConclusionConclusion

Ater classication the -roblems 0hich comeunder class RA are sim-le routing related-roblems.

the com-arati/e anal!sis -ro/es that the antcolon! a--roach or s0arm based a--roachescan -erorm better or class RA -roblems.

=acktracking a--roaches are not the suitablea--roach or the class R= -roblems.

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Tic tac toe using Ant colony optimization