Application of Genetic Algorithm to Pipe Network Optimization

7/31/2019 Application of Genetic Algorithm to Pipe Network Optimization

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PTIMIZATI N PR BLEM

PresentedBySUBHAYANDE

RollNo.000710401064

n er e u anceo

Prof.Amitava Gangopadhyay


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strategyamong all feasible possibilities.

Genetic algorithms in optimization are search algorithmsw c m m c e mec an cs o na ura se ec on annatural genetics.Genetic al orithms have been develo ed b ohn Holland,

his colleagues and his students at the University ofMichigan in the early70s.

probable solutions.

These algorithms are computationally simple yet.Genetic algorithms are now finding more widespreadapplication in business, scientific, and engineering circles.

It can be used for pipe optimization problem also.2


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OBJECTIVEBEHINDUSINGGENETICALGORITHMS

In Fig.1. Starting the search in the neighbourhood of the lower

Fig.1. Fig.2.

pea w cause m ss ng t e g er pea .Calculusbased methods depend upon the existence of

derivatives. For example, noisy search spaces as depicted in aless than calculusfriendly function in Fig 2.

On the other hand, GAs know nothing about the problems theyare de lo ed to solve. The erform well in roblems for which

the fitness landscape is complex.3


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BASICCOMPONENTSOFASIMPLEGENETICALGORITHM

EncodingachromosomeUsing

Binary

Encoding,

Chromosome1 1101100100110110

Chromosome2 1101111000011110

FitnessFunctionFormaximizationproblem, ( ) ( )F x f x =1 1

, . x = ,

Reproduction

( )f x 1 ( )f x+

.

Chromosomesareselectedfromthepopulationtobeparentstocrossoverandproduceoffspring.

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SelectionParentsareselectedaccordingtotheirfitness.

Roulettewheelselection

The commonly used reproduction operator is the proportionate

with a probability proportional to the fitness.

Theprobabilityoftheith selectedstringis, ii N

fp =

where

N

is

the

population

size. 1 jj f=

the roulette wheel and

the chromosome wheres ops s se ec e .

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Theaimofthecrossoveroperatoristosearchtheparameterspace.Crossovercanbeillustratedasfollows:(|isthecrossoverpoint):

y Chromosome 1 11011|00100110110

y Chromosome 2 11011|11000011110

y Offspring 1 11011|11000011110

y Offspring 2 11011|00100110110

Mutation

Mutation is intended to prevent falling of all solutions in thepopulation into a local optimum of the solved problem.

y Original Offspring 1101100100110110

y Mutated Offspring 1101101100110100

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FUNDAMENTALTHEOREMOFstringswithsimilaritiesatcertainstringpositions.

y * **,

FromSchemataTheorem,

Short,loworder,aboveaverageschematareceive

ex onentiall increasin trialsinsubse uent enerations.ThisconclusionistheFundamentalTheoremofGeneticAlgorithms.

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NETWORKOPTIMIZATIONPROBLEM FORMULATION

y Theoptimal

design

of

apipe

network

with

apre

specified

layout

in

its

standardformcanbedescribedas

minm

i iC L C= .

subjectedtofollowingconstraints1i=

Hydraulic Constraints: Nodal head and pipe Pipesizeavailabilityi k

i k

q Q

=maxmin ,kH HH

,i iddd

flow velocity constraints : constra nts:

ii p

i

i i i

Jq K c d

=

maxmin iV VV

8

i

where =2.63,K=3.60,=0.5405 in SI units, k=total no of nodes, p=total no of pipes


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A penalty method is used to formulate the optimal design of a.

N=1

2 2 22

,p pi ii

N N K K H HV V

=

max max1 1min 1 min 1i i k kV V H H= = = =

= + + +

y where X represents a measure of the head and velocityconstraint violation of the trial solution and

pis the penalty

, .

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IMPLE ENETI L RITHM T LVEPIPE NETWORK OPTIMIZATION PROBLEM1.

Generation

of

initial

population.2. .

3.Hydraulicanalysisofeachnetwork.

4. ompu a ono pena ycos .

5.Computationoftotalnetworkcost.

. ompu a ono e ness.

7. Generationofanewpopulationusingtheselectionoperator.

8. ecrossoveroperator.

9. Themutationoperator.

10

10.Pro uctiono successivegenerations.


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PROBLEM CONSTRAINTS

Pipe

No.

Vmin

(m/s)

Vmax

(m/s)

Junction

No.

Hmin

(m)

Hmax

(m)

1 2 2.1 1 135 140

2 1.85 2 2 135 140

3 0.07 0.12 - - -

4 1.1 1.2 - - -5 1.25 1.35 - - -

Pipe Dia.

(mm)150 200 250 300 350 400 500 600

os m

(Abstract

Values)

12

PipeSizeAvailabilityConstraintsandtheirCosts


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SOLUTIONCrossoverpro a i ity,pc =0.5,

Mutationprobability,pm =0.001,

Len thof

Chromosome

=15,

Totalnumberofpopulationinageneration=8,

MaximumnumberofGeneration=12.

y p =

1

p =104

p =10

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.continued

Pipe

No.

a. mm . rom spec e m s

Junction

No.

. rom spec e

(m)

p

= 1

p

=104p

=108p

= 1

p =104

p =108

p = 1 p =104

p =108

1250 250 300

-0.33 -0.33 * 1 +20.57 +20.57 +22.57

2 -0.14 -0.14 +0.72 2 +12.46 +12.46 +20.53

3200 200 500

+1.27 +1.27 +1.03 - - - -

4 * * +0.25 - - - -

5 300 300 200 +1.64 +1.64 * - - - -

Cost of the Network

(+ means above the maximum value specified, - means below the minimum value specified, * means in the range specified)

p = 1 p =104

p =108

330000 330000 420000

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, cTHE SOLUTIONCrossoverrates0.5, 0.6, 0.7, 0.8 and 0.9 arechosen

Penalty

parameter,

p =

10

4

, , m . ,

LengthofChromosome=15,Totalnumberofpopulationinageneration=8,

= .

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, mTHE SOLUTIONTwomutationrates0.001 and0.1 arechosen

Penalty

parameter,

p =

10

4

, , c . ,

LengthofChromosome=15,Totalnumberofpopulationinageneration=8,

= .

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CONCLUSIONs a potent a oo or pt m zat on o pe etwor

Problems.

chosen.

in order to preserve some of good strings for a particularroblem.

Mutation is appropriately considered a secondary

mechanism of genetic algorithm adoption as mutation rateis kept very low.

Finally, for this network p = 104, pc = 0.5, pm = 0.001 can be

suggeste as came out rom t e a ove ana ysis.

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REFERENCES av . o erg, ,

MACHINELEARNING,8th IndianReprint2004,PearsonEducation,ISBN81-

7808-130-Xan y, . ., mpson, . .an urp y, . .

GENETICALGORITHMFORPIPENETWORKOPTIMIZATION.WaterResourceRes.,32(2), 449-458.

Me anieMitc e ,ANINTRODUCTIONTOGENETICALGORITHMCambridge,

MA:

MIT

Press,

1998,

ISBN

13:978-0-262-63185-3

M.H.Afshar,A.Afshar,M.A.Mario ANITERATIVEPENALTYMETHODFORTHEOPTIMALDESIGNOFPIPENETWORKS.InternationalJournalofCivilEngineerng.Vol.7,No.2,June2009

S.Rajasekharan,

G.A.

Vijayalakshmi Pai,

NEURAL

NETWORKS,

FUZZY

LOGICANDGENETICALGORITHMS,SYNTHESISANDAPPLICATIONS,13th Printing,2010,PrenticeHallofIndia,ISBN:978-81-203-2186-1

VictorL.Streeter,E.BenjaminWylie,FLUIDMECHANICS,1st SIEdition1988,McGrawHillBookCompany,ISBN:0-07-Y66578-8.

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Documents

Application of Genetic Algorithm to Pipe Network Optimization