parallel genetic algorithms with distributed-environment multiple population scheme

Parallel Genetic Algorithms with

Distributed-Environment Multiple Population Scheme

Parallel Genetic Algorithms with

Distributed-Environment Multiple Population Scheme

M.Miki

T.Hiroyasu

K.Hatanaka

Doshisha University,Kyoto,Japan

Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan

OutlineOutline

• BackgroundBackground

• Optimization ProblemsOptimization Problems

• Effects of GA ParametersEffects of GA Parameters

• Distributed GADistributed GA

• Distributed Environment GADistributed Environment GA

• ConclusionConclusion


DisadvantageDisadvantage

BackgroundBackground

ParallelParalleland and

Distributed SchemeDistributed Scheme

1) High Computation Cost1) High Computation Cost2) Convergence to local minimum2) Convergence to local minimum3) Difficult to choose proper GA parameters3) Difficult to choose proper GA parameters

Effective for 1 and 2Effective for 1 and 2

Crossover rateCrossover rateMutation rateMutation rate


BackgroundBackground

Distributed Environment SchemeDistributed Environment Scheme

Problem on proper setting of GA parametersProblem on proper setting of GA parameters

　　 The performance of GA The performance of GA heavily depends on the GA heavily depends on the GA

parametersparameters

Proper values of GA Parameters Proper values of GA Parameters depend on problemsdepend on problems

Propose a new parameter-free distributed GAPropose a new parameter-free distributed GA


5KN

5KN

Structural Optimization ProblemsStructural Optimization Problems

11 22

33 44

55 66

10-Member Truss10-Member Truss

ObjectiveObjectiveMinimization of Truss VolumeMinimization of Truss Volume

Design ValuablesDesign ValuablesSectional area ofSectional area of 　　 each membereach member

ConstraintsConstraints

• Tensile StrengthTensile Strength• Compressive bucklingCompressive buckling• Displacement at node 6Displacement at node 6


Constraint on tensile stress

Constraint on tensile stress

Constraint on Compressive buckling

Constraint on Compressive buckling

Constraint on displacementConstraint on displacement

Fitness FunctionFitness Function

H

1Fitness

26ddP dw *

66 ddif

dP tP

mN

i

iP1

ttP

otherwise0

if1P

*

ti

i

mN

i

iP1

bbP

otherwise0

if1P

*

bii

iLL

bPTH VwV

Design VariablesDesign Variables

Sectional area ofSectional area ofeach membereach member

(circular shape)(circular shape)

]mm[ 4095Area 1 2

12Bit ×10 = 120Bits


Experiment on Proper GA ParametersExperiment on Proper GA Parameters

Roulette selection Conservation of Elite

Up to 1000 generationsPop. Size 270,2430

0.6

0.3

0.6

1.0

0.3

0.6

1.0

0.3

0.6

1.01.0

0.3

Cro

ssov

er

　 R

ate

MutationMutation 　　 RateRate

0.1/L

0.1/L

1/L

0.1/L

0.1/L 1/L

1/L

1/L

10/L

10/L

10/L

10/L

L is the length of the chromosome

9 Combinations appli9 Combinations applied to SPGAed to SPGA

ExperimentExperiment

9 combinations 9 combinations (3 mutation rates ×3 crossover rates)(3 mutation rates ×3 crossover rates)

ComparisonComparisonbased on the average of 10 trials based on the average of 10 trials

out of 12 trials omitting out of 12 trials omitting the highest and the lowest valuesthe highest and the lowest values


CrossoverCrossoverRateRate

MutationMutationRateRate

Fitness History in Single Population GA (SPGA)Fitness History in Single Population GA (SPGA)

1

1.2

1.4

1.6

1.8

0 200 400 600 800 1000Number of Generations

Fitn

ess

Val

ue

0.3 - 0.1/L0.6 - 0.1/L1.0 - 0.1/L0.3 - 1/L0.6 - 1/L1.0 - 1/L0.3 - 10/L0.6 - 10/L1.0 - 10/LSPGA

Pop. = 270



MutationMutationRateRate1

1.2

1.4

1.6

1.8

0 200 400 600 800 1000Number of Generations

Fitn

ess

Val

ue

0.3 - 0.1/L0.6 - 0.1/L1.0 - 0.1/L0.3 - 1/L0.6 - 1/L1.0 - 1/L0.3 - 10/L0.6 - 10/L1.0 - 10/LSPGA

Pop. = 2430

Fitness History in Single Population GA (SPGA)Fitness History in Single Population GA (SPGA)


Proper GA Parameters of SPGAProper GA Parameters of SPGAMutation RateMutation Rate

0.1/L0.1/LMutation RateMutation Rate

1/L1/LMutation RateMutation Rate

10/L10/L

1.2

1.3

1.4

1.5

1.6

1.7

1.8

0.3 0.6 1.0 0.3 0.6 1.0 0.3 0.6 1.0Crossover Rate

Fitn

ess

Val

ue

SPGA 270SPGA 2430

The performance of SPGAThe performance of SPGAdepends heavily independs heavily in

the proper choice of GA parametersthe proper choice of GA parameters


Multiple Population GA(MPGA)Multiple Population GA(MPGA)

SPGASPGA

Population

A GA is performed in one entire population.

GA

MPGAMPGAMPGAMPGA

GA GA GA

GA GA GA

GA GA GA

Same GAs are performed in multiple

sub population


Computation timeComputation timeSPGASPGA

GA

GA GA

GA GA

MPGAMPGA

Slow

Fast


Migration in MPGAMigration in MPGA

BetterWorse

MigrationMigration

Exchange of Exchange of individuals among individuals among sub populations.sub populations.

Randomly selected Randomly selected source and destination source and destination

sub populationssub populations

Migration RateMigration RateMigration intervalMigration interval


Problem : Same as SPGAMPGA:9 sub populations

Migration rate = 0.3Migration interval = 50

[generations]


Proper GA Parameters fo MPGAProper GA Parameters fo MPGAMutation RateMutation Rate



10/L10/L

1.2

1.3

1.4

1.5

1.6

1.7

1.8

0.3 0.6 1.0 0.3 0.6 1.0 0.3 0.6 1.0Crossover Rate

Fitn

ess

Val

ue

MPGA 270MPGA 2430


Comparison between SPGA and MPGAComparison between SPGA and MPGAMutation RateMutation Rate



10/L10/L

1.2

1.3

1.4

1.5

1.6

1.7

1.8

0.3 0.6 1.0 0.3 0.6 1.0 0.3 0.6 1.0Crossover Rate

Fitn

ess

Val

ue

SPGA 270MPGA 270


Comparison between SPGA and MPGAComparison between SPGA and MPGAMutation RateMutation Rate



10/L10/L

1.2

1.3

1.4

1.5

1.6

1.7

1.8

0.3 0.6 1.0 0.3 0.6 1.0 0.3 0.6 1.0Crossover Rate

Fitn

ess

Val

ue

SPGA 2430MPGA 2430




Effect of Multiple PopulationEffect of Multiple Population

1.3

1.4

1.5

1.6

1.7

1.8

SPGA MPGA

0.3 - 0.1/L

0.6 - 01/L

1.0 - 0.1/L

0.3 - 1/L

0.6 - 1/L

1.0 - 1/L

0.3 - 10/L

0.6 - 10/L

1.0 - 10/L

Increase in the Increase in the quality of Solutions.quality of Solutions.

However, However, proper setting of proper setting of GA parameters is GA parameters is

necessary.necessary.


Distributed Environment GA

Distributed Environment GA

Conventional Environment GA

Conventional Environment GA

Distributed Environment GA(DEGA)Distributed Environment GA(DEGA)

Different GA Different GA parameters are used.parameters are used.

Same parameters Same parameters are used.are used.

　　　 Crossover Rate

Mutation Rate


Problem : Same as MPGA

9 Different environments9 Different environments(3 mutation rates ×3 crossover rates)(3 mutation rates ×3 crossover rates)

for evaluationfor evaluation




1.3

1.4

1.5

1.6

1.7

1.8

SPGA MPGA

Fitn

ess

Val

ue

0.3 - 0.1/L

0.6 - 01/L

1.0 - 0.1/L

0.3 - 1/L

0.6 - 1/L

1.0 - 1/L

0.3 - 10/L

0.6 - 10/L

1.0 - 10/LPop.size = 270Worst = 1.38Worst = 1.38

Avg.Avg.1.581.58

Best = 1.74Best = 1.74Best = 1.78Best = 1.78

Avg.1.70

Worst = 1.58Worst = 1.58

Effect of DEGAEffect of DEGA

1.3

1.4

1.5

1.6

1.7

1.8

SPGA MPGA DE

Fitn

ess

Val

ue

0.3 - 0.1/L

0.6 - 01/L

1.0 - 0.1/L

0.3 - 1/L

0.6 - 1/L

1.0 - 1/L

0.3 - 10/L

0.6 - 10/L

1.0 - 10/L

3×3

1.75ResultsResults

1. DEGA outperforms the best SPGA.

2.DEGA provides good performance even comparing to

MPGA


ConclusionConclusion

(1) The multiple population GA yields better solutions (1) The multiple population GA yields better solutions than single population GA because the diversity of than single population GA because the diversity of

individuals are maintained in the multiple population individuals are maintained in the multiple population GA during the evolutional process.GA during the evolutional process.

(2) The distributed environment scheme in the multiple (2) The distributed environment scheme in the multiple population GA shows a good performance compared to population GA shows a good performance compared to other conventional GA. This scheme does not need to other conventional GA. This scheme does not need to predetermine the GA parameters,and it is very useful predetermine the GA parameters,and it is very useful for many problems where the proper values of those for many problems where the proper values of those

parameters are not known.parameters are not known.

parallel genetic algorithms with distributed-environment multiple population scheme

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