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
Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan
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
Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan
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
Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan
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
Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan
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
Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan
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
Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan
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
Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan
CrossoverCrossoverRateRate
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)
Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan
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
Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan
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
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Computation timeComputation timeSPGASPGA
GA
GA GA
GA GA
MPGAMPGA
Slow
Fast
Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan
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
ExperimentExperiment
Problem : Same as SPGAMPGA:9 sub populations
Migration rate = 0.3Migration interval = 50
[generations]
Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan
Proper GA Parameters fo MPGAProper GA Parameters fo MPGAMutation 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
MPGA 270MPGA 2430
Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan
Comparison between SPGA and MPGAComparison between SPGA and MPGAMutation 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 270MPGA 270
Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan
Comparison between SPGA and MPGAComparison between SPGA and MPGAMutation 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 2430MPGA 2430
Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan
CrossoverCrossoverRateRate
MutationMutationRateRate
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.
Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan
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
ExperimentExperiment
Problem : Same as MPGA
9 Different environments9 Different environments(3 mutation rates ×3 crossover rates)(3 mutation rates ×3 crossover rates)
for evaluationfor evaluation
Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan
CrossoverCrossoverRateRate
MutationMutationRateRate
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
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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.
Intelligent Systems LaboratoryIntelligent Systems Laboratory Doshisha University,Kyoto,JapanDoshisha University,Kyoto,Japan