A Parallel Genetic Algorithm with Distributed Environment Scheme
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Intelligent Systems Design Lab., Doshisha Univ., Japan
A Parallel Genetic Algorithm withDistributed Environment Scheme
M. Kaneko
M. Miki
T. Hiroyasu
Doshisha University, Kyoto, Japan
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Intelligent Systems Design Lab., Doshisha Univ., Japan
Background
GAs(Genetic Algorithms)Stochastic search algorithms based on the mechanics of n
atural selection and natural genetics
Disadvantage A huge amount of computational resource is required.
The performance of GAs depends on a choice for the rates of parameters. However, it is difficult to choose proper rates of parameters.
Parallel Distributed GA (PDGA)
PDGA with Distributed Environment
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Intelligent Systems Design Lab., Doshisha Univ., Japan
Parallel Distributed GA
Some GAs are performed in multiple subpopulations. Migration: Exchange of individuals among subpopulations
Population
Individual
Single Population GA(SPGA) Subpopulation
Parallel Distributed GA(PDGA)
Migration
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Intelligent Systems Design Lab., Doshisha Univ., Japan
CrossoverTo perform direct information exchange between individuals
MutationTo avoid stagnation in evolution
Crossover and Mutation
parent A
parent B
child A
child B
0.6 DeJong (1975) 0.95 Grefenstette (1986)0.75~0.95 Bäck (1996)
0.001 DeJong (1975) 0.01 Grefenstette (1986)0.005~0.01 Schaffer (1989)1/L Bäck (1996) L: Coromosome Length
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Intelligent Systems Design Lab., Doshisha Univ., Japan
Test Functions
n
iiiii xxxxf
2
222110,1 )1()(100)|(
10
1
210,1 2cos10100)|(
iiiii xxxf
10
110,1 ||sin)|(
iiiii xxxf
10
1
10
1
2
10,1 cos4000
1)|(i i
iiii
i
xxxf
Rastrigin
Schwefel
Griewank
Rosenbrock
100(10bits×10variables)
100(10bits×10variables)
100(10bits×10variables)
120(12bits×10variables)
Name FunctionsChromosomelength (bit)
none
none
weak
strong
Epistasis
Rastrigin Schwefel Griewank Rosenbrlck
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Intelligent Systems Design Lab., Doshisha Univ., Japan
Number of Subpopulations
Subpopulation size
Total Population size
Migration Interval
Migration Rate
Max Generations
0.3
0.6
1.0
0.1/L 1/L 10/L
Mutation Rate
0.3
0.1/L
0.3
1/L
0.3
10/L
0.6
0.1/L
0.6
1/L
0.6
10/L
1.0
0.1/L
1.0
1/L
1.0
10/L
Cro
ssov
er R
ate
L: Chromosome length
Roulette selection
Conservation of elite
One point crossoverThe average of 10 trials out of 12 trials omitting the highest and lowest values
9
20, 180
180,1620
20
0.3
1000
Procedures of Experiments
nCUBE2 with 64 processorsProcessor network : HypercubeOne processor is assigned to one subpopulation.
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Intelligent Systems Design Lab., Doshisha Univ., Japan
History of Fitness (SPGA)
RastriginPop. Size 180
Pm = 0.1/L Pm = 1/L Pm = 10/L
Pc 1.0 0.6 0.3
Fitn
ess
valu
e
-10
-8
-6
-4
-2
0
0 500 1000Generations
-10
-8
-6
-4
-2
0
0 500 1000Generations
-50
-40
-30
-20
-10
0
0 500 1000Generations
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Intelligent Systems Design Lab., Doshisha Univ., Japan
The Effect of Crossover and Mutation Rates(SPGA)
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
180 1620 180 1620 180 1620 180 1620
Func
tion
valu
e
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/L
Rastrigin Schwefel Griewank Rosenbrock
Population sizes and Functions
Pc - Pm
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Intelligent Systems Design Lab., Doshisha Univ., Japan
History of Fitness (PDGA)
RastriginPop. Size 180
Pm = 0.1/L Pm = 1/L Pm = 10/L
Fitn
ess
valu
e
-10
-8
-6
-4
-2
0
0 500 1000Generations
-10
-8
-6
-4
-2
0
0 500 1000Generations
-50
-40
-30
-20
-10
0
0 500 1000Generations
Pc 1.0 0.6 0.3
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Intelligent Systems Design Lab., Doshisha Univ., Japan
The Effect of Crossover and Mutation Rates
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
180 1620 180 1620 180 1620 180 1620
Func
tion
valu
e
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/L1.0E-14
1.0E-15
~~~~
Rastrigin Schwefel Griewank Rosenbrock
Population sizes and Functions
(PDGA)
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Intelligent Systems Design Lab., Doshisha Univ., Japan
Comparison of the performance
Pop. Size 180(SPGA and PDGA)
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
SPGA PDGA SPGA PDGA SPGA PDGA SPGA PDGA
Func
tion
valu
e
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/L1.0E-14
1.0E-15
~~~~
Rastrigin Schwefel Griewank Rosenbrock
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Intelligent Systems Design Lab., Doshisha Univ., Japan
PDGA/DE (Distributed Environment)
PDGA/CE (Constant Environment)
PDGA/DE (Distributed Environment)
Crossover rate
Mutation rate
Different crossover ratesDifferent mutation rates
A Constant crossover rateA Constant mutation rate
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Intelligent Systems Design Lab., Doshisha Univ., Japan
Effectiveness of PDGA/DEPop. Size 180
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
SPGA CE DE SPGA CE DE SPGA CE DE SPGA CE DE
Func
tion
valu
e
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/LDE
Rastrigin Schwefel Griewank Rosenbrock
1.0E-14
1.0E-15
~~
~~
PDGA PDGA PDGA PDGA
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Intelligent Systems Design Lab., Doshisha Univ., Japan
0
5
10
15
20
25
30
Spee
dup
Rastrigin Schwefel Griewank Rosenbrock
Speedup
(1) 8.6 (similar to the ideal speedup)
(2) between 22 and 25 (except for the Rosenbrock function) PDGA/DE provides solution 2.6 to 2.9 times faster than SPGA
Ideal speedup
1000 generations
same quality of solutions (at 1000 generations in PDGA/DE)
Pop. Size = 450Number of Subpopulations = 9 (9PEs)
PDGA/DE vs. SPGA (with the best combination)
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Intelligent Systems Design Lab., Doshisha Univ., Japan
Conclusions
The optimum crossover and mutation rates vary according to the population size and the problem to be solved.
A parallel distributed GA with distributed environment(PDGA/DE) is proposed, and the superiority of this scheme is experimentally proved.
PDGA/DE is the fastest way to gain the best solution under uncertainty of the appropriate crossover and mutation rates.