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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
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
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
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
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
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.
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
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
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
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)
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
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
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
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)
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.