A Parallel Genetic Algorithm with Distributed Environment Scheme

1
A Parallel Genetic Algorithm withDistributed
Environment Scheme

• M. Kaneko
• M. Miki
• T. Hiroyasu

Doshisha University, Kyoto, Japan
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Background

• GAs(Genetic Algorithms)
• Stochastic search algorithms based on the
  mechanics of natural 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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Parallel Distributed GA
Single Population GA (SPGA)
Parallel Distributed GA (PDGA)
Subpopulation
Population
Migration
Individual

• Some GAs are performed in multiple
  subpopulations.
• Migration Exchange of individuals among
  subpopulations

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Crossover and Mutation

• Crossover
• To perform direct information exchange between
  individuals
• Mutation
• To avoid stagnation in evolution

0.6 DeJong (1975) 0.95 Grefenstette
(1986) 0.750.95 Bäck (1996)
child A
child B
0.001 DeJong (1975) 0.01 Grefenstette
(1986) 0.0050.01 Schaffer (1989) 1/L
Bäck (1996) L Coromosome Length
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Test Functions
Name
Functions
Chromosome length (bit)
Epistasis
Rastrigin
100 (10bits10variables)
none
none
Schwefel
100 (10bits10variables)
100 (10bits10variables)
Griewank
weak
120 (12bits10variables)
strong
Rosenbrock
Rastrigin
Schwefel
Griewank
Rosenbrlck
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Procedures of Experiments
Mutation Rate
9 20, 180 180,1620 20 0.3 1000
Number of Subpopulations Subpopulation size Total
Population size Migration Interval Migration
Rate Max Generations
0.1/L
1/L
10/L
0.3
0.1/L
1/L
10/L
0.3
0.3
0.3
0.6
0.1/L
1/L
10/L
Crossover Rate
Roulette selection Conservation of elite One
point crossover The average of 10 trials out of
12 trials omitting the highest and lowest values
0.6
0.6
0.6
1.0
0.1/L
1/L
1.0
1.0
LChromosome length
nCUBE2 with 64 processors Processor network
Hypercube One processor is assigned to one
subpopulation.
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History of Fitness (SPGA)
Rastrigin Pop. Size 180
Fitness value
Pm 0.1/L
Pm 1/L
Pm 10/L
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The Effect of Crossover and Mutation Rates
(SPGA)
Pc - Pm
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History of Fitness (PDGA)
Rastrigin Pop. Size 180
Fitness value
Pm 0.1/L
Pm 1/L
Pm 10/L
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The Effect of Crossover and Mutation Rates
(PDGA)
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Comparison of the performance
(SPGA and PDGA)
Pop. Size 180
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PDGA/DE (Distributed Environment)
PDGA/DE (Distributed Environment)
Different crossover rates Different mutation rates
PDGA/CE (Constant Environment)
A Constant crossover rate A Constant mutation rate
Mutation rate
Crossover rate
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Effectiveness of PDGA/DE
Pop. Size 180
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Speedup
PDGA/DE vs. SPGA (with the best combination)
Ideal 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
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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.