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A Parallel Genetic Algorithm with Distributed Environment Scheme

A Parallel Genetic Algorithm with Distributed Environment Scheme. M. Kaneko M. Miki T. Hiroyasu. Doshisha University, Kyoto, Japan. Background. GAs(Genetic Algorithms) Stochastic search algorithms based on the mechanics of natural selection and natural genetics Disadvantage

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A Parallel Genetic Algorithm with Distributed Environment Scheme

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  1. A Parallel Genetic Algorithm withDistributed Environment Scheme M. Kaneko M. Miki T. Hiroyasu Doshisha University, Kyoto, Japan

  2. 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

  3. 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

  4. Crossover and Mutation parent A parent B • Crossover • To perform direct information exchange between individuals • Mutation • To avoid stagnation in evolution 0.6 DeJong (1975) 0.95 Grefenstette (1986) 0.75~0.95 Bäck (1996) child A child B 0.001 DeJong (1975) 0.01 Grefenstette (1986) 0.005~0.01 Schaffer (1989) 1/L Bäck (1996) L: Coromosome Length

  5. Test Functions Epistasis Name Functions Chromosome length (bit) none Rastrigin 100 (10bits×10variables) none Schwefel 100 (10bits×10variables) 100 (10bits×10variables) weak Griewank 120 (12bits×10variables) strong Rosenbrock Rastrigin Schwefel Griewank Rosenbrlck

  6. Procedures of Experiments 10/L 1.0 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 10/L 0.1/L 1/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 0.1/L 1/L 1.0 1.0 1.0 L：Chromosome length nCUBE2 with 64 processors Processor network : Hypercube One processor is assigned to one subpopulation.

  7. History of Fitness (SPGA) Pc 1.0 0.6 0.3 Rastrigin Pop. Size 180 Fitness value Pm = 0.1/L Pm = 1/L Pm = 10/L

  8. The Effect of Crossover and Mutation Rates (SPGA) Pc - Pm

  9. History of Fitness (PDGA) Pc 1.0 0.6 0.3 Rastrigin Pop. Size 180 Fitness value Pm = 0.1/L Pm = 1/L Pm = 10/L

  10. The Effect of Crossover and Mutation Rates (PDGA)

  11. Comparison of the performance 1.0E+03 1.0E+02 0.3-0.1/L 1.0E+01 0.6-0.1/L 1.0E+00 1.0-0.1/L Function value 0.3- 1/L 1.0E-01 0.6- 1/L 1.0E-02 1.0- 1/L 0.3-10/L 1.0E-03 0.6-10/L ～ ～ ～ ～ 1.0E-14 1.0E-04 1.0-10/L 1.0E-15 1.0E-05 SPGA PDGA SPGA PDGA SPGA PDGA SPGA PDGA Rastrigin Schwefel Griewank Rosenbrock (SPGA and PDGA) Pop. Size 180

  12. 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

  13. Effectiveness of PDGA/DE Pop. Size 180

  14. Speedup 1000 generations same quality of solutions (at 1000 generations in PDGA/DE) Pop. Size = 450 Number of Subpopulations = 9 (9PEs) 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

  15. 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.

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