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A Parallel Genetic Algorithm with Distributed Environment Scheme

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A Parallel Genetic Algorithm with Distributed Environment Scheme

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A Parallel Genetic Algorithm with Distributed Environment Scheme

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A Parallel Genetic Algorithm withDistributed Environment Scheme

M. Kaneko

M. Miki

T. Hiroyasu

Doshisha University, Kyoto, Japan

- 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

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

parent A

parent B

- Crossover
- To perform direct information exchange between individuals

- Mutation
- To avoid stagnation in evolution

0.6DeJong (1975)

0.95Grefenstette (1986)

0.75~0.95 Bäck (1996)

child A

child B

0.001DeJong (1975)

0.01Grefenstette (1986)

0.005~0.01 Schaffer (1989)

1/L Bäck (1996)

L: Coromosome Length

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

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.

Pc 1.0

0.6

0.3

Rastrigin

Pop. Size 180

Fitness value

Pm = 0.1/L

Pm = 1/L

Pm = 10/L

(SPGA)

Pc - Pm

Pc 1.0

0.6

0.3

Rastrigin

Pop. Size 180

Fitness value

Pm = 0.1/L

Pm = 1/L

Pm = 10/L

(PDGA)

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

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

Pop. Size 180

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

- 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.