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.