A New Model of Distributed Genetic Algorithm for Cluster Systems: Dual Individual DGA

Tomoyuki HIROYASUMitsunori MIKIMasahiro HAMASAKIYusuke TANIMURA

Doshisha UniversityKyoto, Japan

Cluster,Hyper Cluster, GRID

GRID

A job of application should be divided into some tasks in several ways.

Job

Tasks

Island model (DGAs)

Master Slave

Cellular

Optimization methods Finding the best routings of the network

Designing structures

Constructing systems

Aim of this study

Genetic Algorithms

New model of DGAs

Dual Individual DGAs(DGAs)

Easy to divide into tasks in several ways

High searching ability

Distributed Genetic Algorithms (DGAs)

Simple GA DGAs

In DGAs, the total population is divided into sub populations.

Crossover

Mutation

Selection

Evaluation

Migration

In each sub population, a simple GA is performed.

Individuals are exchanged by migration.

Related work

It is reported that DGAs have high searching ability.

There are several studies concerned with DGAs.

“A survey of parallel distributed genetic algorithms”

E.Alba and J.M. Troya

“A survey of parallel genetic algorithms”E.Cantu-Paz

“A Searching Ability of DGAs”M. Miki, T. Hiroyasu, M. Kaneko and K. Hatanaka

The mechanism of DGAs

The solutions are converged in each island.

An Operation of migration keeps the diversity of the solutions in a total population.

An optimal solution can be derived with smaller number of total population size.

There are are several islands.

Simple GA DGASolutions

are converged

High searching ability

Can be divided into small tasks

Dual Individual DGAs (DuDGAs)

DuDGA There are two individuals in each island

Crossover rate=1.0

Mutation rate= 0.5

Easiness to set up

High searching abilityThe high validity of the solutions because there are numbers of islands.

Operations of DuDGAs

Migrated Individual is chosen randomly.

Migrated individual is copied and moved to the other islnads.

The existed individual that has smaller fitness value is over wrote by the migrated individual.

Selection

Migration

There are 4 individuals after the crossover (two parents and two children).

One of the parents and one of the children are selected with respect to their fitness values.

Overwrite Copy

Parallerization of DGAs

Usually, each processor has one island.

By operation of migration, some individuals are moved.

Migration

Crossover

Mutation

Selection

Evaluation

Parallerization of DuDGAs

In DuDGA, an island is moved by migraion.

Island Crossover

Mutation

Selection

Evaluation

Test functions and used parameters

DuDGA and DGAs (4, 8, 12, 24 islands) are applied to each test function.

F1=200bit Rastrigin

F2=50bit Rosenbrock

F3=100bit Griewank

F4=100bit Ridge

After 5000 generationTerminal condition

1/LMutation rate

0.3

1.0Crossover rate

5Migration interval

0.5Migration rate

240Population size

4,8,12,24120Number of islands

Test Functions

Rastrigin

Griewank

Ridge

Rosenbrok

fRidge= xjΣj=1

N 2

Σi=1

N

fRastrigin=10n+ xi2 – 10cos 2πxiΣ

i=1

n

fGriewank=1+xi

2

4000– cos

xii

Πi=1

n

Σi=1

n

fRosenbrok= 100xi – 12 – xi

2+ xi – 1

2Σi=2

n

Cluster system for calculation

Spec. of Cluster (16 nodes)

Processor Pentium (Deschutes)ⅡClock 400MHz# Processors 1 × 16Main memory 128Mbytes × 16Network Fast Ethernet (100Mbps)Communication TCP/IP, MPICH 1.1.2OS Linux 2.2.10Compiler gcc (egcs-2.91.61)

DuDGA has high searching ability.

Searching ability (covering rate)

Covering rate( it is the success rate of finding the optimum of each problem in 20 trials.)

F1 F2 F3 F4

4

81224DuDGA

1.0

0.5

Number of function calls

DuDGA can find an optimum solution with small number of function calls

4

81224DuDGA

140000

0

70000

F1 F2 F3 F4

Searching Transition

In the beginning of the searching, searching ability of the DuDGA is low.

Generations100

200bit Rastrigin

Evalu

ati

on

V

alu

e

2000

50

100

150

200

250

300

8 islands

DuDGA （ 120)

24 islands

Transition of hamming distance

Generations200 400 600 800

200bit Rastrigin

Ham

min

g D

ista

nce

betw

een t

he e

lite a

nd

avera

ge ind

ivid

uals

10000

20

40

60

80

100

120

diversity

DuDGA can keep the diversity of the solutions

8islands

DuDGA（ 120)

24islands

Searching mechanism of DuDGAs

In the beginning, DuDGA is searching in global area and searching in the local area in the end of the search.

Beginning of search End of search

In this model, the individuals that are not good can survive.

This mechanism keeps the diversity of the solutions.

Because there are only two individuals in each island, the solutions are converged quickly in the end of search.

Distributed effects of DuDGAs

0

500

1000

1500

2000

2500

1 2 4 8 16

Number of processors

Calculation time [s]2 processors

4 processors

Total population size is constant.

Distribution and parallel effects of DuDGAs

5

10

15

20

25

1 5 10 15

The number of processors

Sp

eed

Up

Rate

Speed up rate is the relation between the calculation time of one processor model and that of multi processor model.Therefore, this rate has the factor of the model distribution effects and the parallel effects of DuDGAs

Conclusions

Dual Individual Distributed Genetic Algorithms (DuDGAs)

Some parameters needless to be set

High searching abilityThere are many islands

DuDGAs can be divided into several tasks in many ways

DuDGAs will be applied to GRID systems (may be CCGrid 2000).

Difficult problem for DuDGAs

• Goldberg problem

11130

1010

1100

10014

011001022

00126

00028

f(000) = 28　f(001) = 26　f(010) = 22　f(100) = 14　f(110) = 0　f(101) = 0　f(011) = 0　f(111) = 30

Fitness values