a new model of distributed genetic algorithm for cluster systems: dual individual dga tomoyuki...
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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