A New Model of Distributed Genetic Algorithm for Cluster Systems: Dual Individual DGA Tomoyuki HIROYASU Mitsunori MIKI Masahiro HAMASAKI Yusuke TANIMURA Doshisha University Kyoto, 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 GADGAs  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 GADGA Solutions 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 ability The 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. OverwriteCopy

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 generation Terminal condition 1/L Mutation rate Crossover rate 5 Migration interval 0.5 Migration rate 240 Population size 4,8,12,24120 Number of islands

Test Functions Rastrigin Griewank Ridge Rosenbrok

Cluster system for calculation Spec. of Cluster (16 nodes) Processor Pentium Ⅱ (Deschutes) Clock 400MHz # Processors 1 × 16 Main memory 128Mbytes × 16 Network Fast Ethernet (100Mbps) Communication TCP/IP, MPICH OS Linux Compiler gcc (egcs )

 DuDGA has high searching ability. Searching ability (covering rate) 見率 A Covering rate( it is the success rate of finding the optimum of each problem in 20 trials.) F1F2F3F DuDGA

Number of function calls 回数 A  DuDGA can find an optimum solution with small number of function calls DuDGA F1F2F3F4

Searching Transition  In the beginning of the searching, searching ability of the DuDGA is low. Generations bit Rastrigin Evaluation Value islands DuDGA （ 120) 24 islands

Transition of hamming distance Generations bit Rastrigin Hamming Distance between the elite and average individuals 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 2 processors 4 processors Total population size is constant.

Distribution and parallel effects of DuDGAs The number of processors Speed 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 ability There 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 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