1. 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

2. Cluster,Hyper Cluster, GRID GRID A job of application should be divided into some tasks in several ways. Job Tasks

3.  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

4. 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.

5. 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

6. 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

7. 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.

8. 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

9. Parallerization of DGAs  Usually, each processor has one island.  By operation of migration, some individuals are moved. Migration Crossover Mutation Selection Evaluation

10. Parallerization of DuDGAs  In DuDGA, an island is moved by migraion. Island Crossover Mutation Selection Evaluation

11. 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 0.3 1.0 Crossover rate 5 Migration interval 0.5 Migration rate 240 Population size 4,8,12,24120 Number of islands

12. Test Functions Rastrigin Griewank Ridge Rosenbrok

13. 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 1.1.2 OS Linux 2.2.10 Compiler gcc (egcs-2.91.61)

14.  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.) F1F2F3F4 4 8 12 24 DuDGA 1.0 0.5

15. Number of function calls 回数 A  DuDGA can find an optimum solution with small number of function calls 4 8 12 24 DuDGA 140000 0 70000 F1F2F3F4

16. Searching Transition  In the beginning of the searching, searching ability of the DuDGA is low. Generations 100 200bit Rastrigin Evaluation Value 200 0 50 100 150 200 250 300 8 islands DuDGA （ 120) 24 islands

17. Transition of hamming distance Generations 200400 600800 200bit Rastrigin Hamming Distance between the elite and average individuals 1000 0 20 40 60 80 100 120 diversity  DuDGA can keep the diversity of the solutions 8islands DuDGA （ 120 ) 24islands

18. 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.

19. Distributed effects of DuDGAs 2 processors 4 processors Total population size is constant.

20. Distribution and parallel effects of DuDGAs 5 10 15 20 25 151015 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

21. 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).

22. Difficult problem for DuDGAs Goldberg problem 111 30 101 0 110 0 100 14 011 0 010 22 001 26 000 28 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