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

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

3. Aim of this study • Optimization methods • Finding the best routings of the network • Designing structures • Constructing systems New model of DGAs Genetic Algorithms Dual Individual DGAs (DGAs) • Island model (DGAs) • Master Slave • Cellular • Easy to divide into tasks in several ways • High searching ability

4. Distributed Genetic Algorithms (DGAs) Simple GA DGAs Selection Crossover Mutation Evaluation Migration • In DGAs, the total population is divided into sub populations. • In each sub population, a simple GA is performed. • Individuals are exchanged by migration.

5. Related work • There are several studies concerned with DGAs. • It is reported that DGAs have high searching ability. “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 Simple GA DGA Solutions are converged • 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. High searching ability Can be divided into small tasks

7. High searching ability The high validity of the solutions because there are numbers of islands. Dual Individual DGAs (DuDGAs) DuDGA • There are two individuals in each island • Easiness to set up Crossover rate=1.0 Mutation rate= 0.5

8. Operations of DuDGAs Selection • 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. Migration • 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. Overwrite Copy

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

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

11. Test functions and used parameters • DuDGA and DGAs (4, 8, 12, 24 islands) are applied to each test function. Number of islands 120 4,8,12,24 F1=200bit Rastrigin F2=50bit Rosenbrock F3=100bit Griewank F4=100bit Ridge Population size 240 Migration rate 0.5 0.3 Migration interval 5 Crossover rate 1.0 Mutation rate 1/L Terminal condition After 5000 generation

12. Test Functions Rastrigin Griewank Ridge Rosenbrok

13. Cluster system for calculation Processor PentiumⅡ(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) Spec. of Cluster (16 nodes)

14. Searching ability (covering rate) Covering rate( it is the success rate of finding the optimum of each problem in 20 trials.) 見 率 1.0 4 8 0.5 12 24 A DuDGA F1 F2 F3 F4 • DuDGA has high searching ability.

15. Number of function calls 回 数 140000 4 8 70000 12 24 A DuDGA 0 F1 F2 F3 F4 • DuDGA can find an optimum solution with small number of function calls

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

17. DuDGA（120) 24islands 8islands Transition of hamming distance 200bit Rastrigin 120 100 diversity 80 Hamming Distance between the elite and average individuals 60 40 20 0 200 400 600 800 1000 Generations • DuDGA can keep the diversity of the solutions

18. Searching mechanism of DuDGAs End of search Beginning 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. • In the beginning, DuDGA is searching in global area and searching in the local area in the end of the search.

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

20. 25 20 15 10 5 1 5 10 15 Distribution and parallel effects of DuDGAs Speed Up Rate The number of processors 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) • High searching ability • Some parameters needless to be set • 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 Fitness values 0110 01022 f(000) = 28f(001) = 26f(010) = 22f(100) = 14f(110) = 0f(101) = 0f(011) = 0f(111) = 30 1100 11130 00126 00028 10014 1010