1. Parallel Genetic Algorithms By Larry Hale and Trevor McCasland

2. Introduction to Genetic Algorithms Genetic algorithms are search algorithms that use the principles of natural selection to find more optimal solutions to modeling, simulation, and optimization problems. Generate “good but not optimal” solutions to brute-forceable problems They then recombine these in an attempt to find an optimal or near optimal solution These candidate solutions are then evaluated for “fitness”. Fitness is computationally expensive to evaluate

3. Biological Background Individual - Any possible solution Population - The working group of all individuals Gene - A particular trait of an individual Chromosome - A set of genes that make a model for an individual Genome - Set of all chromosomes of an individual Genotype - Particular set of genes in a genome of an individual Phenotype - Physical and mental characteristics of an individual

4. Search Space All possible solutions Solution Fitness

5. Selection Deciding which members of the population that will be used to generate new solutions through either of the following Random selection Selection proportional to fitness

6. Evaluation Fitness - each individual is evaluated for its effectiveness For example, fitness of the following individual is 23 - 10 = 13 23 - best possible fitness 10 - inferior genes 13 - resulting fitness score 10010101000010101010100 Solution 10100101010101010010101 Individual

7. Evaluation Continued A good fitness evaluation gives a fitness that is proportional to how close to the optimal solution it is A more practical example, 12 total possible conflicts 2 conflicts fitness = 12 - 2 = 10

8. Recombination (or Crossover) Selected solutions are recombined in various ways to generate new solutions The most common solution to this is called a one-point crossover 101100011010010101001101 Parent 1Parent 2 100110101010010101001101 Child 1Child 2 101100010100101010100111 100110100100101010100111

9. Mutation Random changes introduced to aid in finding a better solution Chance of mutation is usually between 1 and 2 tenths of a percent 101100011010010101001101 Before: 101100011010110101001101 After:

10. Genetic Algorithm Process Initialize Population Evaluate Select Mutate Recombine End? Solution YesNo Next Generation

11. Advantages of Parallel Genetic Algorithms Shares all of the advantages of a serial GA Higher efficiency and efficacy Less likely to find suboptimal solutions Parallel search from multiple points in search space Can yield alternative solutions to a problem Robust and not very restrictive because they run independently

12. Classification of Parallel Genetic Algorithms Ratio is low for fine grain parallel GAs Fine grain examples Master-slave Toroidal cluster Ratio is high for coarse grain parallel GAs Coarse grain examples Ring GA (hypercube or other topology) Dual Species GA Classification relies of the computation/communication ratio

13. Master-Slave Global single-population Evaluation of fitness is distributed among slaves Selection, recombination, and mutation are all done in the master processor Slaves Master Genetic Operators Calculate Fitness Fitness Individuals

14. Toroidal Cluster Separated single-population Population is distributed over processors of a 2D mesh Neighbors share members of their population for parent selection

15. Ring GA Multiple populations Each processor is assigned a simple GA and there is little communication between populations This also restricts the size of the selection and mating pools Migration Island

16. Dual Species Genetic Algorithm Population 1 favors crossovers of parents that are high in similarity low mutation rate Population 2 favors crossovers of parents that are low in similarity high mutation rate A coarse grained GA with only two subpopulations The populations exploit the use of different crossover probability and mutation operators to prevent premature convergence Migration occurs when one of the populations have converged

17. DSGA Process Initialize Populations Evaluate Populations End? Solution Yes Selection 1 Selection 2 Crossover 1 Crossover 2 Mutation 1 Mutation 2 Migrate? No Migrate Yes No

18. Parallel GA Hybrids Coarse and fine grain Coarse grain and master slave Coarse grain and coarse grain

19. Coarse Grained Vs Fine Grained (Rastrigin function) Generally coarse grained genetic algorithms perform better because of their efficiency and global population Fine grained genetic algorithms are favored when fitness calculation time is large

20. MAXSAT FGA Vs SGA Number of fitness evaluations: 30000 Population size: 30 Offspring size: 200 Speedup: 43/40 = 1.08

21. MAXSAT FGA Vs SGA Number of fitness evaluations: 30000 Population size: 30 Offspring size: 600 Speedup: 117/75 = 1.56

22. MAXSAT FGA Vs SGA Number of fitness evaluations: 50000 Population size: 30 Offspring size: 1000 Speedup: 211/115 = 1.83

23. MAXSAT FGA Vs SGA Number of fitness evaluations: 100000 Population size: 30 Offspring size: 2000 Speedup: 416/240 = 1.83

24. Sources http://neo.lcc.uma.es/Articles/albatroyaxx_2.pdf http://tracer.uc3m.es/tws/cEA/documents/cant98.pdf http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.45.8861&rep=rep1&ty pe=pdf http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4636604 http://neo.lcc.uma.es/cEA-web/documents/hiroyasu.pdf