Parallel Genetic Algorithms By Larry Hale and Trevor McCasland

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

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

Search Space All possible solutions Solution Fitness

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

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

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 = = 10

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 Parent 1Parent Child 1Child

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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