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Transcript
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 Fitness Solution 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 23 - 10 = 13 • 23 - best possible fitness • 10 - inferior genes • 13 - resulting fitness score Solution 10010101000010101010100 Individual 10100101010101010010101 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 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 1 Parent 2 10110001 1010010101001101 10011010 0100101010100111 Child 1 Child 2 10011010 1010010101001101 10110001 0100101010100111 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: 101100011010010101001101 After: 101100011010110101001101 Genetic Algorithm Process Initialize Population Evaluate End? Next Generation No Yes Mutate Select Solution Recombine 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 • Classification relies of the computation/communication ratio • 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 Master-Slave • Global single-population • Evaluation of fitness is distributed among slaves • Selection, recombination, and mutation are all done in the master processor Genetic Operators Master Individuals Slaves Calculate Fitness Calculate Fitness Fitness Calculate Fitness Calculate Fitness Toroidal Cluster • Separated single-population • Population is distributed over processors of a 2D mesh • Neighbors share members of their population for parent selection Island 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 Island Dual Species Genetic Algorithm • 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 • 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 DSGA Process Initialize Populations Evaluate Populations End? Yes Solution No Migrate Yes Migrate? Mutation 1 Crossover 1 Selection 1 Mutation 2 Crossover 2 Selection 2 No Yes Migrate? 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: 30000 Population size: 30 Offspring size: 200 Speedup: 43/40 = 1.08 MAXSAT FGA Vs SGA Number of fitness evaluations: 30000 Population size: 30 Offspring size: 600 Speedup: 117/75 = 1.56 MAXSAT FGA Vs SGA Number of fitness evaluations: 50000 Population size: 30 Offspring size: 1000 Speedup: 211/115 = 1.83 MAXSAT FGA Vs SGA Number of fitness evaluations: 100000 Population size: 30 Offspring size: 2000 Speedup: 416/240 = 1.83 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