This paper proposes a recombination

operator, “selective crossover” for use in

genetic algorithm

Clack, C

Vekaria, K

English

UCL Discovery

Selective Crossover in Genetic AlgorithmsKanta Vekaria and Chris ClackDepartment of Computer ScienceUniversity College LondonGower StreetLondon WC1E 6BTUnited KingdomEmail: {K.Vekaria, C.Clack}@cs.ucl.ac.ukABSTRACTThis paper proposes a recombinationoperator, “selective crossover” for use ingenetic algorithms.1. Selective CrossoverGenetic Algorithms (GAs) have a vast parameter-space andour knowledge of which parameter settings are appropriatefor which classes of problem is rudimentary, being basedprimarily on anecdotal evidence (case-based reasoning). IfGAs are to become more effective, we need to improve ourunderstanding (and control) of this parameter-space. As afirst step, we are investigating just one such parameter: therecombination (crossover) operator. We restrict ourinvestigation to epistatic problems and are exploring thedesign of a recombination technique which never gives badperformance yet exhibits similar best performance totraditional crossover operators.We start with the observation that, partly, theunpredictable performance of traditional crossover operatorsis due to the way that they interact with the epistatic linkageinherent in the encoding of the chromosome. We focus onthe gene as the unit of natural selection and develop arecombination technique that evolves knowledge about thecontribution of groups of (one or more) genes to the fitnessof the individual - these groups need not be contiguous inthe chromosome and this technique is therefore independentof the representation of epistatic linkage in the chromosome.We call this technique “selective crossover”.Selective crossover associates a real-valued vector witheach chromosome, such that each gene has an associated“dominance” value (see Figure 1). We use the term“dominance” to draw an analogy with the way that genesexert their influence in nature. However, we retain thetraditional GA haploid characteristics.On initialisation, the dominance values are randomlygenerated, as is the population, but are restricted to be in therange [0,1]. During crossover, the dominance values of eachgene for both parents are compared linearly and twochildren are produced. The first child receives all thedominant alleles (and their dominance values), whereas thesecond child receives all the recessive alleles (and theirdominance values). The subsequent fitness of both childrenis compared with that of their parents: where an increase infitness occurs, we increase the dominance values in the fitterchild of those genes that have changed:Parent 1 – fitness = 0.360.4 0.3 0.01 0.9 0.1 0.21 0 0 1 0 0Parent 2 – fitness = 0.300.01 0.2 0.4 0.2 0.9 0.30 1 1 1 1 0Child 1 – fitness = 0.460.4 0.3 0.4 0.9 0.9 0.31 0 1 1 1 0Child 2 – fitness = 0.200.01 0.2 0.01 0.2 0.1 0.20 1 0 1 0 0Figure 1: Reproduction with Selective CrossoverChild 1 – fitness = 0.460.4 0.3 0.5 0.9 1.0 0.31 0 1 1 1 0Child 2 – fitness = 0.200.01 0.2 0.01 0.2 0.1 0.20 1 0 1 0 0Figure 2: Updating Dominance ValuesUnlike one-point or two-point crossover, selective crossoveris not biased against schema with high defining length.Selective crossover propagates good schema regardless oftheir defining length – for example, interacting genes at thetwo extremes of the chromosome can be propagated aseasily as those located adjacent to each other.ResultsWe have some encouraging initial experimental results:selective crossover was applied to the L-Sat problemgenerator [DePoSp97] where epistasis can be varied. In thisexperiment, selective crossover performed exceptionallybetter than two-point and uniform crossover.Bibliography[DePoSp97] De Jong, K. A., Potter, M. A. and Spears,W. M. (1997) Using Problem Generators to Explore theEffects of Epistasis. In T. Bäck (editor), Proceedings ofthe Seventh International Conference on GeneticAlgorithms, 338-345. Morgan KauffmanDominance valuesAllelesNew dominance values

Selective crossover in genetic algorithms

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Selective crossover in genetic algorithms

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