Haploid Genetic Programming with Dominance

This paper presents a new crossover operator for genetic programming – dominance crossover. Dominance crossover is similar to the use of dominance in nature. In nature, dominance is used as a genotype to phenotype mapping when an organism carries pairs (or more than one) chromosome, but here we use dominance on a haploid structure. The haploid form contains all the information relevant to the problem, and is the structure that is widely used in evolutionary algorithms. Dominance crossover is used as a way of retaining and promoting successful genes (those which increased the individual’s fitness in the current generation) into the next generation. Current crossover operators fail to exploit knowledge acquired in previous generations and rely highly on selection pressures. Dominance crossover in theory allows this exploitation to occur during crossover but we highlight a problem with the application of dominance crossover with genetic programming. Introduction Dawkin’s model of evolution is based on the gene. He presents his theory of the gene as the fundamental unit of natural selection [Dawk89]. Chromosomes have a life span of one generation but a genetic unit lasts for many generations, thus natural selection favours the genetic unit. Genetic material in complex organisms is often presented using diploid chromosomes. In the diploid form a genotype carries one or more pairs of chromosomes, each containing information for the same functions. The genes contained in one set can be regarded as a direct alternative to the genes in the other set. When building the body the genes in one set compete with those in the other set. Genes that are expressed in the phenotype of an organism are dominant and those that are not are recessive. The relationship between a dominant and recessive gene is not a simple binary relationship [Merr94]: some genes that have been known to be dominant have become more recessive in successive generations and vice versa. These dominance characteristics have evolved over generations and have been promoted via natural selection. Much work (see next section) has been done to model diploidy and dominance in GA but dominance has not been used as an evolving factor for crossover on haploid structures. Assuming a correlation between program fitness and subtree fitness, an alternative method of crossover “Dominance Crossover” was proposed [VeCl97] for GP. Dominance crossover is not what happens in nature although it extracts the same characteristics as used in nature. Dominance is used here during crossover in haploid structures rather than a genotype to phenotype mapping, it evolves over successive generations and these characteristics are promoted via selection pressures. In addition dominance is used to exploit knowledge acquired in previous generations. Diploidy and Dominance in GAs Hollstien (1971) (in [Gold89]), [GoSm87] and most recently [HaEi97] have modelled diploidy or polyploidy and dominance in genetic algorithms. Hollstien’s (1971) work done on diploidy and dominance contained diploid genotypes. Each individual in the population carried a pair of chromosomes. A dominance map was proposed to map a diploid chromosome pair to a particular phenotype and the phenotype was used for fitness evaluation. He used a triallelic dominance map. His chromosomes were drawn up from the 3-alphabet {0,1,2} where both 2 and 1 map to a phenotype value of '1' (in the case of a binary functional gene), but 2 dominates 0 and 0 dominates 1. This results in a dominance map like this: