Strongly biased crossover operator for subgraph selection in edge-set based graph representation

Abstract

The performance of crossover operator is a complex interplay of the various characteristics of the genetic algorithm (GA) and sometimes also of the problem under question. The fundamental design choices in a GA therefore, are its representation of candidate solutions and the operators that will act on that representation. This paper suggests a new strongly biased multiparent crossover operator that offers a strong locality and provides a strong heritability quotient but can still escape the local optima when the sample space is over represented by similar building blocks. The proposed operator uses a dynamic 2-D vector representation for the chromosomes and this data structure may evolve as the execution of the crossover operator proceeds. On a population which consists of solutions near to optimal and mostly lying in the basin of attraction of single optima, the bias towards the optima in the generated offsprings is proportional to the sample size from the search space. Based on this reasoning, the effect of arity of the proposed crossover operator is tested using a population in which all the candidates lie in close neighborhood of each other. To analyze the dynamic search behavior of the proposed crossover operator and the impact of the representation scheme on the locality, heritability and exploratory power of the operator, we suggest a no mutation, zero selection pressure GA model that generates bounded diameter minimum spanning trees from the underlying complete graphs on random and Euclidean instances.