An analysis of the locality of binary representations in genetic and evolutionary algorithms

Abstract

Mutation and recombination operators play a key role in determining the performance of Genetic and Evolutionary Algorithms (GEAs). Prior work has analyzed the effects of these operators on genotypic variation, often using locality metrics that measure the sensitivity and stability of genotype-phenotype representations to these operators. In this paper, we focus on an important subset of representations, namely nonredundant bitstring-to-integer representations, and analyze them through the lens of Rothlauf’s widely used locality metrics. Our main research question is, does strong locality predict good GEA performance for these representations? Our main findings, both theoretical and empirical, show the answer to be negative. To this end, we define locality metrics equivalent to Rothlauf’s that are tailored to our domain: the point locality for single-bit mutation and general locality for recombination. With these definitions, we derive tight bounds and a closed-form expected value for point locality. For general locality we show that it is asymptotically equivalent across all representations and operators. We also reproduce three established GEA empirical results to understand the predictive power of point locality on GEA performance, focusing on two popular and often juxtaposed representations: standard binary and binary-reflected Gray.