Distance functions for order-based encodings

Distance functions permeate the field of Genetic Algorithms especially in relation to mating strategies, incest prevention, diversity preservation, and techniques that find multiple solutions. Distance functions can be found in the literature for genotypes which use binary or numerical parameter encodings. Various phenotypic distance functions that act on the properties of the decoded genotype have also been presented. There is, however, a gap in the literature regarding distance functions for order-based encodings. This paper presents a new distance function based on allele adjacency for permutation encodings. It is shown that this distance function is one possible member of a family of order-based metrics that respond to different properties in order-based encodings. This, and other, new distance measures will allow a wider range of Genetic Algorithm techniques to applied to problems in the order-based domain.