Complex Systems

Nonbinary Transforms for Genetic Algorithm Problems Download PDF

Paul Field
Department of Computer Science,
Queen Mary and Westfield College, University of London,
Mile End Road, London E1 4NS, England


The Walsh transform is a powerful tool for transforming from a string-based to a schema-based perspective. It has traditionally been used in the study of deception to see fitnesses from a schema perspective but it has uses in studying the dynamics of genetic algorithms (GAs) and the structure of GA models.

In this paper, Walsh coefficients and the closely related partition coefficients are generalized to nonbinary alphabets. For both cases, the matrix form of the transform and inverse transform are presented. The relationship between the two types of coefficient is examined and, finally, an efficient algorithm for performing the nonbinary transforms is developed.