Nonbinary transforms for genetic algorithm problems

Abstract

GA theory tends to be biased towards binary representations of problems. To try to redress the balance somewhat, this paper takes two important, related ideas, Walsh and partition coefficients, and generalises them to the nonbinary case. These coefficients provide an efficient way of calculating the fitnesses of low order schemata and of writing the conditions that characterise deceptive functions. Functions can be analysed for deception or created with varying degrees of deception by transforming between string fitnesses and coefficients or vice versa. In this paper, the matrix forms of the transforms are presented, the relationship between them examined and an efficient algorithm for performing the transforms is presented. Finally, an example of the coefficients' use is given.