Non-Linear Genetic Representations

The limitations of linear chromosomes and conventional recombination operators are reviewed. It is argued that there are at least three classes of problems for which such representations and operators are likely to be ineffective. Methods for constructing operators which manipulate more complex structures with evolutionary search methods are presented, and it is argued that whenever possible, genetic operators and analogues of schemata should be defined directly in space of phenotypes, rather than in the genotype (representation) space. This paper considers the implications of earlier theoretical work on evolutionary search concerning the relationship between genetic representation, idealised genetic operators and performance correlations between solutions in the search space. The central thesis of the paper is that for many problems conventional linear chromosomes and recombination operators are inadequate for effective genetic search, and that for general problems non-linear representations are required. Section 2 considers representation issues in the abstract, focusing initially on the genotype-phenotype mapping, intrinsic parallelism and the ability of schemata to capture important regularities in performance characteristics in the search space, before discussing the various ways in which different workers have tried to respond to perceived limitations. Section 3 discusses various generalisations of the standard analysis of genetic algorithms, which are then used to explore three specific limitations of linear chromosomes with conventional operators. Briefly, these limitations arise when schemata are unable to describe important subsets of the search space (section 4), when key characteristics of solutions cannot by independently assigned (section 5), and when constraints are involved (section 6). The paper closes with a summary.