Genetic Programming using Genotype-Phenotype Mapping from Linear Genomes into Linear Phenotypes

In common genetic programming approaches, the space of genotypes, that is the search space, is identical to the space of phenotypes, that is the solution space. Facts and theories from molecular biology suggest the introduction of non-identical ge-nospaces and phenospaces, and a generic genotype-phenotype mapping which maps unconstrained genotypes into syntactically correct phenotypes. Neutral variants come into eeect due to this mapping. They enhance genetic diversity and allow for escaping local optima in phenospace via high-dimensional saddle surfaces in genospace. We propose a concrete mapping that maps linear binary genotypes into linear phenotypes of an arbitrary context-free programming language. Empirical results are presented which show that the mapping improves the performance of GP under mutation and reproduction. 1 Introduction Common GP approaches (e.g. \Koza (1992)") do not distinguish between a genotype, i.e. a point in search space, and its phenotype, i.e. a point in solution space, that is search space and solution space are identical. Recently, however, a strict distinction between the search space and the solution space as well as a genotype phenotype mapping (GPM) from the search space into the solution space have been suggested in \Banzhaf (1994)". In that contribution, the author extends the common GP approach by a GPM and demonstrates the practicability of this GP/GPM approach. Note that a GPM in itself is not a special GP variant. The principle behind a GPM is the distinction between the search space and the solution space of an underlying search process. The process locates points in the search space as results of the search. However, a potential solution must be a point from the solution space. Thus, a GPM is needed which maps an arbitrary search point onto a solution point. This principle can be used with every search process, like an arbitrary evolutionary algorithm. Finally, it is hypothesized in \Banzhaf (1994)" that the GP/GPM approach enhances the performance of systems using evolutionary algorithms (EA). The present paper focuses on a basic empirical investigation of this hypothesis with respect to the area of GP. To that end, we compare the performance of both approaches by applying them to the same non-toy test problem. In order to do so, we use our Binary-Genetic-Programming system, which incorporates both approaches. One starting point towards the GP/GPM approach given in \Banzhaf (1994)" is Kimura's neutral theory of molecular evolution \Kimura (1968)" \Kimura (1983)" which postulates that molecular evolution is essentially driven …