A network perspective on genotype–phenotype mapping in genetic programming

Genotype–phenotype mapping plays an essential role in the design of an evolutionary algorithm. Variation occurs at the genotypic level but fitness is evaluated at the phenotypic level, therefore, this mapping determines if and how variations are effectively translated into quality improvements. In evolutionary algorithms, this mapping has often been observed as highly redundant, i.e., multiple genotypes can map to the same phenotype, as well as heterogeneous, i.e., some phenotypes are represented by a large number of genotypes while some phenotypes only have few. We numerically study the redundant genotype–phenotype mapping of a simple Boolean linear genetic programming system and quantify the mutational connections among phenotypes using tools of complex network analysis. The analysis yields several interesting statistics of the phenotype network. We show the evidence and provide explanations for the observation that some phenotypes are much more difficult to find as the target of a search than others. Our study provides a quantitative analysis framework to better understand the genotype–phenotype map, and the results may be utilized to inspire algorithm design that allows the search of a difficult target to be more effective.