Measuring Evolvability and Accessibility using the Hyperlink-Induced Topic Search Algorithm

The redundant mapping from genotype to phenotype is common in evolutionary algorithms, where multiple genotypes can map to the same phenotype. Such a redundancy has been suggested to make an evolutionary system robust as well as evolvable. However, the impact of the redundant genotype-to-phenotype mapping and its resulted robustness and evolvability have not been well characterized quantitatively. In this article, we used a Boolean linear genetic programming system to construct a weighted and directed pheno-type network, where vertices are phenotypes and a weighted link represents the number of possible point mutations that can transition genotypes from one phenotype to another. The direction of the links ensures moving from less fit phenotypes to fitter or equally fit ones. We used two fitness functions to investigate how it influences the network structure. Then we employed the Hyperlink-Induced Topic Search (HITS) algorithm to quantitatively characterize the evolvability and accessibility of phenotypes in the network. We found more robust phenotypes are both more evolvable and accessible. Our results help elucidate the effects of redundant mapping and the relationship of robustness, evolvability, and accessibility.