Robustness, Evolvability, and Accessibility in Linear Genetic Programming

Abstract

Abstract. Whether neutrality has positive or negative effects on evolutionary search is a contentious topic, with reported experimental results supporting both sides of the debate. Most existing studies use performance statistics, e.g., success rate or search efficiency, to investigate if neutrality, either embedded or artificially added, can benefit an evolutionary algorithm. Here, we argue that understanding the influence of neutrality on evolutionary optimization requires an understanding of the interplay between robustness and evolvability at the genotypic and phenotypic scales. As a concrete example, we consider a simple linear genetic programming system that is amenable to exhaustive enumeration, and allows for the full characterization of these properties. We adopt statistical measurements from RNA systems to quantify robustness and evolvability at both genotypic and phenotypic levels. Using an ensemble of random walks, we demonstrate that the benefit of neutrality crucially depends upon its phenotypic distribution.

Robustness and Evolvability of Recombination in Linear Genetic Programming

“…the total number of genotypes that map to the same phenotype i. s i ranges from a minimum of 24,832 genotypes (for phenotype EQUAL and NOTEQUAL) to a maximum of 60,393,728 genotypes (for FALSE), occupying between 1% and 23% of the genotype space, respectively. As examined previously [14], for this particular Boolean LGP system, all phenotypes are connected to each other in the mutational genotypic space. That is, for any given phenotype, there exists a genotype that belongs to this phenotype and can transform to another genotype in any other phenotypes through a point mutation.…”

“…We consider a simple Linear Genetic Programming system as in the previous study [14]. In the LGP representation, an individual (or computer program) consists of a set of L instructions, which are structurally similar to those found in register machine languages.…”

“…Similar to mutational metrics [6,14,15], we capture recombinational evolvability as the potential to change from one phenotype to another (different) phenotype. Let…”

“…We now compare the recombinational measures to the previously investigated mutational measures [14,15]. Fig.3 shows recombinational robustness, evolvability, and accessibility relative to mutational robustness.…”

“…In a previous study [14], a quantitative characterization of mutational robustness and evolvability was performed in a simple Linear GP (LGP) system, where the entire genotype and phenotype spaces are finite and enumerable. In the current study, we adopt the same LGP system to utilize its compact properties and extend the quantitative metrics to recombination.…”