Punctuated Equilibrium and Neutral Networks in Genetic Algorithms

Abstract

Taking focused inspiration from biological evolution, we present an empirical study which shows that a Simple Genetic Algorithm (SGA) exhibits punctuated equilibria and punctuated gradualism in its evolution. Using the concept of consensus sequences, and comparing genotype change to phenotype change, we show how an SGA explores candidate solutions along a neutral network - Hamming-proximal bitstrings of similar fit-ness. Alongside mapping the normal functioning of an SGA, we monitor the formation of error thresholds “from above” by starting with a high mutation probability and slowly lowering it, during hundreds of thousands of generations. The formation of a stable consensus sequence is marked by a measurable upheaval in the dynamics of the population, leading to an efficient exploration of the search space in a short time. After the global optimum is found, we can still measure the degree of exploration the SGA performs on that neutral network, and observe punctuated equilibria. We use 11 numerical benchmark functions, along with the Royal Road Function, and a similar bit block Trap Function; the phenomena observed are largely similar on all of them, pointing to a generic behaviour of Genetic Algorithms, rather than problem particularities. Using a consensus sequence (a per-locus-mode chromosome) obscures quasispecies dynamics. This is why we use a per-locus-mean chromosome to measure information change between successive generations, and plot the number and maximal size of Quasispecies and Neutral Networks.