Optimizing Epochal Evolutionary Search: Population-Size Dependent Theory

摘要

Epochal dynamics, in which long periods of stasis in an evolving population are punctuated by a sudden burst of change, is a common behavior in both natural and artificial evolutionary processes. We analyze the population dynamics for a class of fitness functions that exhibit epochal behavior using a mathematical framework developed recently, which incorporates techniques from the fields of mathematical population genetics, molecular evolution theory, and statistical mechanics. Our analysis predicts the total number of fitness function evaluations to reach the global optimum as a function of mutation rate, population size, and the parameters specifying the fitness function. This allows us to determine the optimal evolutionary parameter settings for this class of fitness functions.