About the time complexity of evolutionary algorithms based on finite search space

Abstract

We consider some problems about the computation time of evolutionary algorithms in this paper. First, some exact analytic expressions of the mean first hitting times of general evolutionary algorithms in finite search spaces are obtained theoretically by using the properties of Markov chain associated with evolutionary algorithms considered here. Then, by introducing drift analysis and applying Dynkin's Formula, the general upper and lower bounds of the mean first hitting times of evolutionary algorithms are estimated rigorously under some mild conditions listed in the paper. Those results in this paper are commonly useful. Also, the analytic techniques adopted in the paper are widely instructive for analyzing the computation time of evolutionary algorithms in a given search space as long as some specific mathematical arts are introduced accordingly. © Springer-Verlag Berlin Heidelberg 2007.