About the Limit Behaviors of the Transition Operators Associated with EAs

Abstract

This paper focuses on the limit behaviors of evolutionary algorithms based on finite search space by using the properties of Markov chains and Perron-Frobenius Theorem. Some convergence results of general square matrices are given, and some useful properties of homogeneous Markov chains with finite states are investigated. The geometric convergence rates of the transition operators, which is determined by the revised spectral of the corresponding transition matrix of a Markov chain associated with the EA considered here, are estimated. Some applications of the theoretical results in this paper are also discussed.