An Analysis about the Asymptotic Convergence of Evolutionary Algorithms

This paper discusses the asymptotic convergence of evolutionary algorithms based on finite search space by using the properties of Markov chains and Perron-Frobenius theorem. First, some convergence results of general square matrices are given. Then, some useful properties of homogeneous Markov chains with finite states are investigated. Finally, 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 by combining the acquired results in this paper