Analysis of convergence properties of a stochastic evolution algorithm

In this paper, the convergence properties of a stochastic optimization algorithm called the stochastic evolution (SE) algorithm is analyzed. We show that a generic formulation of the SE algorithm can be modeled by an ergodic Markov chain. As such, the global convergence of the SE algorithm is established as the state transition from any initial state to the globally optimal states. We propose a new criterion called the mean first visit time (MFVT) to characterize the convergence rate of the SE algorithm. With MFVT, we are able to show analytically that on average, the SE algorithm converges faster than the random search method to the globally optimal states. This result Is further confirmed using the Monte Carlo simulation.