Analysis of Differential Evolution's Markov Chain Model and Convergence
Sun Cheng-f · Computer Technology and Development · 2013
As a modern optimization algorithm,differential evolution algorithm which is based on the individual differential reconstruction idea is designed for the global continuous optimization problem. Up to now,the improvement and application of the algorithm are mainly focused by researchers but theoretical analysis of the algorithm is seldom taken into account. In order to analyze the convergence of the algorithm,the concepts of state transition for individual and population are defined and the optimal state set of population is proposed. The individual state transition probability is computed according to the operators of differential evolution algorithm. The state sequence of population has been proved to be Finite Nonhomogeneous Markov chain and the Markov chain model of differential evolution is proposed. At last,the theory analysis of the differential evolution demonstrates that it is not able to guarantee the global convergence. The result of the theory research shows that keeping the population diversity will improve the performance of the algorithm.