Convergence properties of Bayesian evolutionary algorithms with population size greater than 1

A Bayesian evolutionary algorithm is a probabilistic model of evolutionary computation for learning and optimization. It explicitly estimates the posterior distribution of the individuals and then samples offspring from the distribution. In the previous paper, using the asymptotic results from Markov chain Monte Carlo and annealing techniques, the asymptotic convergence of Bayesian evolutionary algorithms was shown for the case of population size 1. This paper presents convergence properties of Bayesian evolutionary algorithms with population size greater than 1. The basic idea is that BEAs can be reduced to Bayesian particle filters. The Bayesian particle filter approximates the posterior distribution of individuals at each generation. As the individuals evolve, the approximated posterior distribution also evolves. Then using the convergence properties of particle filters under some mild conditions, it is shown that as the number of individuals increases, a BEA converges to the posterior distribution