On the Optimal Convergence Probability of Univariate Estimation of Distribution Algorithms

In this paper, bounds on the probability of convergence to the optimal solution have been obtained for the compact Genetic Algorithm (cGA) and the Population Based Incremental Learning (PBIL). The sufficient condition for convergence of these algorithms to the optimal solution and a range of possible values for their parameters for which the algorithms converge to the optimal solution with a confidence level are determined.