Bayesian evolutionary optimization using Helmholtz machines. Parallel Problem Solving from Nature

A b s t r a c t. Recently, several evolutionary algorithms have been proposed that build and use an explicit distribution model of the population to perform optimization. One of the main issues in this class of algorithms is how to estimate the distribution of selected samples. In this paper, we present a Bayesian evolutionary algorithm (BEA) that learns the sample distribution by a probabilistic graphical model known as Helmholtz ma-chines. Due to the generative nature and availability of the wake-sleep learning algorithm, the Helmholtz machines provide an effective tool for modeling and sampling from the distribution of selected individuals. The proposed method has been applied to a suite of GA-deceptive functions. Experimental results show that the BEA with the Helmholtz machine outperforms the simple genetic algorithm.