Estimation of distribution algorithm using factor graph and Markov blanket canonical factorization

Abstract

Finding a good model and efficiently estimating the distribution is still an open challenge in estimation of distribution algorithms (EDAs). Factorization encoded by models in most of the EDAs are constrained. However for optimization of many real-world problems, finding the model capable of representing complex interactions without much computational complexity overhead is the key challenge. On the other hand factor graph which is the most natural graphical model for representing additively decomposable functions is rarely employed in EDAs. In this paper we introduce Factor Graph based EDA (FGEDA) which learns factor graph as the model and estimate the probability distribution represented by the learned factor graph using Markov blanket canonical factorization. The class of factorization that is employed for approximation of distribution in FGEDA is expanded relative to famous EDAs. We have used matrix factorization for learning the factor graph of the problem based on the pairwise mutual information between pair of variables. Gibbs sampling and BB-wise crossover are used to generate new samples. Empirical evaluation as well as theoretical analysis of the approach show the efficiency and power of FGEDA in the optimization of functions with complex interactions. It is showed experimentally that FGEDA outperform other well-known EDAs.