Graphical model based continuous estimation of distribution algorithm

Abstract

In this paper, a new estimation of distribution algorithm is introduced. The goal is to propose a method that avoids complex approximations of learning a probabilistic graphical model and considers multivariate dependencies between continuous random variables. A parallel model of some subgraphs with a smaller number of variables is learned as the probabilistic graphical model. In each generation, the joint probability distribution of the selected solutions is estimated using a Gaussian Mixture model. Then, learning the graphical model of dependencies among random variables and sampling are done separately for each Gaussian component. In the learning step, using the selected solutions of each Gaussian mixture component, the structure of a Markov network is learned. This network is decomposed to maximal cliques and a clique graph. Then, complete Bayesian network structures are learned for these subgraphs using an optimization algorithm. The proposed optimization problem is a 0–1 constrained quadratic programming which finds the best permutation of variables. Then, sampling is done from each Bayesian network of each Gaussian component. The introduced method is compared with the other network-based estimation of distribution algorithms for optimization of continuous numerical functions.