Analyzing the probability of the optimum in EDAs based on Bayesian networks
This paper incorporates Belief Propagation into an instance of Estimation of Distribution Algorithms called Estimation of Bayesian Networks Algorithm. Estimation of Bayesian Networks Algorithm learns a Bayesian network at each step. The objective of the proposed variation is to increase the search capabilities by extracting information of the, computationally costly to learn, Bayesian network. Belief Propagation applied to graphs with cycles, allows to find (with a low computational cost), in many scenarios, the point with the highest probability of a Bayesian network. We carry out some experiments to show how this modification can increase the potentialities of Estimation of Distribution Algorithms. Due to the computational time implied in the resolution of high dimensional optimization problems, we give a parallel version of the Belief Propagation algorithm for graphs with cycles and introduce it in a parallel framework for Estimation of Distribution Algorithms . In addition we point out many ideas on how to incorporate Belief Propagation algorithms into Estimation Distribution Algorithms.