Effective Structure Learning in Bayesian Network Based EDAs

Abstract

Estimation of Distribution Algorithms (EDAs) is a high impact area in evolutionary computation and global optimization. One of the main EDAs strengths is the explicit codification of variable dependencies. The search engine is a joint probability distribution (the search distribution), which is usually computed by fitting the best solutions in the current population. Even though using the best known solutions for biasing the search is a common rule in evolutionary computation, it is worth to notice that most evolutionary algorithms (EAs) derive the new population directly from the selected set, while EDAs do not. Hence, a different bias can be introduced for EDAs. In this article we introduce the so called Empirical Selection Distribution for biasing the search of an EDA based on a Bayesian Network. Bayesian networks based EDAs had shown impressive results for solving deceptive problems, by estimating the adequate structure (dependencies) and parameters (conditional probabilities) needed to tackle the optimum. In this work we show that a Bayesian Network based EDA (BN-EDA) can be enhanced by using the empirical selection distribution instead of the standard selection method. We introduce weighted estimators for the K2 metric which is capable of detecting better the variable correlations than the original BN-EDA, in addition, we introduce formulas to compute the conditional probabilities (local probability distributions). By providing evidence and performing statistical comparisons, we show that the enhanced version: 1) detects more true variable correlations, 2) has a greater probability of finding the optimum, and 3) requires less number of evaluations and/or population size than the original BN-EDA to reach the optimum. Our results suggest that the Empirical Selection Distribution provides to the algorithm more useful information than the usual selection step.