Toward Understanding EDAs Based on Bayesian Networks Through a Quantitative Analysis

The successful application of estimation of distribution algorithms (EDAs) to solve different kinds of problems has reinforced their candidature as promising black-box optimization tools. However, their internal behavior is still not completely understood and therefore it is necessary to work in this direction in order to advance their development. This paper presents a methodology of analysis which provides new information about the behavior of EDAs by quantitatively analyzing the probabilistic models learned during the search. We particularly focus on calculating the probabilities of the optimal solutions, the most probable solution given by the model and the best individual of the population at each step of the algorithm. We carry out the analysis by optimizing functions of different nature such as Trap5, two variants of Ising spin glass and Max-SAT. By using different structures in the probabilistic models, we also analyze the impact of the structural model accuracy in the quantitative behavior of EDAs. In addition, the objective function values of our analyzed key solutions are contrasted with their probability values in order to study the connection between function and probabilistic models. The results not only show information about the internal behavior of EDAs, but also about the quality of the optimization process and setup of the parameters, the relationship between the probabilistic model and the fitness function, and even about the problem itself. Furthermore, the results allow us to discover common patterns of behavior in EDAs and propose new ideas in the development of this type of algorithms.

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