Analyzing the probability of the optimum in EDAs based on Bayesian networks

Authors:
Carlos Echegoyen;Alexander Mendiburu;Roberto Santana;Jose A. Lozano
Affiliations:
Intelligent Systems Group, Department of Computer Science and Artificial Intelligence, University of the Basque Country, San Sebastián, Donostia, Spain;Intelligent Systems Group, Department of Computer Science and Artificial Intelligence, University of the Basque Country, San Sebastián, Donostia, Spain;Intelligent Systems Group, Department of Computer Science and Artificial Intelligence, University of the Basque Country, San Sebastián, Donostia, Spain;Intelligent Systems Group, Department of Computer Science and Artificial Intelligence, University of the Basque Country, San Sebastián, Donostia, Spain
Venue:
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Year:
2009

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Abstract

In this paper we quantitatively analyze the probability distributions generated by an EDA during the search. In particular, we record the probabilities to the optimal solution, the solution with the highest probability and that of the best individual of the population, when the EDA is solving a trap function. By using different structures in the probabilistic models we can analyze the influence of the structural model accuracy on the aforementioned probability values. In addition, the objective function values of these solutions are contrasted with their probability values in order to study the connection between the function and the probabilistic model. The results provide new information about the behavior of the EDAs and they open a discussion regarding which are the minimum (in)dependences necessary to reach the optimum.