Abstract
Sampling methods are a fundamental component of estimation of distribution algorithms (EDAs). In this paper we propose new methods for generating solutions in EDAs based on Markov networks. These methods are based on the combination of message passing algorithms with decimation techniques for computing the maximum a posteriori solution of a probabilistic graphical model. The performance of the EDAs on a family of non-binary deceptive functions shows that the introduced approach improves results achieved with the sampling methods traditionally used by EDAs based on Markov networks.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kroc, L., Sabharwal, A., Selman, B.: Message-passing and local heuristics as decimation strategies for satisfiability. In: Proceedings of the 2009 ACM Symposium on Applied Computing, pp. 1408–1414. ACM (2009)
Kschischang, F.R., Frey, B.J., Loeliger, H.A.: Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory 47(2), 498–519 (2001)
Larrañaga, P., Karshenas, H., Bielza, C., Santana, R.: A review on probabilistic graphical models in evolutionary computation. Journal of Heuristics 18(5), 795–819 (2012)
Larrañaga, P., Lozano, J.A. (eds.): Estimation of Distribution Algorithms. A New Tool for Evolutionary Computation. Kluwer Academic Publishers, Boston (2002)
Lozano, J.A., Larrañaga, P., Inza, I., Bengoetxea, E. (eds.): Towards a New Evolutionary Computation: Advances on Estimation of Distribution Algorithms. Springer (2006)
McDonald, J.: Handbook of biological statistics, vol. 2. Sparky House Publishing, Baltimore (2009)
Mendiburu, A., Santana, R., Lozano, J.A.: Introducing belief propagation in estimation of distribution algorithms: A parallel framework. Technical Report EHU-KAT-IK-11/07, Department of Computer Science and Artificial Intelligence, University of the Basque Country (October 2007)
Mendiburu, A., Santana, R., Lozano, J.A.: Fast fitness improvements in estimation of distribution algorithms using belief propagation. In: Santana, R., Shakya, S. (eds.) Markov Networks in Evolutionary Computation, pp. 141–155. Springer (2012)
Mooij, J.: libDAI: A free and open source C++ library for discrete approximate inference in graphical models. The Journal of Machine Learning Research 11, 2169–2173 (2010)
Mühlenbein, H.: Convergence theorems of estimation of distribution algorithms. In: Shakya, S., Santana, R. (eds.) Markov Networks in Evolutionary Computation, pp. 91–108. Springer (2012)
Mühlenbein, H., Paaß, G.: From recombination of genes to the estimation of distributions I. Binary parameters. In: Voigt, H.-M., Ebeling, W., Rechenberg, I., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 178–187. Springer, Heidelberg (1996)
Pearl, J.: Causality: Models, Reasoning and Inference. Cambridge University Press (2000)
Santana, R.: A markov network based factorized distribution algorithm for optimization. In: Lavrač, N., Gamberger, D., Todorovski, L., Blockeel, H. (eds.) ECML 2003. LNCS (LNAI), vol. 2837, pp. 337–348. Springer, Heidelberg (2003)
Santana, R.: Estimation of distribution algorithms with Kikuchi approximations. Evolutionary Computation 13(1), 67–97 (2005)
Santana, R.: MN-EDA and the use of clique-based factorisations in EDAs. In: Shakya, S., Santana, R. (eds.) Markov Networks in Evolutionary Computation, pp. 73–87. Springer (2012)
Santana, R., Larrañaga, P., Lozano, J.A.: Research topics on discrete estimation of distribution algorithms. Memetic Computing 1(1), 35–54 (2009)
Santana, R., Ochoa, A., Soto, M.R.: Solving problems with integer representation using a tree based factorized distribution algorithm. In: Electronic Proceedings of the First International NAISO Congress on Neuro Fuzzy Technologies. NAISO Academic Press (2002)
Shakya, S., McCall, J.: Optimization by estimation of distribution with DEUM framework based on Markov random fields. International Journal of Automation and Computing 4(3), 262–272 (2007)
Shakya, S., Santana, R.: An EDA based on local Markov property and Gibbs sampling. In: Keijzer, M. (ed.) Proceedings of the 2008 Genetic and Evolutionary Computation Conference (GECCO), pp. 475–476. ACM, New York (2008)
Shakya, S., Santana, R. (eds.): Markov Networks in Evolutionary Computation. Springer (2012)
Shakya, S., Santana, R., Lozano, J.A.: A Markovianity based optimisation algorithm. Genetic Programming and Evolvable Machines 13(2), 159–195 (2012)
Zhang, Q., Sun, J., Tsang, E.P.K.: Evolutionary algorithm with guided mutation for the maximum clique problem. IEEE Transactions on Evolutionary Computation 9(2), 192–200 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Santana, R., Mendiburu, A., Lozano, J.A. (2013). Message Passing Methods for Estimation of Distribution Algorithms Based on Markov Networks. In: Panigrahi, B.K., Suganthan, P.N., Das, S., Dash, S.S. (eds) Swarm, Evolutionary, and Memetic Computing. SEMCCO 2013. Lecture Notes in Computer Science, vol 8298. Springer, Cham. https://doi.org/10.1007/978-3-319-03756-1_38
Download citation
DOI: https://doi.org/10.1007/978-3-319-03756-1_38
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03755-4
Online ISBN: 978-3-319-03756-1
eBook Packages: Computer ScienceComputer Science (R0)