Message Passing Methods for Estimation of Distribution Algorithms Based on Markov Networks

  • Roberto Santana
  • Alexander Mendiburu
  • Jose A. Lozano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8298)


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.


estimation of distribution algorithms message passing Markov networks probabilistic modeling belief propagation abductive inference 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    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)Google Scholar
  2. 2.
    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)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    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)CrossRefGoogle Scholar
  4. 4.
    Larrañaga, P., Lozano, J.A. (eds.): Estimation of Distribution Algorithms. A New Tool for Evolutionary Computation. Kluwer Academic Publishers, Boston (2002)zbMATHGoogle Scholar
  5. 5.
    Lozano, J.A., Larrañaga, P., Inza, I., Bengoetxea, E. (eds.): Towards a New Evolutionary Computation: Advances on Estimation of Distribution Algorithms. Springer (2006)Google Scholar
  6. 6.
    McDonald, J.: Handbook of biological statistics, vol. 2. Sparky House Publishing, Baltimore (2009)Google Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    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)Google Scholar
  9. 9.
    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)zbMATHGoogle Scholar
  10. 10.
    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)Google Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Pearl, J.: Causality: Models, Reasoning and Inference. Cambridge University Press (2000)Google Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    Santana, R.: Estimation of distribution algorithms with Kikuchi approximations. Evolutionary Computation 13(1), 67–97 (2005)CrossRefGoogle Scholar
  15. 15.
    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)Google Scholar
  16. 16.
    Santana, R., Larrañaga, P., Lozano, J.A.: Research topics on discrete estimation of distribution algorithms. Memetic Computing 1(1), 35–54 (2009)CrossRefGoogle Scholar
  17. 17.
    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)Google Scholar
  18. 18.
    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)CrossRefGoogle Scholar
  19. 19.
    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)Google Scholar
  20. 20.
    Shakya, S., Santana, R. (eds.): Markov Networks in Evolutionary Computation. Springer (2012)Google Scholar
  21. 21.
    Shakya, S., Santana, R., Lozano, J.A.: A Markovianity based optimisation algorithm. Genetic Programming and Evolvable Machines 13(2), 159–195 (2012)CrossRefGoogle Scholar
  22. 22.
    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)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Roberto Santana
    • 1
  • Alexander Mendiburu
    • 1
  • Jose A. Lozano
    • 1
  1. 1.Intelligent Systems Group, Department of Computer Science and Artificial IntelligenceUniversity of the Basque Country (UPV/EHU)San SebastianSpain

Personalised recommendations