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A Markov Network Based Factorized Distribution Algorithm for Optimization

  • Roberto Santana
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2837)

Abstract

In this paper we propose a population based optimization method that uses the estimation of probability distributions. To represent an approximate factorization of the probability, the algorithm employs a junction graph constructed from an independence graph. We show that the algorithm extends the representation capabilities of previous algorithms that use factorizations. A number of functions are used to evaluate the performance of our proposal. The results of the experiments show that the algorithm is able to optimize the functions, outperforming other evolutionary algorithms that use factorizations.

Keywords

Genetic algorithms EDA FDA evolutionary optimization estimation of distributions 

References

  1. 1.
    Bron, C., Kerbosch, J.: Algorithm 457—finding all cliques of an undirected graph. Communications of the ACM 16(6), 575–577 (1973)zbMATHCrossRefGoogle Scholar
  2. 2.
    Brown, D.F., Garmendia-Doal, A., McCall, J.A.W.: Markov random field modelling of royal road genetic algorithms. In: Collet, P., Fonlupt, C., Hao, J.-K., Lutton, E., Schoenauer, M. (eds.) EA 2001. LNCS, vol. 2310, pp. 65–76. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Henrion, M.: Propagating uncertainty in Bayesian networks by probabilistic logic sampling. Uncertainty in Artificial Intelligence 2, 317–324 (1988)Google Scholar
  4. 4.
    Holland, J.H.: Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor (1975)Google Scholar
  5. 5.
    Larrañaga, P., Lozano, J.A.: Estimation Distribution Algorithms. A new tool for Evolutionary Optimization. Kluwer Academic Publishers, Boston (2001)Google Scholar
  6. 6.
    Mühlenbein, H.: The equation for response to selection and its use for prediction. Evolutionary Computation 5(3), 303–346 (1997)CrossRefGoogle Scholar
  7. 7.
    Mühlenbein, H., Mahnig, T.: Evolutionary Algorithms: From Recombination to Search. In: DistributionsTheoretical Aspects of Evolutionary Computing, pp. 137–176. Springer, Berlin (2000)Google Scholar
  8. 8.
    Mühlenbein, H., Mahnig, T.: Evolutionary synthesis of Bayesian networks for optimization. In: Advances in Evolutionary Synthesis of Neural Systems, pp. 429–455. MIT Press, Cambridge (2001)Google Scholar
  9. 9.
    Mühlenbein, H., Mahnig, T., Ochoa, A.: Schemata, distributions and graphical models in evolutionary optimization. Journal of Heuristics 5(2), 213–247 (1999)CrossRefGoogle Scholar
  10. 10.
    Mühlenbein, H., Paaß, G.: From recombination of genes to the estimation of distributions I. Binary parameters. In: Eiben, A., Bäck, T., Shoenauer, M., Schwefel, H. (eds.) Parallel Problem Solving from Nature - PPSN IV, pp. 178–187. Springer, Berlin (1996)CrossRefGoogle Scholar
  11. 11.
    Santana, R., Ochoa, A., Soto, M.R.: The Mixture of Trees Factorized Distribution Algorithm. In: Proceedings of the Genetic and Evolutionary Computation Conference GECCO 2001, pp. 543–550. Morgan Kaufmann Publishers, San Francisco (2001)Google Scholar
  12. 12.
    Spirtes, P., Glymour, C., Scheines, R.: Causation, Prediction and search. Lecture Notes in Statistics. Springer, New York (1993)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Roberto Santana
    • 1
  1. 1.Institute of Cybernetics, Mathematics, and Physics (ICIMAF)C-HabanaCuba

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