A Framework for Multi-model EDAs with Model Recombination

  • Thomas Weise
  • Stefan Niemczyk
  • Raymond Chiong
  • Mingxu Wan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6624)

Abstract

Estimation of Distribution Algorithms (EDAs) are evolutionary optimization methods that build models which estimate the distribution of promising regions in the search space. Conventional EDAs use only one single model at a time. One way to efficiently explore multiple areas of the search space is to use multiple models in parallel. In this paper, we present a general framework for both single- and multi-model EDAs. We propose the use of clustering to divide selected individuals into different groups, which are then utilized to build separate models. For the multi-model case, we introduce the concept of model recombination. This novel framework has great generality, encompassing the traditional Evolutionary Algorithm and the EDA as its extreme cases. We instantiate our framework in the form of a real-valued algorithm and apply this algorithm to some well-known benchmark functions. Numerical results show that both single- and multi-model EDAs have their own strengths and weaknesses, and that the multi-model EDA is able to prevent premature convergence.

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References

  1. 1.
    Ahn, C.W., Ramakrishna, R.S.: Clustering-based probabilistic model fitting in estimation of distribution algorithms. IEICE Transactions on Information and Systems E89-D(1), 381–383 (2006)CrossRefGoogle Scholar
  2. 2.
    Baluja, S.: Population-based incremental learning – a method for integrating genetic search based function optimization and competitive learning. Technical Report CMU-CS-94-163, Carnegy Mellon University (1994)Google Scholar
  3. 3.
    Beyer, H.G., Schwefel, H.P.: Evolution strategies – a comprehensive introduction. Natural Computing 1(1), 3–52 (2002)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Bosman, P.A.N., Thierens, D.: Mixed idas. Technical Report UU-CS-2000-45, Utrecht University (2000)Google Scholar
  5. 5.
    Bosman, P.A.N., Thierens, D.: Advancing continuous idas with mixture distributions and factorization selection metrics. In: GECCO 2001, pp. 208–212. Morgan Kaufmann, San Francisco (2001)Google Scholar
  6. 6.
    Cao, A., Chen, Y., Wei, J., Li, J.: A hybrid evolutionary algorithm based on edas and clustering analysis. In: Chin. Ctrl. Conf., pp. 754–758. IEEE, Los Alamitos (2007)Google Scholar
  7. 7.
    Gallagher, M., Frean, M.R., Downs, T.: Real-valued evolutionary optimization using a flexible probability density estimator. In: GECCO 1999, Orlando, USA, pp. 840–846. Morgan Kaufmann, San Francisco (1999)Google Scholar
  8. 8.
    Kaufman, L., Rousseeuw, P.J.: Finding Groups in Data – An Introduction to Cluster Analysis, vol. 59. Wiley Interscience, Hoboken (1990)MATHGoogle Scholar
  9. 9.
    Larrañaga, P., Lozano, J.A. (eds.): Estimation of Distribution Algorithms – A New Tool for Evolutionary Computation. Springer, Heidelberg (2001)Google Scholar
  10. 10.
    Lu, Q., Yao, X.: Clustering and learning gaussian distribution for continuous optimization. IEEE Transactions on Systems, Man, and Cybernetics Part C 35(2), 195–204 (2005)CrossRefGoogle Scholar
  11. 11.
    Miquélez, T., Bengoetxea, E., Larrañaga, P.: Evolutionary computation based on bayesian classifiers. International Journal of Applied Mathematics and Computer Science 14(3), 335–349 (2004)MathSciNetMATHGoogle Scholar
  12. 12.
    Mühlenbein, H., Paaß, G.: From recombination of genes to the estimation of distributions i. binary parameters. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN IV 1996. LNCS, vol. 1141, pp. 178–187. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  13. 13.
    Niemczyk, S., Weise, T.: A general framework for multi-model estimation of distribution algorithms. Technical report, University of Kassel (2010), http://www.it-weise.de/documents/files/NW2010AGFFMMEODA.pdf
  14. 14.
    Okabe, T., Jin, Y., Sendhoff, B., Olhofer, M.: Voronoi-based estimation of distribution algorithm for multi-objective optimization. In: CEC 2004, vol. 2, pp. 1594–1601. IEEE, Los Alamitos (2004)Google Scholar
  15. 15.
    Pelikan, M., Goldberg, D.E.: Genetic algorithms, clustering, and the breaking of symmetry. In: PPSN VI, pp. 385–394. Springer, Heidelberg (2000)Google Scholar
  16. 16.
    Pelikan, M., Goldberg, D.E., Lobo, F.G.: A survey of optimization by building and using probabilistic models. Technical Report 99018, IlliGAL (1999)Google Scholar
  17. 17.
    Pelikan, M., Sastry, K., Cantú-Paz, E. (eds.): Scalable Optimization via Probabilistic Modeling – From Algorithms to Applications. Springer, Heidelberg (2006)MATHGoogle Scholar
  18. 18.
    Platel, M.D., Schliebs, S., Kasabov, N.: Quantum-inspired evolutionary algorithm: A multimodel eda. IEEE Trans. on Evol. Comp. 13(6), 1218–1232 (2009)CrossRefGoogle Scholar
  19. 19.
    Armañanzas, R., et al.: A review of estimation of distribution algorithms in bioinformatics. BioData Mining 1(6) (2008)Google Scholar
  20. 20.
    Sałustowicz, R., Schmidhuber, J.: Probabilistic incremental program evolution: Stochastic search through program space. In: van Someren, M., Widmer, G. (eds.) ECML 1997. LNCS, vol. 1224, pp. 213–220. Springer, Heidelberg (1997)Google Scholar
  21. 21.
    Sastry, K., Goldberg, D.E.: Multiobjective hboa, clustering, and scalability. In: GECCO 2005, pp. 663–670. ACM, New York (2005)Google Scholar
  22. 22.
    Weise, T., et al.: A tunable model for multi-objective, epistatic, rugged, and neutral fitness landscapes. In: GECCO 2008, pp. 795–802. ACM, New York (2008)Google Scholar
  23. 23.
    Wallin, D., Ryan, C.: Maintaining diversity in edas for real-valued optimisation problems. In: FBIT 2007, pp. 795–800. IEEE, Los Alamitos (2007)Google Scholar
  24. 24.
    Wallin, D., Ryan, C.: On the diversity of diversity. In: CEC 2007, pp. 95–102. IEEE, Los Alamitos (2007)Google Scholar
  25. 25.
    Weise, T.: Global Optimization Algorithms – Theory and Application. it-weise.de (2009), http://www.it-weise.de/

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Thomas Weise
    • 1
  • Stefan Niemczyk
    • 2
  • Raymond Chiong
    • 3
  • Mingxu Wan
    • 1
  1. 1.University of Science and Technology of China (USTC)HefeiChina
  2. 2.Distributed Systems GroupUniversity of KasselKasselGermany
  3. 3.Swinburne University of TechnologyMelbourneAustralia

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