Elliptical and Archimedean Copulas in Estimation of Distribution Algorithm with Model Migration

Martin Hyrš, Josef Schwarz

Abstract

Estimation of distribution algorithms (EDAs) are stochastic optimization techniques that are based on building and sampling a probability model. Copula theory provides methods that simplify the estimation of a probability model. An island-based version of copula-based EDA with probabilistic model migration (mCEDA) was tested on a set of well-known standard optimization benchmarks in the continuous domain. We investigated two families of copulas – Archimedean and elliptical. Experimental results confirm that this concept of model migration (mCEDA) yields better convergence as compared with the sequential version (sCEDA) and other recently published copula-based EDAs.

References

  1. Aas, K. (2004). Modelling the dependence structure of financial assets: A survey of four copulas.
  2. Aas, K., Czado, C., Frigessi, A., and Bakken, H. (2009). Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics, 44(2):182 - 198.
  3. Cherubini, U., Luciano, E., and Vecchiato, W. (2004). Copula Methods in Finance. John Wiley & Sons, Hoboken, NJ.
  4. De Bonet, J. S., Isbell, C. L., and Viola, P. A. (1997). MIMIC: Finding optima by estimating probability densities. In Advances in Neural Information Processing Systems, volume 9, pages 424-430. The MIT Press, Cambridge.
  5. delaOssa, L., Gámez, J. A., and Puerta, J. M. (2004). Migration of probability models instead of individuals: An alternative when applying the island model to edas. In Parallel Problem Solving from Nature - PPSN VIII, volume 3242 of LNCS of Lecture Notes in Computer Science, pages 242-252. Springer.
  6. delaOssa, L., Gámez, J. A., and Puerta, J. M. (2005). Improving model combination through local search in parallel univariate edas. In Congress on Evolutionary Computation, volume 2, pages 1426-1433. IEEE.
  7. Frühwirth-Schnatter, S. (2006). Finite Mixture and Markov Switching Models. Springer, New York.
  8. Hauschild, M. and Pelikan, M. (2011). An introduction and survey of estimation of distribution algorithms. Swarm and Evolutionary Computation, 1(3):111 - 128.
  9. Hyrs?, M. and Schwarz, J. (2014). Multivariate gaussian copula in estimation of distribution algorithm with model migration. In 2014 IEEE Symposium on Foundations of Computational Intelligence Proceedings, pages 114-119, Piscataway. Institute of Electrical and Electronics Engineers.
  10. Jia, B., Wang, L., and Cui, Z. (2013). Copula for estimation of distribution algorithm based on goodness-of-fit test. In Journal of Theoretical and Applied Information Technology, number 3, pages 1128-1132.
  11. Larran˜aga, P. and Lozano, J. A. (2001). Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer Academic Publishers, Norwell, MA, USA.
  12. Mai, J. and Scherer, M. (2012). Simulating Copulas: Stochastic Models, Sampling Algorithms, and Applications, volume 4 of Series in quantitative finance. Imperial College Press.
  13. Melchiori, M. R. (2006). Tools for sampling multivariate archimedean copulas. YieldCurve, April.
  14. Méndez, M. and Landa, R. (2012). An EDA based on bayesian networks constructed with archimedean copulas. In 2012 Fourth World Congress on Nature and Biologically Inspired Computing (NaBIC), pages 188-193.
  15. Nelsen, R. B. (2006). An Introduction to Copulas. Springer Series in Statistics. Springer New York.
  16. Pelikan, M., Goldberg, D., and Cantú-Paz, E. (1999). BOA: The bayesian optimization algorithm. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-99), volume I, pages 525-532 also IlliGAL Report no. 99003.
  17. Pelikan, M. and M ühlenbein, H. (1999a). The bivariate marginal distribution algorithm. In Advances in Soft Computing, pages 521-535. Springer London.
  18. Pelikan, M. and M ühlenbein, H. (1999b). Marginal distributions in evolutionary algorithms. In In Proceedings of the International Conference on Genetic Algorithms Mendel 98, pages 90-95.
  19. Póczos, B., Ghahramani, Z., and Schneider, J. (2012). Copula-based kernel dependency measures. In Langford, J. and Pineau, J., editors, Proceedings of the 29th International Conference on Machine Learning (ICML-12), pages 775-782, New York, NY, USA. ACM.
  20. Rey, M. and Roth, V. (2012). Copula mixture model for dependency-seeking clustering. In Langford, J. and Pineau, J., editors, Proceedings of the 29th International Conference on Machine Learning (ICML-12), pages 927-934, New York, NY, USA. ACM.
  21. Salinas-Gutiérrez, R., Hernández-Aguirre, A., and VillaDiharce, E. R. (2009). Using copulas in estimation of distribution algorithms. In MICAI 2009: Advances in Artificial Intelligence, volume 5845 of Lecture Notes in Computer Science, pages 658-668. Springer Berlin Heidelberg.
  22. Salinas-Gutiérrez, R., Hernández-Aguirre, A., and VillaDiharce, E. R. (2011). Estimation of distribution algorithms based on copula functions. In Proceedings of the 13th Annual Conference Companion on Genetic and Evolutionary Computation, GECCO 7811, pages 795-798, New York, NY, USA. ACM.
  23. Schwarz, J. and Jaros?, J. (2008). Parallel bivariate marginal distribution algorithm with probability model migration. In Linkage in Evolutionary Computation, volume 157 of Studies in Computational Intelligence, pages 3-23. Springer Berlin Heidelberg.
  24. Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications de l'Institut de Statistique de l'Université de Paris, 8:229-231.
  25. Soto, M., González-Fernández, Y., and Ochoa, A. (2012). Modeling with copulas and vines in estimation of distribution algorithms. CoRR, abs/1210.5500.
  26. Wang, L.-F., Guo, X., Zeng, J.-C., and Hong, Y. (2010a). Using gumbel copula and empirical marginal distribution in estimation of distribution algorithm. In Advanced Computational Intelligence (IWACI), 2010 Third International Workshop on, pages 583-587. IEEE.
  27. Wang, L.-F., Zeng, J.-C., and Hong, Y. (2009). Estimation of distribution algorithm based on copula theory. In Evolutionary Computation, 2009. CEC 7809. IEEE Congress on, pages 1057-1063.
  28. Wang, L.-F., Zeng, J.-C., Hong, Y., and Guo, X. (2010b). Copula estimation of distribution algorithm sampling from clayton copula. Journal of Computational Information Systems, 6(7):2431-2440.
  29. Zhao, H. and Wang, L. (2012). Marginal distribution in copula estimation of distribution algorithm based dynamic K-S test. In IJCSI International Journal of Computer Science Issues, number 3, pages 507-514.
  30. Zimmer, D. M. and Trivedi, P. K. (2006). Using trivariate copulas to model sample selection and treatment effects. Journal of Business & Economic Statistics, 24(1):63-76.
Download


Paper Citation


in Harvard Style

Hyrš M. and Schwarz J. (2015). Elliptical and Archimedean Copulas in Estimation of Distribution Algorithm with Model Migration . In Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 1: ECTA, ISBN 978-989-758-157-1, pages 212-219. DOI: 10.5220/0005594602120219


in Bibtex Style

@conference{ecta15,
author={Martin Hyrš and Josef Schwarz},
title={Elliptical and Archimedean Copulas in Estimation of Distribution Algorithm with Model Migration},
booktitle={Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 1: ECTA,},
year={2015},
pages={212-219},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005594602120219},
isbn={978-989-758-157-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 1: ECTA,
TI - Elliptical and Archimedean Copulas in Estimation of Distribution Algorithm with Model Migration
SN - 978-989-758-157-1
AU - Hyrš M.
AU - Schwarz J.
PY - 2015
SP - 212
EP - 219
DO - 10.5220/0005594602120219