Abstract
The idea of multi-population parallel strategy and the copula theory are introduced into the Estimation of Distribution Algorithm (EDA), and a new parallel EDA is proposed in this paper. In this algorithm, the population is divided into some subpopulations. Different copula is used to estimate the distribution model in each subpopulation. Two copulas, Clayton and Gumbel, are used in this paper. To estimate the distribution function is to estimate the copula and the margins. New individuals are generated according to the copula and the margins. In order to increase the diversity of the subpopulation, the elites of one subpopulation are learned by the other subpopulation. The experiments show the proposed algorithm performs better than the basic copula EDA and some classical EDAs in speed and in precision.
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References
Zhou, S.D., Sun, Z.Q.: A Survey on Estimation of Distribution Algorithms. Acta Automatica Sinica 33(2), 114–121 (2007)
Baluja, S.: Population-Based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning. Technical Rep. CMU-CS-94-163. Carnegie Mellon University, Pittsburgh, PA (1994)
Muhlenbein, 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 1996. LNCS, vol. 1141, pp. 178–187. Springer, Heidelberg (1996)
De Bonet, J.S., Isbell, C.L., Viola, P.: MIMIC: Finding Optima by Estimation Probability Densities. In: Advances in Neural Information Processing Systems, pp. 424–430. MIT Press, Cambridge (1997)
Pelican, M., Muhlenbein, H.: The Bivariate Marginal Distribution Algorithm. In: Advances in Soft Computing-Engineering Design and Manufacturing, pp. 521–535. Springer, London (1999)
Harik, G.: Linkage Learning via Probabilistic Modeling in the ECGA. Illigal Rep. No.99010, Illinois Genetic Algorithms Lab. University of Illinois, Urbana-Champaign, Illinois (1999)
Muhlenbein, H., Mahnig, T.: FDA- a Scalable evolutionary Algorithm for the Optimization of Additively Decomposed Functions. Evolutionary Computation 7(4), 353–376 (Winter 1999)
Pelikan, M., Goldberg, D.E., Cantu-Paz, E.: BOA: the Bayesian Optimization Algorithm. In: Proc. Genetic and Evolutionary Computation Conference (GECCO-1999), Orlando, FL, pp. 525–532 (1999)
Larranaga, P., Etxeberria, R., Lozano, J.A., Pena, J.M.: Optimization in Continuous Domains by Learning and Simulation of Gaussian Networks. In: Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2000, Las Vegas, Nevada, USA, July 8-12, pp. 201–204. Morgan Kaufmann, San Francisco (2000)
Sebag, M., Ducoulombier, A.: Extending Population-Based Incremental Learning to Continuous Search Spaces. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 418–427. Springer, Heidelberg (1998), http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.1884
Larranaga, P., Lozano, J.A., Bengoetxea, E.: Estimation of Distribution Algorithms based on Multivariate Normal a Gaussian Nerworks. Technical Report KZZA-IK-1-01. Department of Computer Science and Artificial Intelligence, University of the Basque Country (2001)
Wang, L.F., Zeng, J.C., Hong, Y.: Estimation of Distribution Algorithm Based on Archimedean Copulas. In: Proceedings of the First ACM/SIGEVO Summit on Genetic and Evolutionary Computation (GECS 2009), Shanghai, China, June 12-14, pp. 993–996 (2009)
Wang, L.F., Zeng, J.C., Hong, Y.: Estimation of Distribution Algorithm Based on Copula Theory. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2009), Trondheim, Norway, May 18-21, pp. 1057–1063 (2009)
Nelsen, R.B.: An introduction to copulas, 2nd edn. Springer, New York (2006)
Cantú-Paz, E.: A Survey of Parallel Genetic Algorithms. Illinois Genetic Algorithms Laboratory, Urbana-Champaign (1996)
Cantú-Paz, E.: Efficient and accurate parallel genetic algorithms. Kluwer, Dordrecht (2001)
Wang, L., Guo, X., Zeng, J., Hong, Y.: Using Gumbel Copula and Empirical Marginal Distribution in Estimation of Distribution Algorithm. In: 2010 Third International Workshop on Advanced Computational Intelligence (IWACI 2010), Suzhou, China, August 25-27, pp. 583–587 (2010); (EI:20104613386525)
Wang, L., Wang, Y., Zeng, J., Hong, Y.: An estimation of distribution algorithm based on clayton copula and empirical margins. In: Li, K., Li, X., Ma, S., Irwin, G.W. (eds.) LSMS 2010, Part 1. CCIS, vol. 98, pp. 82–88. Springer, Heidelberg (2010), doi:10.1007/978-3-642-15859-9_12, (EI:20104513368882) 04
Marshall, A.W., Olkin, I.: Families of Multivariate Distributions. Journal of the American Statistical Association 83, 834–841 (1988)
Melchiori, M.R.: Tools For Sampling Multivariate Archimedean Copulas. Yield Curve (April 2006), SSRN: http://ssrn.com/abstract=1124682
Dong, W., Yao, X.: Unified Eigen Analysis On Multivariate Gaussian Based Estimation of Distribution Algorithms. Information Science 178, 3000–3023 (2008)
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Chang, C., Wang, L. (2011). A Multi-population Parallel Estimation of Distribution Algorithms Based on Clayton and Gumbel Copulas. In: Deng, H., Miao, D., Lei, J., Wang, F.L. (eds) Artificial Intelligence and Computational Intelligence. AICI 2011. Lecture Notes in Computer Science(), vol 7002. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23881-9_81
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