Estimation of distribution algorithm based on archimedean copulas

Both Estimation of Distribution Algorithms (EDAs) and Copula Theory are hot topics in different research domains. The key of EDAs is modeling and sampling the probability distribution function which need much time in the available algorithms. Moreover, the modeled probability distribution function can not reflect the correct relationship between variables of the optimization target. Copula Theory provides a correlation between univariable marginal distribution functions and the joint probability distribution function. Therefore, Copula Theory could be used in EDAs. Because Archimedean copulas possess many nice properties, an EDA based on Archimedean copulas is presented in this paper. The experimental results show the effectiveness of the proposed algorithm.

[1]  R. Nelsen.  An Introduction to Copulas (Springer Series in Statistics) , 2006 .

[2]  Paul A. Viola,et al.  MIMIC: Finding Optima by Estimating Probability Densities , 1996, NIPS.

[3]  J. A. Lozano,et al.  Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation , 2001 .

[4]  Pedro Larrañaga,et al.  Optimization in Continuous Domains by Learning and Simulation of Gaussian Networks , 2000 .

[5]  Dean Fantazzini,et al.  A New Approach for Firm Value and Default Probability Estimation beyond Merton Models , 2008 .

[6]  A. McNeil,et al.  The t Copula and Related Copulas , 2005 .

[7]  P. A. Simionescu,et al.  Teeth-Number Synthesis of a Multispeed Planetary Transmission Using an Estimation of Distribution Algorithm , 2006 .

[8]  David E. Goldberg,et al.  Multi-objective bayesian optimization algorithm , 2002 .

[9]  David E. Goldberg,et al.  Multiobjective hBOA, clustering, and scalability , 2005, GECCO '05.

[10]  R. Nelsen.  An Introduction to Copulas , 1998 .

[11]  Dirk Thierens,et al.  Multi-objective Optimization with the Naive MIDEA , 2006 .

[12]  E. Luciano,et al.  Copula methods in finance , 2004 .

[13]  D. Goldberg,et al.  BOA: the Bayesian optimization algorithm , 1999 .

[14]  Zhong Wei.  Second Order Estimation of Distribution Algorithms Based on Kalman Filter , 2004 .

[15]  Michèle Sebag,et al.  Extending Population-Based Incremental Learning to Continuous Search Spaces , 1998, PPSN.

[16]  H. Mühlenbein,et al.  From Recombination of Genes to the Estimation of Distributions I. Binary Parameters , 1996, PPSN.

[17]  David E. Goldberg,et al.  Military antenna design using simple and competent genetic algorithms , 2006, Math. Comput. Model..

[18]  Shumeet Baluja,et al.  A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning , 1994 .

[19]  Qingfu Zhang,et al.  An estimation of distribution algorithm with guided mutation for a complex flow shop scheduling problem , 2007, GECCO '07.

[20]  Jianchao Zeng,et al.  Estimation of Distribution Algorithm based on copula theory , 2009, 2009 IEEE Congress on Evolutionary Computation.