Nonconvex Functions Optimization Using an Estimation of Distribution Algorithm Based on a Multivariate Extension of the Clayton Copula

This paper presents a copula-based estimation of a distribution algorithm with parameter updating for numeric optimization problems. This model implements an estimation of a distribution algorithm using a multivariate extension of Clayton’s bivariate copula (MEC-EDA) to estimate the conditional probability for generating a population of individuals. Moreover, the model uses traditional mutation and elitism operators jointly with a heuristic for a population restarting in the evolutionary process. We show that these approaches improve the overall performance of the optimization compared to other copula-based EDAs.

[1]  H. Joe.  Families of $m$-variate distributions with given margins and $m(m-1)/2$ bivariate dependence parameters , 1996 .

[2]  C. Genest,et al.  Statistical Inference Procedures for Bivariate Archimedean Copulas , 1993 .

[3]  H. Joe.  Multivariate models and dependence concepts , 1998 .

[4]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[5]  Jianchao Zeng,et al.  VQ Codebook Design Algorithm Based on Copula Estimation of Distribution Algorithm , 2011, 2011 First International Conference on Robot, Vision and Signal Processing.

[6]  José Ignacio Hidalgo,et al.  Bivariate empirical and n-variate Archimedean copulas in estimation of distribution algorithms , 2010, IEEE Congress on Evolutionary Computation.

[7]  Barnabás Póczos,et al.  Copula-based Kernel Dependency Measures , 2012, ICML.

[8]  Jose Miguel Puerta,et al.  Avoiding premature convergence in estimation of distribution algorithms , 2009, 2009 IEEE Congress on Evolutionary Computation.

[9]  Pedro Larrañaga,et al.  Estimation of Distribution Algorithms , 2002, Genetic Algorithms and Evolutionary Computation.

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

[11]  Marta Soto,et al.  copulaedas: An R Package for Estimation of Distribution Algorithms Based on Copulas , 2012, ArXiv.

[12]  E. Luciano,et al.  Copula Methods in Finance: Cherubini/Copula , 2004 .

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

[14]  Martin Pelikan,et al.  An introduction and survey of estimation of distribution algorithms , 2011, Swarm Evol. Comput..