Estimation of Distribution Algorithm based on copula theory

Estimation of Distribution Algorithm (EDA) is a novel evolutionary computation, which mainly depends on learning and sampling mechanisms to manipulate the evolutionary search, and has been proved a potential technique for complex problems. However, EDA generally spend too much time on the learning about the probability distribution of the promising individuals. The paper propose an improved EDA based on copula theory (copula-EDA) to enhance the learning efficiency, which models and samples the joint probability function by selecting a proper copula and learning the marginal probability distributions of the promising population. The simulating results prove the approach is easy to implement and is validated on several problems.

[1]  M. Pelikán,et al.  The Bivariate Marginal Distribution Algorithm , 1999 .

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

[3]  Marcus Gallagher,et al.  Population-Based Continuous Optimization, Probabilistic Modelling and Mean Shift , 2005, Evolutionary Computation.

[4]  G. Harik.  Linkage Learning via Probabilistic Modeling in the ECGA , 1999 .

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

[6]  Yong Gao,et al.  Space Complexity of Estimation of Distribution Algorithms , 2005, Evolutionary Computation.

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

[8]  Markus H ohfeld,et al.  Random keys genetic algorithm with adaptive penalty function for optimization of constrained facility layout problems , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[9]  P. Bosman,et al.  IDEAs based on the normal kernels probability density function , 2000 .

[10]  Jianchao Zeng,et al.  Estimation of distribution algorithm based on archimedean copulas , 2009, GEC '09.

[11]  Dong-Yeon Cho,et al.  Continuous estimation of distribution algorithms with probabilistic principal component analysis , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

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

[13]  David E. Goldberg,et al.  Scalability of the Bayesian optimization algorithm , 2002, Int. J. Approx. Reason..

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

[15]  Rajkumar Roy,et al.  Advances in Soft Computing: Engineering Design and Manufacturing , 1998 .

[16]  Xin Yao,et al.  Parallel Problem Solving from Nature PPSN VI , 2000, Lecture Notes in Computer Science.

[17]  Petros Koumoutsakos,et al.  A Mixed Bayesian Optimization Algorithm with Variance Adaptation , 2004, PPSN.

[18]  David E. Goldberg,et al.  The compact genetic algorithm , 1999, IEEE Trans. Evol. Comput..

[19]  Qiu Xiao-xia.  Dependence Measure Based on Copula Theory , 2008 .

[20]  Heinz Mühlenbein,et al.  The Equation for Response to Selection and Its Use for Prediction , 1997, Evolutionary Computation.

[21]  Qingfu Zhang,et al.  On the convergence of a class of estimation of distribution algorithms , 2004, IEEE Transactions on Evolutionary Computation.

[22]  Jonathan L. Shapiro,et al.  Drift and Scaling in Estimation of Distribution Algorithms , 2005, Evolutionary Computation.

[23]  T. Mahnig,et al.  Evolutionary algorithms: from recombination to search distributions , 2001 .

[24]  Johann Christoph Strelen,et al.  Analysis and generation of random vectors with copulas , 2007, 2007 Winter Simulation Conference.

[25]  S. Baluja.  An Empirical Comparison of Seven Iterative and Evolutionary Function Optimization Heuristics , 1995 .

[26]  Heinz Mühlenbein,et al.  FDA -A Scalable Evolutionary Algorithm for the Optimization of Additively Decomposed Functions , 1999, Evolutionary Computation.

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

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

[29]  Dirk Thierens,et al.  Expanding from Discrete to Continuous Estimation of Distribution Algorithms: The IDEA , 2000, PPSN.

[30]  Thomas Bäck,et al.  Parallel Problem Solving from Nature — PPSN V , 1998, Lecture Notes in Computer Science.

[31]  Hans-Paul Schwefel,et al.  Parallel Problem Solving from Nature — PPSN IV , 1996, Lecture Notes in Computer Science.

[32]  Yao Qing-zhu.  A Method of Improving Copula Fited to Data , 2004 .

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

[34]  Qingfu Zhang,et al.  On the convergence of a factorized distribution algorithm with truncation selection , 2004, Complex..

[35]  Martin Pelikan,et al.  Hierarchical Bayesian optimization algorithm: toward a new generation of evolutionary algorithms , 2010, SICE 2003 Annual Conference (IEEE Cat. No.03TH8734).

[36]  David E. Goldberg,et al.  Bayesian Optimization Algorithm, Population Sizing, and Time to Convergence , 2000, GECCO.

[37]  Niall Whelan,et al.  Sampling from Archimedean copulas , 2004 .

[38]  J. A. Lozano,et al.  Analyzing the PBIL Algorithm by Means of Discrete Dynamical Systems , 2000 .

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

[40]  S. Baluja,et al.  Using Optimal Dependency-Trees for Combinatorial Optimization: Learning the Structure of the Search Space , 1997 .

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

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

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

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

[45]  Martin Pelikan,et al.  Marginal Distributions in Evolutionary Algorithms , 2007 .

[46]  Heinz Mühlenbein,et al.  Schemata, Distributions and Graphical Models in Evolutionary Optimization , 1999, J. Heuristics.