Estimation of Distribution Algorithm with Multivariate T-Copulas for Multi-Objective Optimization

Ying Gao, Lingxi Peng, Fufang Li, Miao Liu, Xiao Hu

Department of Computer Science and Technology, Guangzhou University, Guangzhou, China.

DOI: 10.4236/ica.2013.41009                

Abstract

Estimation of distribution algorithms are a class of evolutionary optimization algorithms based on probability distribution model. In this article, a Pareto-based multi-objective estimation of distribution algorithm with multivariate T-copulas is proposed. The algorithm employs Pareto-based approach and multivariate T-copulas to construct probability distribution model. To estimate joint distribution of the selected solutions, the correlation matrix of T-copula is firstly estimated by estimating Kendall’s tau and using the relationship of Kendall’s tau and correlation matrix. After the correlation matrix is estimated, the degree of freedom of T-copula is estimated by using the maximum likelihood method. Afterwards, the Monte Carte simulation is used to generate new individuals. An archive with maximum capacity is used to maintain the non-dominated solutions. The Pareto optimal solutions are selected from the archive on the basis of the diversity of the solutions, and the crowding-distance measure is used for the diversity measurement. The archive gets updated with the inclusion of the non-dominated solutions from the combined population and current archive, and the archive which exceeds the maximum capacity is cut using the diversity consideration. The proposed algorithm is applied to some well-known benchmark. The relative experimental results show that the algorithm has better performance and is effective.

Keywords

Estimation of Distribution Algorithm; Pareto-Based Approach; T-Copulas; Multi-Objective Optimization

Conflicts of Interest

The authors declare no conflicts of interest.

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