Title: Archimedean copula-based estimation of distribution algorithm for multi-objective optimisation

Authors: Ying Gao; Lingxi Peng; Fufang Li; Miao Liu; Waixi Liu

Addresses: Department of Computer Science and Technology, Guangzhou University, Guangzhou, 510006, China ' Department of Computer Science and Technology, Guangzhou University, Guangzhou, 510006, China ' Department of Computer Science and Technology, Guangzhou University, Guangzhou, 510006, China ' Department of Computer Science and Technology, Guangzhou University, Guangzhou, 510006, China ' Department of Computer Science and Technology, Guangzhou University, Guangzhou, 510006, China

Abstract: Estimation of distribution algorithms (EDAs) are a class of evolutionary optimisation algorithms based on probability distribution model. This article extends the basic EDAs for tackling multi-objective optimisation problems by incorporating Archimedean copulas for constructing probability distribution model, and using the concept of Pareto dominance. In the algorithm, the marginal distributions from the current population are firstly estimated by kernel estimation method and are used to estimate the parameter of the Archimedean copula function generator by using the maximum likelihood method. Afterwards, the multivariate Archimedean copula sample algorithm is used to generate current offsprings population by sampling the n-dimensional Laplace transform Archimedean copula. The population with the current population and current offsprings population is sorted based on non-domination, and the best individuals are selected to form the next population based on rank and the crowding distance. The proposed algorithm is tested to compare with NSGA-II, PAES and SPEA2 using a set of benchmark functions. Both convergence and diversity metrics are used to evaluate the performance of the algorithm. The experimental results show that the algorithm outperforms NSGA-II, PAES and SPEA2 in two metrics.

Keywords: Archimedean copula; multi-objective optimisation; estimation of distribution algorithms; EDA; Pareto optimal; Laplace transform; probability distribution; Pareto dominance; evolutionary optimisation.

DOI: 10.1504/IJTMCC.2013.056430

International Journal of Trust Management in Computing and Communications, 2013 Vol.1 No.3/4, pp.200 - 211

Received: 26 Oct 2012
Accepted: 28 Feb 2013

Published online: 16 Sep 2013 *

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