Using Copulas in Estimation of Distribution Algorithms

Salinas-Gutiérrez, Rogelio; Hernández-Aguirre, Arturo; Villa-Diharce, Enrique

doi:10.1007/978-3-642-05258-3_58

Cited by 31 publications

(20 citation statements)

References 13 publications

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“…Copula is a function that embodies the relationship of the variables [23,24]. The use of Copulabased models in continuous EDAs places these algorithms in an advantageous position in comparison with other EDAs that rely on the assumption of a particular multivariate distribution, such as the multivariate normal distribution [25,26]. By means of Copulas, any multivariate distribution can be decomposed into the marginal distribution and the Copula that determines the dependence structure between the variables.…”

Section: End Whilementioning

confidence: 99%

A Posteriori Pareto Front Diversification Using a Copula-Based Estimation of Distribution Algorithm

Cheriet¹,

Cherif²

2015

ijacsa

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Abstract-We propose CEDA, a Copula-based Estimation of Distribution Algorithm, to increase the size, achieve high diversity and convergence of optimal solutions for a multiobjective optimization problem. The algorithm exploits the statistical properties of Copulas to produce new solutions from the existing ones through the estimation of their distribution. CEDA starts by taking initial solutions provided by any MOEA (Multi Objective Evolutionary Algorithm), construct Copulas to estimate their distribution, and uses the constructed Copulas to generate new solutions. This design saves CEDA the need of running an MOEA every time alternative solutions are requested by a Decision Maker when the found solutions are not satisfactory. CEDA was tested on a set of benchmark problems traditionally used by the community, namely UF1, UF2, ..., UF10 and CF1, CF2, ..., CF10. CEDA used along with SPEA2 and NSGA2 as two examples of MOEA thus resulting in two variants CEDA-SPEA2 and CEDA-NSGA2 and compare them with SPEA2 and NSGA2. The results of The experiments show that, with both variants of CEDA, new solutions can be generated in a significantly smaller without compromising quality compared to those found SPEA2 and NSGA2.

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Section: End Whilementioning

confidence: 99%

A Posteriori Pareto Front Diversification Using a Copula-Based Estimation of Distribution Algorithm

Cheriet¹,

Cherif²

2015

ijacsa

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“…Copula-based EDAs (CEDAs) (Salinas-Gutierrez et al 2009;Wang et al 2009;Wang and Zeng 2010;Cuesta-Infante et al 2010) use the copula function for estimating the joint probability distribution of the variables according to Sklar's theorem. The copula function only uses the marginal univariate probabilities to compute the joint probability distribution.…”

Section: Other Modeling Approachesmentioning

confidence: 99%

A review on probabilistic graphical models in evolutionary computation

et al. 2012

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Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Evolutionary algorithms is one such discipline that has employed probabilistic graphical models to improve the search for optimal solutions in complex problems. This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems. Specifically, we give a survey of probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compare different methods for probabilistic modeling in these algorithms.

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“…Recent years have seen an increasing interest in the use of copula theory in EDAs [11]- [13]. But they are all based on the 2-dimensional copulas.…”

Section: Multivariate Interactionsmentioning

confidence: 99%

Using Gumbel copula and empirical marginal distribution in Estimation of Distribution Algorithm

Wang

Guo

Zeng

et al. 2010

Third International Workshop on Advanced Computational Intelligence

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Estimation of Distribution Algorithms (EDAs) is a novel evolutionary algorithm originated from Genetic Algorithms. The probability distribution model of promising population is estimated iteratively in EDAs, and the new generation is sampled from the estimated model. An EDA with Gumbel copula is proposed in this paper. In order to estimating the joint, the empirical margins of each variable are estimated separately, and the relationship of variables is presented by Gumbel copula. On the ground of copula theory, the joint is the composite function of the copula and the margins. This algorithm simplifies the operator to estimating the multivariate distribution. The experimental results show that the proposed algorithm is equivalent to some conventional continuous EDAs in performance.

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Using Copulas in Estimation of Distribution Algorithms

Cited by 31 publications

References 13 publications

A Posteriori Pareto Front Diversification Using a Copula-Based Estimation of Distribution Algorithm

A Posteriori Pareto Front Diversification Using a Copula-Based Estimation of Distribution Algorithm

A review on probabilistic graphical models in evolutionary computation

Using Gumbel copula and empirical marginal distribution in Estimation of Distribution Algorithm

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