ABSTRACT
Probabilistic modeling in multi-objective optimization problems (MOPs) has mainly focused on capturing and representing the dependencies between decision variables in a set of selected solutions. Recently, some works have proposed to model also the dependencies between the objective variables, which are represented as random variables, and the decision variables. In this paper, we investigate the suitability of copula models to capture and exploit these dependencies in MOPs with a continuous representation. Copulas are very flexible probabilistic models able to represent a large variety of probability distributions.
- Marcella SR Martins, Myriam RBS Delgado, Ricardo Lüders, Roberto Santana, Richard Aderbal Gonçalves, and Carolina Paula de Almeida. 2017. Hybrid multi-objective Bayesian estimation of distribution algorithm: a comparative analysis for the multi-objective knapsack problem. Journal of Heuristics (2017). In press.Google Scholar
- H. Mühlenbein and G. Paaß. 1996. From recombination of genes to the estimation of distributions I. Binary parameters. In Parallel Problem Solving from Nature - PPSN IV (Lectures Notes in Computer Science), Vol. 1141. Springer, Berlin, 178--187. Google ScholarDigital Library
- Abe Sklar. 1973. Random variables, distribution functions, and copulas. Kybernetica (1973), 449--460.Google Scholar
- Marta Soto, Yasser Gonzalez-Fernandez, and Alberto Ochoa. 2012. Modeling with copulas and vines in estimation of distribution algorithms. CoRR abs/1210.5500 (2012). http://arxiv.org/abs/1210.5500Google Scholar
Index Terms
- Modeling dependencies between decision variables and objectives with copula models
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