DEMORS: A hybrid multi-objective optimization algorithm using differential evolution and rough set theory for constrained problems. The aim of this paper is to show how the hybridization of a multi-objective evolutionary algorithm (MOEA) and a local search method based on the use of rough set theory is a viable alternative to obtain a robust algorithm able to solve difficult constrained multi-objective optimization problems at a moderate computational cost. This paper extends a previously published MOEA [the authors, in: Mike Cattolico (ed.): Genetic and Evolutionary Computation Conference, GECCO 2006, Proceedings, Seattle, Washington, USA, July 8-12, 2006. ACM 2006 (2006)], which was limited to unconstrained multi-objective optimization problems. Here, the main idea is to use this sort of hybrid approach to approximate the Pareto front of a constrained multi-objective optimization problem while performing a relatively low number of fitness function evaluations. Since in real-world problems the cost of evaluating the objective functions is the most significant, our underlying assumption is that, by aiming to minimize the number of such evaluations, our MOEA can be considered efficient. As in its previous version, our hybrid approach operates in two stages: in the first one, a multi-objective version of differential evolution is used to generate an initial approximation of the Pareto front. Then, in the second stage, rough set theory is used to improve the spread and quality of this initial approximation. To assess the performance of our proposed approach, we adopt, on the one hand, a set of standard bi-objective constrained test problems and, on the other hand, a large real-world problem with eight objective functions and 160 decision variables. The first set of problems are solved performing 10,000 fitness function evaluations, which is a competitive value compared to the number of evaluations previously reported in the specialized literature for such problems. The real-world problem is solved performing 250,000 fitness function evaluations, mainly because of its high dimensionality. Our results are compared with respect to those generated by NSGA-II, which is a MOEA representative of the state-of-the-art in the area.
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References in zbMATH (referenced in 7 articles , 1 standard article )
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- Lin, Qiuzhen; Zhu, Qingling; Huang, Peizhi; Chen, Jianyong; Ming, Zhong; Yu, Jianping: A novel hybrid multi-objective immune algorithm with adaptive differential evolution (2015)
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- Qian, Feng; Xu, Bin; Qi, Rongbin; Tianfield, Huaglory: Self-adaptive differential evolution algorithm with $\alpha $-constrained-domination principle for constrained multi-objective optimization (2012)
- Hernández-Díaz, Alfredo G.; Santana-Quintero, Luis V.; Coello, Carlos A.Coello; Molina, Julián; Caballero, Rafael: Improving the efficiency of $\epsilon $-dominance based grids (2011)
- Santana-Quintero, Luis V.; Hernández-Díaz, Alfredo G.; Molina, Julián; Coello Coello, Carlos A.; Caballero, Rafael: DEMORS: A hybrid multi-objective optimization algorithm using differential evolution and rough set theory for constrained problems (2010)
- Vincenti, Angela; Ahmadian, Mohammad Reza; Vannucci, Paolo: BIANCA: a genetic algorithm to solve hard combinatorial optimisation problems in engineering (2010)