Alternative techniques to solve hard multi-objective optimization problems

In this paper, we propose the combination of different optimization techniques in order to solve "hard" two- and three-objective optimization problems at a relatively low computational cost. First, we use the ε-constraint method in order to obtain a few points over (or very near of) the true Pareto front, and then we use an approach based on rough sets to spread these solutions, so that the entire Pareto front can be covered. The constrained single-objective optimizer required by the ε-constraint method, is the cultured differential evolution, which is an efficient approach for approximating the global optimum of a problem with a low number of fitness function evaluations. The proposed approach is validated using several difficult multi-objective test problems, and our results are compared with respect to a multi-objective evolutionary algorithm representative of the state-of-the-art in the area: the NSGA-II.

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