Epsilon-constraint with an efficient cultured differential evolution

In this paper we present the use of a previously developed single-objective optimization approach, together with the ε-constraint method, to provide an approximation of the Pareto front in a multiobjective optimization problem. This approximation is usually very near of the true Pareto front, but its cost grows with the desired number of points in the output set. As an alternative, it is possible to generate only a few points, and execute a second phase which will generate intermediate points, to increase the size of the output set. We use a rough sets-based approach for this second phase, which is a very robust approach. The results of this two-phase approach are very competitive in hard multiobjective problems, and is less expensive than the ε-constraint method alone. This approach is very effective on hard multiobjective problems, where is able to find good approximations of the Pareto front with less funtion evaluations than other approaches, as the NSGA-II (against which is compared).