Accelerating convergence using rough sets theory for multi-objective optimization problems

We propose the use of rough sets theory to improve the first approximation provided by a multi-objective evolutionary algorithm and retain the nondominated solutions using a new adaptive grid based on the ε-dominance concept that tries to overcome the main limitation of ε-dominance: the loss of several nondominated solutions from the hypergrid adopted in the archive because of the way in which solutions are selected within each box. We decided to use a multi-objective version of differential evolution to build a first approximation of the Pareto front and in a second stage, we use the rough sets theory in order to improve the spread of the solutions found so far. To assess our proposed hybrid approach, we adopt a set of standard test functions and metrics taken from the specialized literature. Our results are compared with respect to the NSGA-II, which is an approach representative of the state-of-the-art in the area.