Obtaining Better Non-Dominated Sets Using Volume Dominance

An important goal in multiobjective optimisation is to find a good set of non-dominated solutions that is both well-distributed and well-converged. Most multiobjective optimisation algorithms use the conventional Pareto dominance relationship. Over recent years, new approaches for the dominance relationship such as relaxed Pareto dominance, have been proposed. The interest in relaxed forms of Pareto dominance has been increasing due to their capability to find extreme values in the objective space. This paper conducts a short review on relaxed forms of Pareto dominance in the literature. A new form of relaxed Pareto dominance, called volume dominance, is presented afterward. The results based on comparison between volume dominance and Pareto dominance using SEAM02, SPEA2 and NSGA2 show that the proposed volume dominance is capable of obtaining a better and smoother trade-off front, and it is more robust than Pareto dominance.