A comparison of dominance criteria in many-objective optimization problems

In this paper, we analyze four dominance criteria in terms of their ability to adequately order sets of points in multi- and many-objective optimization problems. The use of relaxed and alternative dominance relationships has been an important tool for improving the performance of multiobjective evolutionary optimization algorithms, and their ordering ability is among the most important characteristics responsible for such improvement. Three relaxed formulations of dominance are investigated, along with the traditional Pareto ordering, in order to provide a comparison baseline. The results obtained show that all three relaxed dominance approaches presented greater robustness to the increase in the number of objectives, and are therefore more appropriate for use in many-objective optimization algorithms.