Using ε-Dominance for Hidden and Degenerated Pareto-Fronts

Scalable multi-objective test problems are known to be useful in testing and analyzing the abilities of algorithms. In this paper we focus on test problems with degenerated Pareto-fronts and provide an in-depth insight into the properties of some problems which show these characteristics. In some of the problems with degenerated fronts such as Distance Minimization Problem (DMP) with the Manhattan metric, it is very difficult to dominate some of the non-optimal solutions as the optimal solutions are hidden within a set of so called pseudo-optimal solutions. Hence the algorithms based on Pareto-domination criterion are shown to be inefficient. In this paper, we explore the pseudo-optimal solutions and examine how and why the use of ε-dominance can help to achieve a better approximation of the hidden Pareto-fronts or of degenerated fronts in general. We compare the performance of the ε-MOEA with 3 other algorithms (NSGA-II, NSGA-III and MOEA/D) and show that ε- dominance performs better when dealing with pseudo-optimal kind of solutions. Furthermore, we analyze the performance on the WFG3 test problem and illustrate the advantages and disadvantages of ε-dominance for this degenerated problem.