It Is Hard to Distinguish Between Dominance Resistant Solutions and Extremely Convex Pareto Optimal Solutions

It has been acknowledged that dominance resistant solutions (DRSs) often exist in the feasible region of multi-objective optimization problems. DRSs can severely degrade the performance of many multi-objective evolutionary algorithms (MOEAs). In previous work, some coping strategies (e.g., the \(\epsilon \)-dominance and the modified objective calculation) have been demonstrated to be effective in eliminating DRSs. However, these strategies may in turn cause algorithm inefficiency in other aspects. We argue that these coping strategies prevent the algorithm from obtaining extremely convex Pareto optimal solutions (ECPOSs), which are located around the boundary of the convex Pareto front (PF). That is, there is a dilemma between eliminating DRSs and preserving ECPOSs. To illustrate such a dilemma, we propose a new multi-objective optimization test problem with the extremely convex PF as well as the hardly dominated boundaries. Using this test problem, we investigate the performance of six representative MOEAs in terms of ECPOS preservation and DRS elimination. The results indicate that it is indeed challenging to distinguish between ECPOSs and DRSs.