Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal?

Many multi-objective evolutionary algorithms (MOEAs) have been proposed over the years. The main part of the most successful algorithms such as PESA, or NSGA-II, are the Pareto based selection strategy that decide survivors using dominance among individuals. However, does the Pareto based selection strategy always succeed in finding the Pareto optimal solutions? This paper shows a very simple example that can cause serious trouble for the Pareto based MOEAs. In such an instance, various solutions, which are apart from the true Pareto-optimums, are left as hardly-dominated solutions. We define such solutions as dominance resistant solutions (DRSs), and show a class of problems which produces DRSs easily. To cope with this difficulty we propose the α-domination strategy that relaxes the domination introducing a weak trade-off among objectives. With the α-domination strategy, the DRSs are effectively purged from the population