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Benefits and Drawbacks for the Use of ǫ-Dominance in Evolutionary Multi-Objective Optimization

Using diversity mechanisms in evolutionary algorithms for multi-objective optimization problems is considered as an important issue for the design of successful algorithms. This is in particular the case for problems where the number of non-dominated feasible objective vectors is exponential with respect to the problem size. In this case the goal is to compute a good approximation of the Pareto front. We investigate how this goal can be achieved by using the diversity mechanism of ε-dominance and point out where this concept is provably helpful to obtain a good approximation of an exponentially large Pareto front in expected polynomial time. Afterwards, we consider the drawbacks of this approach and point out situations where the use of ε-dominance slows down the optimization process significantly.