Generalization of Pareto-Optimality for Many-Objective Evolutionary Optimization

The vast majority of multiobjective evolutionary algorithms presented to date are Pareto-based. Usually, these algorithms perform well for problems with few (two or three) objectives. However, due to the poor discriminability of Pareto-optimality in many-objective spaces (typically four or more objectives), their effectiveness deteriorates progressively as the problem dimension increases. This paper generalizes Pareto-optimality both symmetrically and asymmetrically by expanding the dominance area of solutions to enhance the scalability of existing Pareto-based algorithms. The generalized Pareto-optimality (GPO) criteria are comparatively studied in terms of the distribution of ranks, the ranking landscape, and the convergence of the evolutionary process over several benchmark problems. The results indicate that algorithms equipped with a generalized optimality criterion can acquire the flexibility of changing their selection pressure within certain ranges, and achieve a richer variety of ranks to attain faster and better convergence on some subsets of the Pareto optima. To compensate for the possible diversity loss induced by the generalization, a distributed evolution framework with adaptive parameter setting is also proposed and briefly discussed. Empirical results indicate that this strategy is quite promising in diversity preservation for algorithms associated with the GPO.