The (g)over-cap-dominance Relation for Preference-Based Evolutionary Multi-Objective Optimization

In evolutionary multi-objective optimization, the results generated by an evolutionary algorithm usually contain an approximation, as good as possible, of the entire Paretooptimal front. However, sometimes the number of Pareto-optimal solutions may be so large that the decision maker (DM) is incapable of manipulating or understanding them. Methods for considering only the Pareto-optimal solutions that the DM prefers indeed constitute a hot research topic in the evolutionary computation field. In this paper, we introduce a new dominance relation called r''-dominance, which is an improved version of the g-dominance relation and can be easily implemented in traditional multi-objective evolutionary algorithms. In this work, the proposed r''-dominance is implemented in NSGA-II. Our experimental results show the effectiveness of r''-NSGA-II with respect to the original g-NSGA-II.