Substitute Distance Assignments in NSGA-II for Handling Many-objective Optimization Problems

Many-objective optimization refers to optimization problems with a number of objectives considerably larger than two or three. In this paper, a study on the performance of the Fast Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) for handling such many-objective optimization problems is presented. In its basic form, the algorithm is not well suited for the handling of a larger number of objectives. The main reason for this is the decreasing probability of having Pareto-dominated solutions in the initial external population. To overcome this problem, substitute distance assignment schemes are proposed that can replace the crowding distance assignment, which is normally used in NSGA-II. These distances are based on measurement procedures for the highest degree, to which a solution is nearly Pareto-dominated by any other solution: like the number of smaller objectives, the magnitude of all smaller or larger objectives, or a multi-criterion derived from the former ones. For a number of many-objective test problems, all proposed substitute distance assignments resulted into a strongly improved performance of the NSGA-II.