Substitute distance assignments in NSGA-II for handling many-objective optimization problems

  • Authors:

  • Mario Köppen;Kaori Yoshida

  • Affiliations:

  • Kyushu Institute of Technology, Dept. Artificial Intelligence, Iizuka, Fukuoka, Japan;Kyushu Institute of Technology, Dept. Artificial Intelligence, Iizuka, Fukuoka, Japan

  • Venue:
  • EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
  • Year:
  • 2007

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Abstract

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 Nondominated 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.