# mk:emo07

### Summary

*Substitute Distance Assignments in NSGA-II for Handling Many-Objective Optimization Problems*. Mario Köppen and Kaori Yoshida. In Evolutionary Multi-Criterion Optimization, 4th International Conference, EMO 2007, Matsushima, Japan, March 2007. Proceedings, pages 727-741, 2007.

### 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 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.

### Bibtex entry

`@INPROCEEDINGS { mk:emo07,`

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 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. },

AUTHOR = { Mario Köppen and Kaori Yoshida },

BOOKTITLE = { Evolutionary Multi-Criterion Optimization, 4th International Conference, EMO 2007, Matsushima, Japan, March 2007. Proceedings },

ADDED = { 2007-04-06 14:05:35 +0900 },

MODIFIED = { 2008-02-28 11:16:27 +0900 },

EDITOR = { Shigeru Obayashi and Kalyanmoy Deb and Carlo Poloni and Tomoyuki Hiroyasu and Tadahiko Murata },

HASABSTRACT = { Yes },

PAGES = { 727-741 },

PDF = { emo07.pdf },

PUBLISHER = { Springer Berlin, Heidelberg },

SERIES = { LNCS 4403 },

TITLE = { Substitute Distance Assignments in NSGA-II for Handling Many-Objective Optimization Problems },

YEAR = { 2007 },

}