# mk:his07a

### Summary

*Visualization of Pareto-Sets in Evolutionary Multi-Objective Optimization*. Mario Köppen and Kaori Yoshida. In Seventh International Conference on Hybrid Intelligent Systems (HIS'07), pages 156-161, Kaiserslautern, Germany, 2007.

### Abstract

In this paper, a method for the visualization of the population of an evolutionary multi-objective optimization (EMO) algorrithm is presented. The main characteristic of this approach is the preservation of Pareto-dominance relations among the individuals as good as possible. It will be shown that in general, a Pareto-dominance preserving mapping from higher- to lower-dimensional space does not exist, so the demand to have as few wrong dominance relations after the mapping as possible gives an objective in addition to other mapping objectives like preserving nearest neighbor relations. Thus, the mapping itself poses a multi-objective optimization problem by itself, which is also handled by an EMO algorithm (NSGA-II in this case). The resulting mappings are shown for the run of a modified NSGA-II on the 15 objective DTLZ2? problem as an example. From such plots, some insights into evolution dynamics can be obtained.

### Bibtex entry

`@INPROCEEDINGS { mk:his07a,`

ABSTRACT = { In this paper, a method for the visualization of the population of an evolutionary multi-objective optimization (EMO) algorrithm is presented. The main characteristic of this approach is the preservation of Pareto-dominance relations among the individuals as good as possible. It will be shown that in general, a Pareto-dominance preserving mapping from higher- to lower-dimensional space does not exist, so the demand to have as few wrong dominance relations after the mapping as possible gives an objective in addition to other mapping objectives like preserving nearest neighbor relations. Thus, the mapping itself poses a multi-objective optimization problem by itself, which is also handled by an EMO algorithm (NSGA-II in this case). The resulting mappings are shown for the run of a modified NSGA-II on the 15 objective DTLZ2? problem as an example. From such plots, some insights into evolution dynamics can be obtained. },

ADDRESS = { Kaiserslautern, Germany },

AUTHOR = { Mario Köppen and Kaori Yoshida },

BOOKTITLE = { Seventh International Conference on Hybrid Intelligent Systems (HIS'07) },

ADDED = { 2007-10-30 22:01:23 +0900 },

MODIFIED = { 2008-02-28 11:15:56 +0900 },

DOI = { http://doi.ieeecomputersociety.org/ },

HASABSTRACT = { Yes },

ISBN = { 0-7695-2946-1 },

JOURNAL = { his },

PAGES = { 156-161 },

PDF = { his07a.pdf },

PUBLISHER = { IEEE Computer Society },

TITLE = { Visualization of Pareto-Sets in Evolutionary Multi-Objective Optimization },

VOLUME = { 0 },

YEAR = { 2007 },

1 = { http://doi.ieeecomputersociety.org/ },

}