Operations Research 2025
Abstract Submission

2319. Representation of the Non-dominated Set by the Supported Non-dominated Points

Invited abstract in session TD-5: Multiobjective Optimization 3: Representations, stream Decision Theory and Multi-criteria Decision Making.

Thursday, 14:30-16:00
Room: H7

Authors (first author is the speaker)

1. Michael Stiglmayr
School of Mathematics and Natural Sciences, University of Wuppertal
2. David Könen
Universität Wuppertal
3. Lara Löhken
Department of Mathematics and Informatics, University of Wuppertal
4. Kathrin Klamroth
Department of Mathematics and Informatics, University of Wuppertal

Abstract

While multi-objective linear optimization problems only contain supported nondominated points, the nondominated point set of multi-objective combinatorial optimization problems, such as network optimization problems, also contain nonsupported nondominated points.

These points generally outnumber the supported ones and are more challenging to determine, as they cannot be obtained as optimal solutions of weighted sum problems with weights strictly greater than zero. We consider the set of supported and the set of extreme supported nondominated points as representations for the complete nondominated set. Various quality metrics, such as coverage error, hypervolume ratio, and epsilon-indicator, are used to analyze and compare the quality of these representations.

Multiple classes of network optimization problems are generated to evaluate the representations by the supported nondominated points. The results indicate that the supported nondominated points consistently provide high-quality representations, while considering only the extreme supported nondominated points may only yield sufficiently good representations in network optimization problems where the arc capacities are quite small.

Keywords

Status: accepted


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