PreprintarXiv licencearXiv
Representing the Non-dominated Set of Multi-objective Optimization Problems with Polyhedral Ordering Cones
Abstract
In the literature, research on representing the non-dominated set has focused almost exclusively on multi-objective optimization problems with Pareto-dominance. However, general ordering cones are used to incorporate preferences of decision makers into the optimization process and to model other specific types of optimization problems, such as ordinal optimization problems. In this work, we consider several representation approaches based on representation relations in the context of multi-objective optimization problems with polyhedral ordering cones. Our main research question is whether existing theory and solution approaches developed for the Pareto case can be used to address the more general setting.
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BibTeX
@misc{weuste2026representing,
title = {{Representing the Non-dominated Set of Multi-objective Optimization Problems with Polyhedral Ordering Cones}},
author = {Chiara Weuste and Michael Stiglmayr},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13141},
eprint = {2610.13141},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13141},
}
RIS
TY - UNPB
TI - Representing the Non-dominated Set of Multi-objective Optimization Problems with Polyhedral Ordering Cones
AU - Chiara Weuste
AU - Michael Stiglmayr
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13141
UR - https://arxiv.org/abs/2610.13141
AB - In the literature, research on representing the non-dominated set has focused almost exclusively on multi-objective optimization problems with Pareto-dominance. However, general ordering cones are used to incorporate preferences of decision makers into the optimization process and to model other specific types of optimization problems, such as ordinal optimization problems. In this work, we consider several representation approaches based on representation relations in the context of multi-objective optimization problems with polyhedral ordering cones. Our main research question is whether existing theory and solution approaches developed for the Pareto case can be used to address the more general setting.
ER -