Non-Extreme Individual Minima for Improved Pareto Front Sampling Efficiency and Decision-Making
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917294125350912 |
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| author | Herrmann-Wicklmayr, Markus Flaßkamp, Kathrin |
| author_facet | Herrmann-Wicklmayr, Markus Flaßkamp, Kathrin |
| contents | In multi-objective optimization, the set of optimal trade-offs -- the Pareto front -- often contains regions that are extremely steep or flat. The Pareto optimal points in these regions are typically of limited interest for decision-making, as the marginal rate of substitution is extreme: a marginal improvement in one objective necessitates a significant deterioration in at least one other objective. These unfavorable trade-offs frequently occur near the individual minima, where single objectives attain their minimum values without considering the remaining criteria.
To address this, we propose the concept of \emph{non-extreme individual minima} that relies on the notion of $L$-practical proper efficiency. These points can serve as a less sensitive replacement for \emph{standard} individual minima in subsequent related methods. Specifically, they allow for a more practical restriction of the Pareto front sampling within a refined utopia-nadir hyperbox, provide a meaningful basis for image space normalization, and can enhance decision-making techniques, such as knee-point methods, by focusing on regions with acceptable trade-offs.
We provide a computationally efficient algorithm to determine these non-extreme individual minima by solving at most $2n_J$ standard weighted-sum scalarizations, where $n_J$ is the number of objectives. To ensure robustness across varying objective scales, the method incorporates an integrated image space normalization strategy. Numerical examples, specifically a convex academic case and a non-convex real-world application, demonstrate that the method successfully excludes practically irrelevant regions in the image space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21883 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Extreme Individual Minima for Improved Pareto Front Sampling Efficiency and Decision-Making Herrmann-Wicklmayr, Markus Flaßkamp, Kathrin Optimization and Control In multi-objective optimization, the set of optimal trade-offs -- the Pareto front -- often contains regions that are extremely steep or flat. The Pareto optimal points in these regions are typically of limited interest for decision-making, as the marginal rate of substitution is extreme: a marginal improvement in one objective necessitates a significant deterioration in at least one other objective. These unfavorable trade-offs frequently occur near the individual minima, where single objectives attain their minimum values without considering the remaining criteria. To address this, we propose the concept of \emph{non-extreme individual minima} that relies on the notion of $L$-practical proper efficiency. These points can serve as a less sensitive replacement for \emph{standard} individual minima in subsequent related methods. Specifically, they allow for a more practical restriction of the Pareto front sampling within a refined utopia-nadir hyperbox, provide a meaningful basis for image space normalization, and can enhance decision-making techniques, such as knee-point methods, by focusing on regions with acceptable trade-offs. We provide a computationally efficient algorithm to determine these non-extreme individual minima by solving at most $2n_J$ standard weighted-sum scalarizations, where $n_J$ is the number of objectives. To ensure robustness across varying objective scales, the method incorporates an integrated image space normalization strategy. Numerical examples, specifically a convex academic case and a non-convex real-world application, demonstrate that the method successfully excludes practically irrelevant regions in the image space. |
| title | Non-Extreme Individual Minima for Improved Pareto Front Sampling Efficiency and Decision-Making |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2602.21883 |