An Adaptive Three-Stage Algorithm For Solving Adjustable Min-Max-Regret Problems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866909408072564736 |
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| author | Schneider, Kerstin Krieg, Helene Nowak, Dimitri Küfer, Karl-Heinz |
| author_facet | Schneider, Kerstin Krieg, Helene Nowak, Dimitri Küfer, Karl-Heinz |
| contents | This work uniquely combines an affine linear decision rule known from adjustable robustness with min-max-regret robustness. By doing so, the advantages of both concepts can be obtained with an adjustable solution that is not over-conservative. This combination results in a bilevel optimization problem. For solving this problem, a three-stage algorithm which uses adaptive discretization of the uncertainty set via two criteria is presented and its convergence is proven. The algorithm is applicable for an example of optimizing a robust pump operation plan for a drinking water supply system facing uncertain demand. The algorithm shows a notable ability to scale, presenting an opportunity to solve larger instances that might challenge existing optimization approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19174 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Adaptive Three-Stage Algorithm For Solving Adjustable Min-Max-Regret Problems Schneider, Kerstin Krieg, Helene Nowak, Dimitri Küfer, Karl-Heinz Optimization and Control 90C17 This work uniquely combines an affine linear decision rule known from adjustable robustness with min-max-regret robustness. By doing so, the advantages of both concepts can be obtained with an adjustable solution that is not over-conservative. This combination results in a bilevel optimization problem. For solving this problem, a three-stage algorithm which uses adaptive discretization of the uncertainty set via two criteria is presented and its convergence is proven. The algorithm is applicable for an example of optimizing a robust pump operation plan for a drinking water supply system facing uncertain demand. The algorithm shows a notable ability to scale, presenting an opportunity to solve larger instances that might challenge existing optimization approaches. |
| title | An Adaptive Three-Stage Algorithm For Solving Adjustable Min-Max-Regret Problems |
| topic | Optimization and Control 90C17 |
| url | https://arxiv.org/abs/2411.19174 |