An Adaptive Three-Stage Algorithm For Solving Adjustable Min-Max-Regret Problems

Fuente: arXiv
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Main Authors: Schneider, Kerstin, Krieg, Helene, Nowak, Dimitri, Küfer, Karl-Heinz
Format: Preprint
Published: 2024
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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