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

作     者：Schneider, Kerstin Krieg, Helene Nowak, Dimitri Küfer, Karl-Heinz 

作者机构：Fraunhofer Institute for Industrial Mathematics ITWM Kaiserslautern Germany 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Adaptive algorithms 

摘      要：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 *** Codes 90C17 © 2024, CC BY.