Chassein, André and Goerigk, Marc (2018) Variable-sized uncertainty and inverse problems in robust optimization. European Journal of Operational Research, 264 (1). pp. 17-28. ISSN 0377-2217
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Abstract
In robust optimization, the general aim is to find a solution that performs well over a set of possible parameter outcomes, the so-called uncertainty set. In this paper, we assume that the uncertainty size is not fixed, and instead aim at finding a set of robust solutions that covers all possible uncertainty set outcomes. We refer to these problems as robust optimization with variable-sized uncertainty. We discuss how to construct smallest possible sets of min–max robust solutions and give bounds on their size. A special case of this perspective is to analyze for which uncertainty sets a nominal solution ceases to be a robust solution, which amounts to an inverse robust optimization problem. We consider this problem with a min–max regret objective and present mixed-integer linear programming formulations that can be applied to construct suitable uncertainty sets. Results on both variable-sized uncertainty and inverse problems are further supported with experimental data.