Variable-Sized Uncertainty and Inverse Problems in Robust Optimization

Chassein, André and Goerigk, Marc (2016) Variable-Sized Uncertainty and Inverse Problems in Robust Optimization. Working Paper. UNSPECIFIED.

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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.

Item Type:
Monograph (Working Paper)
Subjects:
ID Code:
86067
Deposited By:
Deposited On:
27 Apr 2017 12:28
Refereed?:
No
Published?:
Published
Last Modified:
24 Jan 2020 05:04