Variable-Sized Uncertainty and Inverse Problems in Robust Optimization
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.
Cite
@article{arxiv.1606.07380,
title = {Variable-Sized Uncertainty and Inverse Problems in Robust Optimization},
author = {André Chassein and Marc Goerigk},
journal= {arXiv preprint arXiv:1606.07380},
year = {2016}
}