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Variable-sized uncertainty and inverse problems in robust optimization

Research output: Contribution to journalJournal article

<mark>Journal publication date</mark>1/01/2018
<mark>Journal</mark>European Journal of Operational Research
Issue number1
Number of pages12
Pages (from-to)17-28
Early online date21/06/17
<mark>Original language</mark>English


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.

Bibliographic note

This is the author’s version of a work that was accepted for publication in European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Operational Research, 264, 1, 2017 DOI: 10.1016/j.ejor.2017.06.042