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Variable-sized uncertainty and inverse problems in robust optimization

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.

    Item Type: Article
    Journal or Publication Title: European Journal of Operational Research
    Additional Information: 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
    Uncontrolled Keywords: Robustness and sensitivity analysis ; Uncertainty sets ; Inverse optimization ; Optimization under uncertainty
    Subjects:
    Departments: Lancaster University Management School > Management Science
    ID Code: 86841
    Deposited By: ep_importer_pure
    Deposited On: 23 Jun 2017 14:24
    Refereed?: Yes
    Published?: Published
    Last Modified: 21 Sep 2017 02:11
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/86841

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