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Variable-sized uncertainty and inverse problems in robust optimization

Research output: Contribution to journalJournal article

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Variable-sized uncertainty and inverse problems in robust optimization. / Chassein, André; Goerigk, Marc.

In: European Journal of Operational Research, Vol. 264, No. 1, 01.01.2018, p. 17-28.

Research output: Contribution to journalJournal article

Harvard

Chassein, A & Goerigk, M 2018, 'Variable-sized uncertainty and inverse problems in robust optimization' European Journal of Operational Research, vol 264, no. 1, pp. 17-28. DOI: 10.1016/j.ejor.2017.06.042

APA

Chassein, A., & Goerigk, M. (2018). Variable-sized uncertainty and inverse problems in robust optimization. European Journal of Operational Research, 264(1), 17-28. DOI: 10.1016/j.ejor.2017.06.042

Vancouver

Chassein A, Goerigk M. Variable-sized uncertainty and inverse problems in robust optimization. European Journal of Operational Research. 2018 Jan 1;264(1):17-28. Available from, DOI: 10.1016/j.ejor.2017.06.042

Author

Chassein, André; Goerigk, Marc / Variable-sized uncertainty and inverse problems in robust optimization.

In: European Journal of Operational Research, Vol. 264, No. 1, 01.01.2018, p. 17-28.

Research output: Contribution to journalJournal article

Bibtex

@article{46e12fdc53e541ffaaf72d204b40a5b0,
title = "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.",
keywords = "Robustness and sensitivity analysis, Uncertainty sets, Inverse optimization, Optimization under uncertainty",
author = "André Chassein and Marc Goerigk",
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",
year = "2018",
month = "1",
doi = "10.1016/j.ejor.2017.06.042",
volume = "264",
pages = "17--28",
journal = "European Journal of Operational Research",
issn = "0377-2217",
publisher = "Elsevier",
number = "1",

}

RIS

TY - JOUR

T1 - Variable-sized uncertainty and inverse problems in robust optimization

AU - Chassein,André

AU - Goerigk,Marc

N1 - 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

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Robustness and sensitivity analysis

KW - Uncertainty sets

KW - Inverse optimization

KW - Optimization under uncertainty

U2 - 10.1016/j.ejor.2017.06.042

DO - 10.1016/j.ejor.2017.06.042

M3 - Journal article

VL - 264

SP - 17

EP - 28

JO - European Journal of Operational Research

T2 - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 1

ER -