Rights statement: 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, 258, 1, 2017 DOI: 10.1016/j.ejor.2016.10.055
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Minmax regret combinatorial optimization problems with ellipsoidal uncertainty sets
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, 258, 1, 2017 DOI: 10.1016/j.ejor.2016.10.055
PY - 2017/4/1
Y1 - 2017/4/1
N2 - We consider robust counterparts of uncertain combinatorial optimization problems, where the difference to the best possible solution over all scenarios is to be minimized. Such minmax regret problems are typically harder to solve than their nominal, non-robust counterparts. While current literature almost exclusively focuses on simple uncertainty sets that are either finite or hyperboxes, we consider problems with more flexible and realistic ellipsoidal uncertainty sets. We present complexity results for the unconstrained combinatorial optimization problem, the shortest path problem, and the minimum spanning tree problem. To solve such problems, two types of cuts are introduced, and compared in a computational experiment.
AB - We consider robust counterparts of uncertain combinatorial optimization problems, where the difference to the best possible solution over all scenarios is to be minimized. Such minmax regret problems are typically harder to solve than their nominal, non-robust counterparts. While current literature almost exclusively focuses on simple uncertainty sets that are either finite or hyperboxes, we consider problems with more flexible and realistic ellipsoidal uncertainty sets. We present complexity results for the unconstrained combinatorial optimization problem, the shortest path problem, and the minimum spanning tree problem. To solve such problems, two types of cuts are introduced, and compared in a computational experiment.
KW - Robust optimization
KW - Minmax regret
KW - Ellipsoidal uncertainty
KW - Complexity
KW - Scenario relaxation
U2 - 10.1016/j.ejor.2016.10.055
DO - 10.1016/j.ejor.2016.10.055
M3 - Journal article
VL - 258
SP - 58
EP - 69
JO - European Journal of Operational Research
JF - European Journal of Operational Research
SN - 0377-2217
IS - 1
ER -