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Compromise Solutions for Robust Combinatorial Optimization with Variable-Sized Uncertainty

Research output: Contribution to journalJournal article

E-pub ahead of print
<mark>Journal publication date</mark>5/02/2018
<mark>Journal</mark>European Journal of Operational Research
<mark>State</mark>E-pub ahead of print
Early online date5/02/18
<mark>Original language</mark>English

Abstract

In classic robust optimization, it is assumed that a set of possible parameter realizations, the uncertainty set, is modeled in a previous step and part of the input. As recent work has shown, finding the most suitable uncertainty set is in itself already a difficult task. We consider robust
problems where the uncertainty set is not completely defined. Only the shape is known, but not its size. Such a setting is known as variable-sized uncertainty.

In this work we present an approach how to find a single robust solution, that performs well on average over all possible uncertainty set sizes. We demonstrate that this approach can be solved efficiently for min-max robust optimization, but is more involved in the case of min-max regret,
where positive and negative complexity results for the selection problem, the minimum spanning tree problem, and the shortest path problem are provided. We introduce an iterative solution procedure, and evaluate its performance in an experimental comparison.

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, ??, ?, 2018 DOI: 10.1016/j.ejor.2018.01.056