A bicriteria approach to robust optimization

Chassein, André and Goerigk, Marc (2016) A bicriteria approach to robust optimization. Computers and Operations Research, 66. pp. 181-189. ISSN 0305-0548

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The classic approach in robust optimization is to optimize the solution with respect to the worst case scenario. This pessimistic approach yields solutions that perform best if the worst scenario happens, but also usually perform bad for an average case scenario. On the other hand, a solution that optimizes the performance of this average case scenario may lack in the worst-case performance guarantee. In practice it is important to find a good compromise between these two solutions. We propose to deal with this problem by considering it from a bicriteria perspective. The Pareto curve of the bicriteria problem visualizes exactly how costly it is to ensure robustness and helps to choose the solution with the best balance between expected and guaranteed performance. In this paper we consider linear programming problems with uncertain cost functions. Building upon a theoretical observation on the structure of Pareto solutions for these problems, we present a column generation approach that requires no direct solution of the computationally expensive worst-case problem. In computational experiments we demonstrate the effectiveness of both the proposed algorithm, and the bicriteria perspective in general.

Item Type:
Journal Article
Journal or Publication Title:
Computers and Operations Research
Additional Information:
This is the author’s version of a work that was accepted for publication in Computers and Operations 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 Computers and Operations Research, 66, 2016 DOI: 10.1016/j.cor.2015.08.007
Uncontrolled Keywords:
?? bicriteria optimizationcolumn generationlinear programmingminimum cost flow problemrobust optimizationgeneral computer sciencemanagement science and operations researchmodelling and simulationcomputer science(all) ??
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Deposited On:
16 Nov 2015 13:10
Last Modified:
16 Jul 2024 09:51