Reformulation versus cutting-planes for robust optimization
Name
10287_2015_236_ReferencePDF.pdf
Size
257.15 KB
Format
Adobe PDF
Checksum (MD5)
2048603ee12873ec6beddf7a68ed8646
Author(s)
Dunning, Iain Robert
Lubin, Miles C
Bertsimas, Dimitris J
Date Issued
July 2015
Journal
Computational Management Science
Publisher
Springer Berlin Heidelberg
Citation
Bertsimas, Dimitris, Iain Dunning, and Miles Lubin. “Reformulation Versus Cutting-Planes for Robust Optimization.” Comput Manag Sci 13, no. 2 (July 21, 2015): 195–217.
Version
Author's final manuscript
Abstract
Robust optimization (RO) is a tractable method to address uncertainty in optimization problems where uncertain parameters are modeled as belonging to uncertainty sets that are commonly polyhedral or ellipsoidal. The two most frequently described methods in the literature for solving RO problems are reformulation to a deterministic optimization problem or an iterative cutting-plane method. There has been limited comparison of the two methods in the literature, and there is no guidance for when one method should be selected over the other. In this paper we perform a comprehensive computational study on a variety of problem instances for both robust linear optimization (RLO) and robust mixed-integer optimization (RMIO) problems using both methods and both polyhedral and ellipsoidal uncertainty sets. We consider multiple variants of the methods and characterize the various implementation decisions that must be made. We measure performance with multiple metrics and use statistical techniques to quantify certainty in the results. We find for polyhedral uncertainty sets that neither method dominates the other, in contrast to previous results in the literature. For ellipsoidal uncertainty sets we find that the reformulation is better for RLO problems, but there is no dominant method for RMIO problems. Given that there is no clearly dominant method, we describe a hybrid method that solves, in parallel, an instance with both the reformulation method and the cutting-plane method. We find that this hybrid approach can reduce runtimes to 50–75 % of the runtime for any one method and suggest ways that this result can be achieved and further improved on.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10287-015-0236-z
