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Robust combinatorial optimization with variable budgeted uncertainty

Content Provider	Springer Nature Link
Author	Poss, Michael
Copyright Year	2012
Abstract	We introduce a new model for robust combinatorial optimization where the uncertain parameters belong to the image of multifunctions of the problem variables. In particular, we study the variable budgeted uncertainty, an extension of the budgeted uncertainty introduced by Bertsimas and Sim. Variable budgeted uncertainty can provide the same probabilistic guarantee as the budgeted uncertainty while being less conservative for vectors with few non-zero components. The feasibility set of the resulting optimization problem is in general non-convex so that we propose a mixed-integer programming reformulation for the problem, based on the dualization technique often used in robust linear programming. We show how to extend these results to non-binary variables and to more general multifunctions involving uncertainty set defined by conic constraints that are affine in the problem variables. We present a computational comparison of the budgeted uncertainty and the variable budgeted uncertainty on the robust knapsack problem. The experiments show a reduction of the price of robustness by an average factor of 18 %.
Ending Page	92
Page Count	18
Starting Page	75
File Format	PDF
ISSN	16194500
e-ISSN	16142411
Journal	4OR
Issue Number	1
Volume Number	11
Language	English
Publisher	Springer-Verlag
Publisher Date	2012-11-08
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Robust optimization Operations Research/Decision Theory Industrial and Production Engineering Variable uncertainty Multifunction Combinatorial optimization Optimization Chance constraint Stochastic programming
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Management Science and Operations Research Management Information Systems Computational Theory and Mathematics

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