Robust two-stage combinatorial optimization problems under convex second-stage cost uncertainty

Marc Goerigk (), Adam Kasperski () and Paweł Zieliński ()
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Marc Goerigk: University of Siegen
Adam Kasperski: Wrocław University of Science and Technology
Paweł Zieliński: Wrocław University of Science and Technology

Journal of Combinatorial Optimization, 2022, vol. 43, issue 3, No 1, 497-527

Abstract: Abstract In this paper a class of robust two-stage combinatorial optimization problems is discussed. It is assumed that the uncertain second-stage costs are specified in the form of a convex uncertainty set, in particular polyhedral or ellipsoidal ones. It is shown that the robust two-stage versions of basic network optimization and selection problems are NP-hard, even in a very restrictive cases. Some exact and approximation algorithms for the general problem are constructed. Polynomial and approximation algorithms for the robust two-stage versions of basic problems, such as the selection and shortest path problems, are also provided.

Keywords: Robust optimization; Combinatorial optimization; Two-stage optimization; Convex uncertainty (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-021-00776-4

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