Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/323262 
Year of Publication: 
2024
Citation: 
[Journal:] OR Spectrum [ISSN:] 1436-6304 [Volume:] 47 [Issue:] 1 [Publisher:] Springer Berlin Heidelberg [Place:] Berlin/Heidelberg [Year:] 2024 [Pages:] 255-285
Publisher: 
Springer Berlin Heidelberg, Berlin/Heidelberg
Abstract: 
Abstract In robust combinatorial optimization, we would like to find a solution that performs well under all realizations of an uncertainty set of possible parameter values. How we model this uncertainty set has a decisive influence on the complexity of the corresponding robust problem. For this reason, budgeted uncertainty sets are often studied, as they enable us to decompose the robust problem into easier subproblems. We propose a variant of discrete budgeted uncertainty for cardinality-based constraints or objectives, where a weight vector is applied to the budget constraint. We show that while the adversarial problem can be solved in linear time, the robust problem becomes NP-hard and not approximable. We discuss different possibilities to model the robust problem and show experimentally that despite the hardness result, some models scale relatively well in the problem size.
Subjects: 
Robust optimization
Combinatorial optimization
Budgeted uncertainty
Knapsack uncertainty
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
Document Version: 
Published Version
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