Robust combinatorial optimization problems under budgeted interdiction uncertainty

Marc Goerigk and Mohammad Khosravi ()
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Marc Goerigk: University of Passau
Mohammad Khosravi: University of Passau

OR Spectrum: Quantitative Approaches in Management, 2025, vol. 47, issue 1, No 8, 255-285

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.

Keywords: Robust optimization; Combinatorial optimization; Budgeted uncertainty; Knapsack uncertainty (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00291-024-00772-0

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