Exact methods for discrete $${\varGamma }$$-robust interdiction problems with an application to the bilevel knapsack problem
Abstract Developing solution methods for discrete bilevel problems is known to be a challenging task—even if all parameters of the problem are exactly known. Many real-world applications of bilevel optimization, however, involve data uncertainty. We study discrete min-max problems with a follower wh...
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| Published in: | Mathematical programming computation 2023-12, Vol.15 (4), p.733-782 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | eng |
| Online Access: | Get full text |
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| Summary: | Abstract Developing solution methods for discrete bilevel problems is known to be a challenging task—even if all parameters of the problem are exactly known. Many real-world applications of bilevel optimization, however, involve data uncertainty. We study discrete min-max problems with a follower who faces uncertainties regarding the parameters of the lower-level problem. Adopting a $$\varGamma $$ Γ -robust approach, we present an extended formulation and a multi-follower formulation to model this type of problem. For both settings, we provide a generic branch-and-cut framework. Specifically, we investigate interdiction problems with a monotone $$\varGamma $$ Γ -robust follower and we derive problem-tailored cuts, which extend existing techniques that have been proposed for the deterministic case. For the $$\varGamma $$ Γ -robust knapsack interdiction problem, we computationally evaluate and compare the performance of the proposed algorithms for both modeling approaches. |
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| ISSN: | 1867-2949 1867-2957 |