TY  - JOUR
A1  - Beck, Yasmine
A1  - Ljubić, Ivana
A1  - Schmidt, Martin
T1  - Exact methods for discrete Γ-robust interdiction problems with an application to the bilevel knapsack problem
T2  - Mathematical Programming Computation
N2  - 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 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 Γ-robust follower and we derive problem-tailored cuts, which extend existing techniques that have been proposed for the deterministic case. For the Γ-robust knapsack interdiction problem, we computationally evaluate and compare the performance of the proposed algorithms for both modeling approaches.
KW  - Bilevel optimization
KW  - Robust optimization
KW  - Knapsack interdiction
KW  - Mixed-integer programming
KW  - Branch-and-Cut
Y1  - 2023
UR  - https://ubt.opus.hbz-nrw.de/frontdoor/index/index/docId/2929
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:385-1-29294
VL  - 2023
IS  - 15 (2023)
PB  - Springer
ER  -