Knapsack interdiction

Heuristic Methods for Mixed-Integer, Linear, and Γ-Robust Bilevel Problems

  • Yasmine Beck
  • Ivana Ljubić
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, Robust Optimization Tags , , ,

    Due to their nested structure, bilevel problems are intrinsically hard to solve–even if all variables are continuous and all parameters of the problem are exactly known. In this paper, we study mixed-integer linear bilevel problems with lower-level objective uncertainty, which we address using the notion of Γ-robustness. To tackle the Γ-robust counterpart of the bilevel … Read more

    Exact Methods for Discrete Γ-Robust Interdiction Problems with an Application to the Bilevel Knapsack Problem

  • Yasmine Beck
  • Ivana Ljubić
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Robust Optimization Tags , , , ,

    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 … Read more