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Exact Methods for Discrete Gamma-Robust Min-Max Problems

Yasmine Beck(becky***at***uni-trier.de)
Ivana Ljubić(ljubic***at***essec.edu)
Martin Schmidt(martin.schmidt***at***uni-trier.de)

Abstract: Developing solution methods for mixed-integer 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 due to some kind of bounded rationality. We study mixed-integer min-max problems with a follower who faces uncertainties regarding the parameters of the lower-level problem. Adopting a Gamma-robust approach, we present an extended formulation and a multi-scenario 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 Gamma-robust follower and we derive problem-tailored cuts, which extend existing techniques that have been proposed for the deterministic case. For the Gamma-robust knapsack interdiction problem, we computationally evaluate and compare the performance of the proposed algorithms for both modeling approaches.

Keywords: Bilevel optimization, Robust optimization, Knapsack interdiction, Mixed-integer programming, Branch-and-Cut

Category 1: Integer Programming ((Mixed) Integer Linear Programming )

Category 2: Integer Programming (Cutting Plane Approaches )

Category 3: Robust Optimization

Citation:

Download: [PDF]

Entry Submitted: 11/10/2021
Entry Accepted: 11/10/2021
Entry Last Modified: 11/10/2021

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