A dynamic reformulation heuristic for Generalized Interdiction Problems

Matteo Fischetti, Michele Monaci and Markus Sinnl

European Journal of Operational Research, 2018, vol. 267, issue 1, 40-51

Abstract: We consider a subfamily of mixed-integer linear bilevel problems that we call Generalized Interdiction Problems. This class of problems includes, among others, the widely-studied interdiction problems, i.e., zero-sum Stackelberg games where two players (called the leader and the follower) share a set of items, and the leader can interdict the usage of certain items by the follower. Problems of this type can be modeled as Mixed-Integer Nonlinear Programming problems, whose exact solution can be very hard. In this paper we propose a new heuristic scheme based on a single-level and compact mixed-integer linear programming reformulation of the problem obtained by relaxing the integrality of the follower variables. A distinguished feature of our method is that general-purpose mixed-integer cutting planes for the follower problem are exploited, on the fly, to dynamically improve the reformulation. The resulting heuristic algorithm proved very effective on a large number of test instances, often providing an (almost) optimal solution within very short computing times.

Keywords: (O) Combinatorial optimization; Bilevel optimization; Interdiction problems; Mixed-integer programming; Heuristics (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:267:y:2018:i:1:p:40-51

DOI: 10.1016/j.ejor.2017.11.043

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