A dynamic reformulation heuristic for Generalized Interdiction Problems

•We propose a generalization of standard interdiction problems.•We describe a single-level (heuristic) mixed-integer linear programming reformulation.•We propose an effective heuristic based on a dynamic improvement of the reformulation.•We compare alternative heuristics on a large testbed of 1200+...

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Bibliographic Details
Published in:European journal of operational research Vol. 267; no. 1; pp. 40 - 51
Main Authors: Fischetti, Matteo, Monaci, Michele, Sinnl, Markus
Format: Journal Article
Language:English
Published: Elsevier B.V 16.05.2018
Elsevier
Subjects:
(O) Combinatorial optimization
Bilevel optimization
Computer Science
Heuristics
Interdiction problems
Mixed-integer programming
Operations Research
Bilevel optimization
(O) Combinatorial optimization
Interdiction problems
Mixed-integer programming
Heuristics
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:•We propose a generalization of standard interdiction problems.•We describe a single-level (heuristic) mixed-integer linear programming reformulation.•We propose an effective heuristic based on a dynamic improvement of the reformulation.•We compare alternative heuristics on a large testbed of 1200+ instances. 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.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2017.11.043