Journal
DISCRETE APPLIED MATHEMATICS
Volume 272, Issue -, Pages 75-89Publisher
ELSEVIER
DOI: 10.1016/j.dam.2018.02.015
Keywords
Bilevel MILP; Power edge set; Zero forcing set
Categories
Funding
- French ADEME agency under SO -grid project
- Fondation Mathematique Jacques Hadamard (FMJH) under the Gaspard Monge Program (PGMO) in optimization and operations research
- European Union [316647]
- EDF
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We study a class of bilevel mixed-integer linear programs with the following restrictions: all upper level variables x are binary, the lower level variables y occur in exactly one upper level constraint gamma x + beta y >= c, and the lower level objective function is min (y)beta y. We propose a new cut generation algorithm to solve this problem class, based on two simplifying assumptions. We then propose a row-and-column generation algorithm that works independently of the assumptions. We apply our methods to two problems: one is related to the optimal placement of measurement devices in an electrical network, and the other is the minimum zero forcing set problem, a variant of the dominating set problem. We exhibit computational results of both methods on the application-oriented instances as well as on randomly generated instances. (C) 2018 Elsevier B.V. All rights reserved.
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