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Algorithms to separate {0,1/2}- Chvatal-Gomory cuts
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Koster, Arie M. C. A., Zymolka, Adrian and Kutschka, Manuel (2007) Algorithms to separate {0,1/2}- Chvatal-Gomory cuts. In: Arge, L. and Hoffmann, M. and Welzl, E., (eds.) Algorithms - ESA 2007: 15th Annual European Symposium, Eilat, Israel, October 8-10, 2007, Proceedings. Lecture Notes in Computer Science, Volume 4698 . Springer-Verlag, pp. 693-704. ISBN 9783540755197
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Official URL: http://dx.doi.org/10.1007/978-3-540-75520-3_61
Abstract
Chvatal-Gomory cuts are among the most well-known classes of cutting planes for general integer linear programs (ILPs). In case the constraint multipliers are either 0 or 1/2, such cuts are known as {0, 1/2}-cuts. It has been proven by Caprara and Fischetti [7] that separation of {0, 1/2}-cuts is NP-hard.
In this paper, we study ways to separate {0,1/2}-cuts effectively in practice. We 2 propose a range of preprocessing rules to reduce the size of the separation problem. The core of the preprocessing builds a Gaussian elimination-like procedure. TO separate the most violated {0,1/2}-cut, we formulate the (reduced) problem as integer linear program and develop some simple heuristic separation routines.
Computational experiments on benchmark instances show that the combination of preprocessing with exact and/or heuristic separation is a very vital idea to generate strong generic cutting planes for integer linear programs and to reduce the overall computation times of state-of-the-art ILP-solvers.
Item Type: | Book Item | ||||
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Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Series Name: | Lecture Notes in Computer Science | ||||
Journal or Publication Title: | ALGORITHMS - ESA 2007, PROCEEDINGS | ||||
Publisher: | Springer-Verlag | ||||
ISBN: | 9783540755197 | ||||
ISSN: | 0302-9743 | ||||
Book Title: | Algorithms - ESA 2007: 15th Annual European Symposium, Eilat, Israel, October 8-10, 2007, Proceedings | ||||
Editor: | Arge, L. and Hoffmann, M. and Welzl, E. | ||||
Official Date: | 2007 | ||||
Dates: |
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Volume: | Volume 4698 | ||||
Number of Pages: | 12 | ||||
Page Range: | pp. 693-704 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Conference Paper Type: | Paper | ||||
Title of Event: | 15th Annual European Symposium on Algorithms (ESA 2007) | ||||
Type of Event: | Other | ||||
Location of Event: | Eilat, Israel | ||||
Date(s) of Event: | 8-10 Oct 2007 |
Data sourced from Thomson Reuters' Web of Knowledge
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