Local cuts for mixed-integer programming

  • A general framework for cutting-plane generation was proposed by Applegate et al. in the context of the traveling salesman problem. The process considers the image of a problem space under a linear mapping, chosen so that a relaxation of the mapped problem can be solved efficiently. Optimization in the mapped space can be used to find a separating hyperplane, if one exists, and via substitution this gives a cutting plane in the original space.We extend this procedure to general mixed-integer programming problems, obtaining a range of possibilities for new sources of cutting planes. Some of these possibilities are explored computationally, both in floating-point arithmetic and in rational arithmetic.

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Metadaten
Author:Vašek Chvátal, William Cook, Daniel Espinoza
DOI:https://doi.org/10.1007/s12532-013-0052-9
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2013
Tag:Software; Theoretical Computer Science
Volume:5
Issue:2
Page Number:30
First Page:171
Last Page:200
Mathematical Programming Computation :MPC 2013 - Issue 2
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