Mathematical Programming Computation, Volume 5, Issue 2, June 2013

Local cuts for mixed-integer programming

Vašek Chvátal, William Cook, Daniel Espinoza

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.

Full Text: PDF

Imprint and privacy statement

For the imprint and privacy statement we refer to the Imprint of ZIB.
© 2008-2023 by Zuse Institute Berlin (ZIB).