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《1993 A lift-and-project cutting plane algorithm for mixed 0–1 programs》.pdf
Mathematical Programming 58 (1993) 295-324 295
North-Holland
A lift-and-project cutting plane algorithm for
mixed 0-1 programs
Egon Balas, Sebasti~in Ceria and G6rard Cornu6jols
Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA, USA
Received 6 November 1991
Revised manuscript received 26 May 1992
We propose a cutting plane algorithm for mixed 0-1 programs based on a family of polyhedra which
strengthen the usual LP relaxation. We show how to generate a facet of a polyhedron in this family
which is most violated by the current fractional point. This cut is found through the solution of a linear
program that has about twice the size of the usual LP relaxation. A lifting step is used to reduce the size
of the LPs needed to generate the cuts. An additional strengthening step suggestedby Balas and Jeroslow
is then applied. We report our computational experience with a preliminary version of the algorithm.
This approach is related to the work of Balas on disjunctive programming, the matrix cone relaxations
of Lov~sz and Schrijver and the hierarchy of relaxations of Sherali and Adams.
Key words: Cutting planes, projection, mixed 0-1 programming, disjunctive programming.
I. Introduction
More than thirty years have elapsed since the emergence of cutting plane algorithms
for mixed integer programming, but branch and b o u n d is still the prevalent way to
handle such problems. In the last 10-15 years there has been considerable progress
in using combinatorial cutting planes for certain classes of pure integer programming
problems, such as the symmetric traveling salesman problem, in c ombina t i o n with
branch and b o u n d (see, for instance [18]). The success of this approach, known as
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