Abstract
The traditional approach towards generating lift-and-project cuts involves solving a cut generating linear program (CGLP) that grows prohibitively large if a multiple-term disjunction is used instead of the classical dichotomy. In this paper we present an alternative approach towards generating lift-and-project cuts that solves the cut generation problem in the original space (i.e. does not introduce any extra variables). We present computational results that show our method to be superior to the classical approach. As soon as the number of terms in the disjunction grows larger than 4, the benefit of not solving the large CGLP directly is clear, and the gap grows larger as more terms are included in the disjunction.
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References
E. Balas, Disjunctive Programming, Annals of Discrete Mathematics, 5 (1979) 3–51.
E. Balas, Disjunctive Programming: Properties of the Convex Hull of Feasible Points, Invited paper in Discrete Applied Mathematics, 89 (1998) 1–44.
E. Balas, S. Ceria, G. Cornuéjols, A Lift-and-Project Cutting Plane Algorithm for Mixed 0-1 Programs, Mathematical Programming, 58 (1993) 295–324.
E. Balas, S. Ceria, G. Cornuéjols, Mixed 0-1 Programming by Lift-and-Project in a Branch-and-Cut Framework, Management Science, 42 (1996) 1229–1246.
E. Balas, M. Perregaard, Lift and Project for Mixed 0-1 Programming: Recent Progress, MSRR No. 627, September 1999, Graduate School of Industrial Administration, Carnegie Mellon University.
E. Balas, M. Perregaard, A Precise Correspondence Between Lift-and-Project Cuts, Simple Disjunctive Cuts, and Mixed Integer Gomory Cuts for 0-1 Programming, MSRR No. 631, August 2000, Graduate School of Industrial Administration, Carnegie Mellon University
S. Ceria, G. Pataki, Solving Integer and Disjunctive Programs by Lift-and-Project, in R.E. Bixby, E.A. Boyd and R.Z. Rios-Mercado (editors), IPCO VI, Lecture Notes in Computer Science 1412, Springer, (1998) 271–283.
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Perregaard, M., Balas, E. (2001). Generating Cuts from Multiple-Term Disjunctions. In: Aardal, K., Gerards, B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2001. Lecture Notes in Computer Science, vol 2081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45535-3_27
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DOI: https://doi.org/10.1007/3-540-45535-3_27
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