Abstract
We discuss an open source implementation and preliminary computational testing of three variants of the Balas-Perregaard procedure for generating lift-and-project cuts from the original simplex tableau, two of which are new. Variant 1 is the original procedure of [6] with minor modifications. Variant 2 uses a new procedure for choosing the pivot element: After identifying the set of row candidates for an improving pivot, the pivot element (and column) is chosen by optimizing over the entries of all candidate rows. Finally, Variant 3 replaces the source row with its disjunctive modularization, and after each pivot it again modularizes the resulting source row. We report on computational results with the above three variants and their combinations on 65 MIPLIB.3 instances.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Balas, E.: Disjunctive Programming. Annals of Discrete Mathematics 5, 3–51 (1979)
Balas, E.: Generating deepest mixed integer cuts by disjunctive modularization. Tepper School of Business, Carnegie Mellon University (May 2002)
Balas, E., Ceria, S., Cornuéjols, G.: A lift-and-project cutting plane algorithm for mixed 0-1 programs. Mathematical Programming 58, 295–324 (1993)
Balas, E., Ceria, S., Cornuéjols, G.: Mixed 0-1 programming by lift-and-project in a branch-and-cut framework. Man. Science 112, 1229–1246 (1996)
Balas, E., Ceria, S., Cornuéjols, G., Natraj, N.: Gomory cuts revisited. OR Letters 19, 1–10 (1996)
Balas, E., Perregaard, M.: A precise correspondence between lift-and-project cuts, simple disjunctive cuts, and mixed integer Gomory cuts for 0-1 programming. Math. Program. B 94, 221–245 (2003)
Balas, E., Saxena, A.: Optimizing over the split closure. MSRR# 674, Tepper School of Business, Carnegie Mellon University, To appear in Math. Programming A (2005)
COIN-OR website: http://www.coin-or.org/
Perregaard, M.: A practical implementation of lift-and-project cuts. In: International Symposium on Mathematical Programming, Copenhagen (2003)
Perregaard, M.: Generating Disjunctive Cuts for Mixed Integer Programs. Ph.D. Thesis, Carnegie Mellon University (2003)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Balas, E., Bonami, P. (2007). New Variants of Lift-and-Project Cut Generation from the LP Tableau: Open Source Implementation and Testing. In: Fischetti, M., Williamson, D.P. (eds) Integer Programming and Combinatorial Optimization. IPCO 2007. Lecture Notes in Computer Science, vol 4513. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72792-7_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-72792-7_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72791-0
Online ISBN: 978-3-540-72792-7
eBook Packages: Computer ScienceComputer Science (R0)