Abstract
Cutting planes (cuts) are very popular in the OR community, where they are used to strengthen the Linear Programming (LP) relaxation of Mixed-Integer Programs (MIPs) in the hope of improving the performance of an exact LP-based solver. In particular, an intense research effort has been devoted to the study of families of general cuts, whose validity does not require the presence of a specific MIP structure—as opposed to problem-specific cuts such as, e.g., subtour elimination or comb inequalities for the traveling salesman problem.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
- Travel Salesman Problem
- Linear Programming Solver
- Operation Research Letter
- Intense Research Effort
- Mixed Integer Problem
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Gomory, R.E.: An algorithm for the mixed integer problem. Technical Report RM-2597, The RAND Cooperation (1960)
Cornuéjols, G.: Revival of the Gomory cuts in the 1990’s. Annals of Operations Research 149(1), 63–66 (2006)
Balas, E., Ceria, S., Cornuéjols, G., Natraj, N.: Gomory cuts revisited. Operations Research Letters 19, 1–9 (1996)
Zanette, A., Fischetti, M., Balas, E.: Lexicography and degeneracy: can a pure cutting plane algorithm work? Mathematical Programming (2009), doi:10.1007/s10107-009-0300-y
Balas, E., Fischetti, M., Zanette, A.: On the enumerative nature of Gomory’s dual cutting plane method. Mathematical Programming B (to appear, 2010)
Fischetti, M., Salvagnin, D.: A relax-and-cut framework for Gomory’s mixed-integer cuts. In: CPAIOR 2010 Proceedings (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fischetti, M. (2010). Towards a MIP-Cut Metascheme. In: Lodi, A., Milano, M., Toth, P. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2010. Lecture Notes in Computer Science, vol 6140. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13520-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-13520-0_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13519-4
Online ISBN: 978-3-642-13520-0
eBook Packages: Computer ScienceComputer Science (R0)