Abstract
We present a scheme for generating new valid inequalities for mixed integer programs by taking pair-wise combinations of existing valid inequalities. Our scheme is related to mixed integer rounding and mixing. The scheme is in general sequence-dependent and therefore leads to an exponential number of inequalities. For some important cases, we identify combination sequences that lead to a manageable set of non-dominated inequalities. We illustrate the framework for some deterministic and stochastic integer programs and we present computational results which show the efficiency of adding the new generated inequalities as cuts.
Keywords
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.
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
Atamtürk, A., Nemhauser, G.L., Savelsbergh, M.W.P.: The mixed vertex packing problem. Mathematical Programming 89, 35–53 (2000)
Barany, I., Van Roy, T., Wolsey, L.A.: Strong formulations for multi-item capacitated lot sizing. Management Science 30, 1255–1262 (1984)
Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming. Springer, Heidelberg (1997)
Guan, Y., Ahmed, S., Nemhauser, G.L.: Sequential pairing of mixed integer inequalities. Technical Report No. TLI-04-04, School of Industrial & Systems Engineering, Georgia Institute of Technology (2004)
Guan, Y., Ahmed, S., Nemhauser, G.L., Miller, A.J.: A branch-and-cut algorithm for the stochastic uncapacitated lot-sizing problem. To appear in Mathematical Programming (2005)
Günluk, O., Pochet, Y.: Mixing mixed-integer inequalities. Mathematical Programming 90, 429–457 (2001)
Loparic, M., Marchand, H., Wolsey, L.A.: Dynamic knapsack sets and capacitated lot-sizing. Mathematical Programming 95, 53–69 (2003)
Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. John Wiley & Sons, Chichester (1988)
Nemhauser, G.L., Wolsey, L.A.: A recursive procedure for generating all cuts for 0-1 mixed integer programs. Mathematical Programming 46, 379–390 (1990)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Guan, Y., Ahmed, S., Nemhauser, G.L. (2005). Sequential Pairing of Mixed Integer Inequalities. In: Jünger, M., Kaibel, V. (eds) Integer Programming and Combinatorial Optimization. IPCO 2005. Lecture Notes in Computer Science, vol 3509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496915_3
Download citation
DOI: https://doi.org/10.1007/11496915_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26199-5
Online ISBN: 978-3-540-32102-6
eBook Packages: Computer ScienceComputer Science (R0)