Abstract
In this paper, we show how to generate Gomory cuts using more than one row of the tableau at a time. We generate a strong cutting plane in this family by solving a sequence of single Diophantine equations. We report computational experience on several instances of pure 0–1 programs.
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Balas, E., Ceria, S. and Cornuéjols, G. (1993), A lift-and-project cutting plane algorithm for mixed 0–1 programs, Mathematical Programming, 58, 295–324.
Balas, E., Ceria, S. and Cornuéjols, G. (1994), Mixed 0–1 Programming by lift-and-project in a branch-and-cut framework, Management Science Research Report MSRR-603, GSIA, Carnegie Mellon University, Pittsburgh, PA., to appear in Management Science.
Balas, E., Ceria, S., Cornuéjols, G. and Natraj, N.R. (1994), Gomory cuts revisited, Management Science Research Report, GSIA, Carnegie Mellon University, Pittsburgh, PA.
Bixby, R.E., Boyd, E.A., and Indovina, R.R. (1992), MIPLIB: A test set of mixed integer programming problems, SIAM News 16.
Ceria, S. (1993), Lift-and-Project Methods for Mixed 0–1 Programs, Ph.D. Dissertation, GSIA, Carnegie Mellon University, Pittsburgh, PA.
Chou, T.J. (1979), Algorithms for the Solution of Systems of Linear Diophantine Equations, Ph.D. Dissertation, Department of Computer Sciences, University of Wisconsin-Madison.
Dickson, L.E. (1952), Theory of Numbers, Chelsea Publishing Company, N.Y.
Garfinkel, R.S. and Nemhauser, G.L. (1972), Integer Programming, John Wiley & Sons.
Gomory, R.E. (1963), An Algorithm for Integer Solutions to Linear Programs, in Recent Advances in Mathematical Programming, Graves, R.L. and Wolfe, P. eds., 269–302. (Originally appeared as Princeton-IBM Math. Res. Project Tech. Rep. No. 1, 1958.)
Jeroslow, R.G. (1974), The Principles of Cutting Plane Theory, Parts I & II Management Science Research Reports MSRR-332 & MSRR-333, GSIA, Carnegie Mellon University, Pittsburgh, PA.
Nemhauser, G.L. and Wolsey, L.A. (1988), Integer Programming, Wiley, N.Y.
Rosser, J.B. (1941), A Note on the Linear Diophantine Equation, American Mathematical Monthly, 48, 662–666.
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© 1995 Springer-Verlag Berlin Heidelberg
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Ceria, S., Cornuéjols, G., Dawande, M. (1995). Combining and strengthening Gomory cuts. In: Balas, E., Clausen, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1995. Lecture Notes in Computer Science, vol 920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59408-6_71
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DOI: https://doi.org/10.1007/3-540-59408-6_71
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