K-Cuts: A Variation of Gomory Mixed Integer Cuts from the LP Tableau

Authors:
Gérard Cornuéjols;Yanjun Li;Dieter Vandenbussche
Affiliations:
-;-;-
Venue:
INFORMS Journal on Computing
Year:
2003

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Abstract

For an integer program, ak-cut is a cutting plane generated by the Gomory mixed integer procedure from a row of the LP tableau after multiplying it by a positive integerk. With this terminology, Gomory mixed integer cuts are just 1-cuts. In this paper, we compare thek-cuts ( k = 2) with Gomory mixed integer cuts. In particular, we prove in the pure case that with exactly 50% probability thek-cuts perform better variable-wise than the Gomory mixed integer cuts. Some computational experiments on knapsack problems are reported to illustrate this property.