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Stronger Inequalities for 0, 1 Integer Programming Using Knapsack Functions

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  • Ferydoon Kianfar

    (Arya-Mehr University of Technology, Tehran, Iran)

Abstract

In deriving the well known cuts for cutting-plane methods in 0, 1 integer programming, the integer points outside the 0,1 space can limit the parallel movement of the hyperplane of the cut toward the solution set. Furthermore it is unnecessarily restrictive to limit the movement of this hyperplane to parallel translations. This paper removes these two limitations in order to derive stronger cuts and reduce the total number of cuts required. Thus, it describes a method based on a special case of the knapsack function that replaces each cut or original constraint by a new inequality whose hyperplane passes through as many integer points in 0, 1 space as possible.

Suggested Citation

  • Ferydoon Kianfar, 1971. "Stronger Inequalities for 0, 1 Integer Programming Using Knapsack Functions," Operations Research, INFORMS, vol. 19(6), pages 1374-1392, October.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:6:p:1374-1392
    DOI: 10.1287/opre.19.6.1374
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    Cited by:

    1. Arnaud Fréville & SaÏd Hanafi, 2005. "The Multidimensional 0-1 Knapsack Problem—Bounds and Computational Aspects," Annals of Operations Research, Springer, vol. 139(1), pages 195-227, October.

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