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A Conditional Logic Approach for Strengthening Mixed 0-1 Linear Programs

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  • R. Lougee-Heimer
  • W. Adams

Abstract

We study a conditional logic approach for tightening the continuous relaxation of a mixed 0-1 linear program. The procedure first constructs quadratic inequalities by computing pairwise products of constraints, and then surrogates modified such inequalities to produce valid linear restrictions. Strength is achieved by adjusting the coefficients on the quadratic restrictions. The approach is a unifying framework for published coefficient adjustment methods, and generalizes the process of sequential lifting. We give illustrative examples and discuss various extensions, including the use of more complex conditional logic constructs that compute and surrogate polynomial expressions, and the application to general integer programs. Copyright Springer Science + Business Media, Inc. 2005

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  • R. Lougee-Heimer & W. Adams, 2005. "A Conditional Logic Approach for Strengthening Mixed 0-1 Linear Programs," Annals of Operations Research, Springer, vol. 139(1), pages 289-320, October.
    • Handle: RePEc:spr:annopr:v:139:y:2005:i:1:p:289-320:10.1007/s10479-005-3452-z
    DOI: 10.1007/s10479-005-3452-z
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    References listed on IDEAS

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    Cited by:

    1. Monique Guignard & Ellis Johnson & Kurt Spielberg, 2005. "Logical Processing for Integer Programming," Annals of Operations Research, Springer, vol. 140(1), pages 263-304, November.
    2. Richard J. Forrester & Warren P. Adams & Paul T. Hadavas, 2010. "Concise RLT forms of binary programs: A computational study of the quadratic knapsack problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(1), pages 1-12, February.

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