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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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    1. Escudero, L. F. & Munoz, S., 1998. "On characterizing tighter formulations for 0-1 programs," European Journal of Operational Research, Elsevier, vol. 106(1), pages 172-176, April.
    2. Karla L. Hoffman & Manfred Padberg, 1991. "Improving LP-Representations of Zero-One Linear Programs for Branch-and-Cut," INFORMS Journal on Computing, INFORMS, vol. 3(2), pages 121-134, May.
    3. Ellis L. Johnson & Michael M. Kostreva & Uwe H. Suhl, 1985. "Solving 0-1 Integer Programming Problems Arising from Large Scale Planning Models," Operations Research, INFORMS, vol. 33(4), pages 803-819, August.
    4. L. Escudero & S. Martello & P. Toth, 1998. "On tightening 0-1 programs based on extensions ofpure 0-1 knapsack and subset-sum problems," Annals of Operations Research, Springer, vol. 81(0), pages 379-404, June.
    5. Hanif D. Sherali & Patrick J. Driscoll, 2002. "On Tightening the Relaxations of Miller-Tucker-Zemlin Formulations for Asymmetric Traveling Salesman Problems," Operations Research, INFORMS, vol. 50(4), pages 656-669, August.
    6. Fred Glover, 1975. "Improved Linear Integer Programming Formulations of Nonlinear Integer Problems," Management Science, INFORMS, vol. 22(4), pages 455-460, December.
    7. Dietrich, B. L. & Escudero, L. F., 1992. "On tightening cover induced inequalities," European Journal of Operational Research, Elsevier, vol. 60(3), pages 335-343, August.
    8. Hanif D. Sherali & Warren P. Adams & Patrick J. Driscoll, 1998. "Exploiting Special Structures in Constructing a Hierarchy of Relaxations for 0-1 Mixed Integer Problems," Operations Research, INFORMS, vol. 46(3), pages 396-405, June.
    9. Harlan Crowder & Ellis L. Johnson & Manfred Padberg, 1983. "Solving Large-Scale Zero-One Linear Programming Problems," Operations Research, INFORMS, vol. 31(5), pages 803-834, October.
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    Cited by:

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