IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v139y2005i1p289-32010.1007-s10479-005-3452-z.html
   My bibliography  Save this article

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

Author

Listed:
  • 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

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-005-3452-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-005-3452-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Fred Glover, 1975. "Improved Linear Integer Programming Formulations of Nonlinear Integer Problems," Management Science, INFORMS, vol. 22(4), pages 455-460, December.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Robert E. Bixby & Eva K. Lee, 1998. "Solving a Truck Dispatching Scheduling Problem Using Branch-and-Cut," Operations Research, INFORMS, vol. 46(3), pages 355-367, June.
    2. Christopher Hojny & Tristan Gally & Oliver Habeck & Hendrik Lüthen & Frederic Matter & Marc E. Pfetsch & Andreas Schmitt, 2020. "Knapsack polytopes: a survey," Annals of Operations Research, Springer, vol. 292(1), pages 469-517, September.
    3. Wei-Kun Chen & Liang Chen & Mu-Ming Yang & Yu-Hong Dai, 2018. "Generalized coefficient strengthening cuts for mixed integer programming," Journal of Global Optimization, Springer, vol. 70(1), pages 289-306, January.
    4. Olivier Briant & Denis Naddef, 2004. "The Optimal Diversity Management Problem," Operations Research, INFORMS, vol. 52(4), pages 515-526, August.
    5. Ambros Gleixner & Leona Gottwald & Alexander Hoen, 2023. "P a PILO: A Parallel Presolving Library for Integer and Linear Optimization with Multiprecision Support," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1329-1341, November.
    6. Manfred Padberg, 2005. "Classical Cuts for Mixed-Integer Programming and Branch-and-Cut," Annals of Operations Research, Springer, vol. 139(1), pages 321-352, October.
    7. Patrick Gemander & Wei-Kun Chen & Dieter Weninger & Leona Gottwald & Ambros Gleixner & Alexander Martin, 2020. "Two-row and two-column mixed-integer presolve using hashing-based pairing methods," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(3), pages 205-240, October.
    8. Richard Laundy & Michael Perregaard & Gabriel Tavares & Horia Tipi & Alkis Vazacopoulos, 2009. "Solving Hard Mixed-Integer Programming Problems with Xpress-MP: A MIPLIB 2003 Case Study," INFORMS Journal on Computing, INFORMS, vol. 21(2), pages 304-313, May.
    9. Ellis L. Johnson & George L. Nemhauser & Martin W.P. Savelsbergh, 2000. "Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 2-23, February.
    10. Escudero, L. F. & Munoz, S., 2003. "On identifying dominant cliques," European Journal of Operational Research, Elsevier, vol. 149(1), pages 65-76, August.
    11. Zonghao Gu & George L. Nemhauser & Martin W. P. Savelsbergh, 1999. "Lifted Cover Inequalities for 0-1 Integer Programs: Complexity," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 117-123, February.
    12. Astrid S. Kenyon & David P. Morton, 2003. "Stochastic Vehicle Routing with Random Travel Times," Transportation Science, INFORMS, vol. 37(1), pages 69-82, February.
    13. Monique Guignard & Ellis Johnson & Kurt Spielberg, 2005. "Logical Processing for Integer Programming," Annals of Operations Research, Springer, vol. 140(1), pages 263-304, November.
    14. Tobias Achterberg & Robert E. Bixby & Zonghao Gu & Edward Rothberg & Dieter Weninger, 2020. "Presolve Reductions in Mixed Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 473-506, April.
    15. Brian Lunday & Hanif Sherali & Kevin Lunday, 2012. "The coastal seaspace patrol sector design and allocation problem," Computational Management Science, Springer, vol. 9(4), pages 483-514, November.
    16. Alves, Maria Joao & Climaco, Joao, 1999. "Using cutting planes in an interactive reference point approach for multiobjective integer linear programming problems," European Journal of Operational Research, Elsevier, vol. 117(3), pages 565-577, September.
    17. Martin Durbin & Karla Hoffman, 2008. "OR PRACTICE---The Dance of the Thirty-Ton Trucks: Dispatching and Scheduling in a Dynamic Environment," Operations Research, INFORMS, vol. 56(1), pages 3-19, February.
    18. Xiangyong Li & Y. P. Aneja, 2012. "A Branch-and-Cut Approach for the Minimum-Energy Broadcasting Problem in Wireless Networks," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 443-456, August.
    19. Chang, Ching-Ter, 2000. "An efficient linearization approach for mixed-integer problems," European Journal of Operational Research, Elsevier, vol. 123(3), pages 652-659, June.
    20. Warren Adams & Hanif Sherali, 2005. "A Hierarchy of Relaxations Leading to the Convex Hull Representation for General Discrete Optimization Problems," Annals of Operations Research, Springer, vol. 140(1), pages 21-47, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:139:y:2005:i:1:p:289-320:10.1007/s10479-005-3452-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.