Advanced Search
MyIDEAS: Login

A Heuristic Ceiling Point Algorithm for General Integer Linear Programming

Contents:

Author Info

  • Robert M. Saltzman

    (School of Business, San Francisco State University, San Francisco, California 94132)

  • Frederick S. Hillier

    (Department of Operations Research, Stanford University, Stanford, California 94305)

Registered author(s):

    Abstract

    This paper first examines the role of ceiling points in solving a pure, general integer linear programming problem (P). Several kinds of ceiling points are defined and analyzed and one kind called "feasible 1-ceiling points" proves to be of special interest. We demonstrate that all optimal solutions for a problem (P) whose feasible region is nonempty and bounded are feasible 1-ceiling points. Consequently, such a problem may be solved by enumerating just its feasible 1-ceiling points. The paper then describes an algorithm called the Heuristic Ceiling Point Algorithm (HCPA) which approximately solves (P) by searching only for feasible 1-ceiling points relatively near the optimal solution for the LP-relaxation; such solutions are apt to have a high (possibly even optimal) objective function value. The results of applying the HCPA to 48 test problems taken from the literature indicate that this approach usually yields a very good solution with a moderate amount of computational effort.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://dx.doi.org/10.1287/mnsc.38.2.263
    Download Restriction: no

    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 38 (1992)
    Issue (Month): 2 (February)
    Pages: 263-283

    as in new window
    Handle: RePEc:inm:ormnsc:v:38:y:1992:i:2:p:263-283

    Contact details of provider:
    Postal: 7240 Parkway Drive, Suite 300, Hanover, MD 21076 USA
    Phone: +1-443-757-3500
    Fax: 443-757-3515
    Email:
    Web page: http://www.informs.org/
    More information through EDIRC

    Related research

    Keywords: integer linear programming; general integer variables; heuristic algorithm; ceiling points; linear programming relaxation; enumeration algorithms;

    References

    No references listed on IDEAS
    You can help add them by filling out this form.

    Citations

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

    Cited by:
    1. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2013. "A new class of functions for measuring solution integrality in the Feasibility Pump approach: Complete Results," DIAG Technical Reports 2013-05, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    2. Joseph, A. & Gass, S. I., 2002. "A framework for constructing general integer problems with well-determined duality gaps," European Journal of Operational Research, Elsevier, vol. 136(1), pages 81-94, January.
    3. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2011. "A new class of functions for measuring solution integrality in the Feasibility Pump approach," DIS Technical Reports 2011-08, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    4. Joseph, Anito & Gass, Saul I. & Bryson, Noel, 1998. "An objective hyperplane search procedure for solving the general all-integer linear programming (ILP) problem," European Journal of Operational Research, Elsevier, vol. 104(3), pages 601-614, February.
    5. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2010. "New concave penalty functions for improving the Feasibility Pump," DIS Technical Reports 2010-10, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    6. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2010. "Feasibility Pump-Like Heuristics for Mixed Integer Problems," DIS Technical Reports 2010-15, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:38:y:1992:i:2:p:263-283. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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