IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v17y1969i4p600-637.html
   My bibliography  Save this article

Efficient Heuristic Procedures for Integer Linear Programming with an Interior

Author

Listed:
  • Frederick S. Hillier

    (Stanford University, Stanford, California)

Abstract

This paper presents and evaluates some new heuristic procedures for seeking an approximate solution of pure integer linear programming problems having only inequality constraints. The computation time required by these methods (after obtaining the optimal noninteger solution by the simplex method) has generally been only a small fraction of that used by the simplex method for the problems tested (which have 15 to 300 original variables). Furthermore, the solution obtained by the better procedures consistently has been close to optimal and frequently has actually been optimal. Plans for generalizing these methods also are outlined. A companion paper presents an optimal “bound-and-scan” algorithm that may be used in conjunction with these approximate procedures.

Suggested Citation

  • Frederick S. Hillier, 1969. "Efficient Heuristic Procedures for Integer Linear Programming with an Interior," Operations Research, INFORMS, vol. 17(4), pages 600-637, August.
  • Handle: RePEc:inm:oropre:v:17:y:1969:i:4:p:600-637
    DOI: 10.1287/opre.17.4.600
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.17.4.600
    Download Restriction: no

    File URL: https://libkey.io/10.1287/opre.17.4.600?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
    ---><---

    Citations

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


    Cited by:

    1. Tsubakitani, Shigeru & Evans, James R., 1998. "An empirical study of a new metaheuristic for the traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 104(1), pages 113-128, January.
    2. 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.
    3. Christoph Neumann & Oliver Stein & Nathan Sudermann-Merx, 2019. "A feasible rounding approach for mixed-integer optimization problems," Computational Optimization and Applications, Springer, vol. 72(2), pages 309-337, March.
    4. Sabah Bushaj & İ. Esra Büyüktahtakın, 2024. "A K-means Supported Reinforcement Learning Framework to Multi-dimensional Knapsack," Journal of Global Optimization, Springer, vol. 89(3), pages 655-685, July.
    5. 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.
    6. 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.
    7. Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.
    8. Robert M. Saltzman & Frederick S. Hillier, 1991. "An exact ceiling point algorithm for general integer linear programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(1), pages 53-69, February.

    More about this item

    Statistics

    Access and download statistics

    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:inm:oropre:v:17:y:1969:i:4:p:600-637. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.