IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v21y1975i12p1417-1427.html
   My bibliography  Save this article

A Simplified Algorithm for Obtaining Approximate Solutions to Zero-One Programming Problems

Author

Listed:
  • Yoshiaki Toyoda

    (Aoyama Gahuin University, Tokyo)

Abstract

This paper is intended to present a simple and quick method for obtaining approximate solutions to large scale zero-one programming problems. The method does not use enumeration. Instead, it assigns measures of preferability to zero-one variables that change the values of the variables from zero to one. The method yields very good approximate solutions to zero-one programming problems in dramatically short computation time. Even for problems involving more than a thousand zero-one variables the computation time is of little concern. The method is applicable not only to those problems associated with obtaining the optimal package of variables with the value one but also to a great variety of binary choice ("Yes-No") problems.

Suggested Citation

  • Yoshiaki Toyoda, 1975. "A Simplified Algorithm for Obtaining Approximate Solutions to Zero-One Programming Problems," Management Science, INFORMS, vol. 21(12), pages 1417-1427, August.
    • Handle: RePEc:inm:ormnsc:v:21:y:1975:i:12:p:1417-1427
    DOI: 10.1287/mnsc.21.12.1417
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.21.12.1417
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.21.12.1417?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. Teng, Junn-Yuan & Tzeng, Gwo-Hshiung, 1996. "A multiobjective programming approach for selecting non-independent transportation investment alternatives," Transportation Research Part B: Methodological, Elsevier, vol. 30(4), pages 291-307, August.
    2. Yanhong Feng & Hongmei Wang & Zhaoquan Cai & Mingliang Li & Xi Li, 2023. "Hybrid Learning Moth Search Algorithm for Solving Multidimensional Knapsack Problems," Mathematics, MDPI, vol. 11(8), pages 1-28, April.
    3. Ang, James S.K. & Cao, Chengxuan & Ye, Heng-Qing, 2007. "Model and algorithms for multi-period sea cargo mix problem," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1381-1393, August.
    4. Cao, Chengxuan & Gao, Ziyou & Li, Keping, 2012. "Capacity allocation problem with random demands for the rail container carrier," European Journal of Operational Research, Elsevier, vol. 217(1), pages 214-221.
    5. Roy A. Marsten & Thomas Morin, 1975. "Parametric Integer Programming the Right Hand Side Case," NBER Working Papers 0106, National Bureau of Economic Research, Inc.
    6. Renata Mansini & Roberto Zanotti, 2020. "A Core-Based Exact Algorithm for the Multidimensional Multiple Choice Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1061-1079, October.
    7. M Hifi & M Michrafy & A Sbihi, 2004. "Heuristic algorithms for the multiple-choice multidimensional knapsack problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1323-1332, December.
    8. Hasan Pirkul, 1987. "A heuristic solution procedure for the multiconstraint zero‐one knapsack problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(2), pages 161-172, April.
    9. Mhand Hifi & Slim Sadfi & Abdelkader Sbihi, 2004. "An Exact Algorithm for the Multiple-choice Multidimensional Knapsack Problem," Post-Print halshs-03322716, HAL.
    10. Oliver Bastert & Benjamin Hummel & Sven de Vries, 2010. "A Generalized Wedelin Heuristic for Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 93-107, February.
    11. Yalçın Akçay & Haijun Li & Susan Xu, 2007. "Greedy algorithm for the general multidimensional knapsack problem," Annals of Operations Research, Springer, vol. 150(1), pages 17-29, March.
    12. Edward Y H Lin & Chung-Min Wu, 2004. "The multiple-choice multi-period knapsack problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(2), pages 187-197, February.
    13. Abdelkader Sbihi, 2007. "A best first search exact algorithm for the Multiple-choice Multidimensional Knapsack Problem," Journal of Combinatorial Optimization, Springer, vol. 13(4), pages 337-351, May.
    14. Dimitris Bertsimas & Ramazan Demir, 2002. "An Approximate Dynamic Programming Approach to Multidimensional Knapsack Problems," Management Science, INFORMS, vol. 48(4), pages 550-565, April.
    15. N. Cherfi & M. Hifi, 2010. "A column generation method for the multiple-choice multi-dimensional knapsack problem," Computational Optimization and Applications, Springer, vol. 46(1), pages 51-73, May.
    16. Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.
    17. Raymond R. Hill & Charles H. Reilly, 2000. "The Effects of Coefficient Correlation Structure in Two-Dimensional Knapsack Problems on Solution Procedure Performance," Management Science, INFORMS, vol. 46(2), pages 302-317, February.
    18. Jorge A. Sefair & Oscar Guaje & Andrés L. Medaglia, 2021. "A column-oriented optimization approach for the generation of correlated random vectors," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 777-808, September.
    19. Bhuiyan, Tanveer Hossain & Medal, Hugh R. & Nandi, Apurba K. & Halappanavar, Mahantesh, 2021. "Risk-averse bi-level stochastic network interdiction model for cyber-security risk management," International Journal of Critical Infrastructure Protection, Elsevier, vol. 32(C).
    20. Yalçin Akçay & Susan H. Xu, 2004. "Joint Inventory Replenishment and Component Allocation Optimization in an Assemble-to-Order System," Management Science, INFORMS, vol. 50(1), pages 99-116, January.
    21. G. Edward Fox & Christopher J. Nachtsheim, 1990. "An analysis of six greedy selection rules on a class of zero‐one integer programming models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(2), pages 299-307, April.
    22. 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.
    23. Lamanna, Leonardo & Mansini, Renata & Zanotti, Roberto, 2022. "A two-phase kernel search variant for the multidimensional multiple-choice knapsack problem," European Journal of Operational Research, Elsevier, vol. 297(1), pages 53-65.
    24. Jaeyoung Yang & Yong-Hyuk Kim & Yourim Yoon, 2022. "A Memetic Algorithm with a Novel Repair Heuristic for the Multiple-Choice Multidimensional Knapsack Problem," Mathematics, MDPI, vol. 10(4), pages 1-15, February.
    25. Mhand Hifi & Slim Sadfi & Abdelkader Sbihi, 2004. "An Exact Algorithm for the Multiple-choice Multidimensional Knapsack Problem," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03322716, HAL.

    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:ormnsc:v:21:y:1975:i:12:p:1417-1427. 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.