IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v166y2009i1p147-16110.1007-s10479-008-0408-0.html
   My bibliography  Save this article

An improved partial enumeration algorithm for integer programming problems

Author

Listed:
  • Mohammad Sabbagh
  • Richard Soland

Abstract

In this paper, we present an improved Partial Enumeration Algorithm for Integer Programming Problems by developing a special algorithm, named PE_SPEEDUP (partial enumeration speedup), to use whatever explicit linear constraints are present to speedup the search for a solution. The method is easy to understand and implement, yet very effective in dealing with many integer programming problems, including knapsack problems, reliability optimization, and spare allocation problems. The algorithm is based on monotonicity properties of the problem functions, and uses function values only; it does not require continuity or differentiability of the problem functions. This allows its use on problems whose functions cannot be expressed in closed algebraic form. The reliability and efficiency of the proposed PE_SPEEDUP algorithm has been demonstrated on some integer optimization problems taken from the literature. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • Mohammad Sabbagh & Richard Soland, 2009. "An improved partial enumeration algorithm for integer programming problems," Annals of Operations Research, Springer, vol. 166(1), pages 147-161, February.
    • Handle: RePEc:spr:annopr:v:166:y:2009:i:1:p:147-161:10.1007/s10479-008-0408-0
    DOI: 10.1007/s10479-008-0408-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-008-0408-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-008-0408-0?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. P. C. Gilmore & R. E. Gomory, 1966. "The Theory and Computation of Knapsack Functions," Operations Research, INFORMS, vol. 14(6), pages 1045-1074, December.
    2. J. T. Linderoth & M. W. P. Savelsbergh, 1999. "A Computational Study of Search Strategies for Mixed Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 173-187, May.
    3. Egon Balas, 1965. "An Additive Algorithm for Solving Linear Programs with Zero-One Variables," Operations Research, INFORMS, vol. 13(4), pages 517-546, August.
    4. E. L. Lawler & M. D. Bell, 1966. "A Method for Solving Discrete Optimization Problems," Operations Research, INFORMS, vol. 14(6), pages 1098-1112, December.
    5. AARDAL, Karen & WEISMANTEL, Robert & WOLSEY, Laurence, 2002. "Non-standard approaches to integer programming," LIDAM Reprints CORE 1568, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Ha, Chunghun & Kuo, Way, 2006. "Reliability redundancy allocation: An improved realization for nonconvex nonlinear programming problems," European Journal of Operational Research, Elsevier, vol. 171(1), pages 24-38, May.
    Full references (including those not matched with items on IDEAS)

    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. Paola Cappanera & Marco Trubian, 2005. "A Local-Search-Based Heuristic for the Demand-Constrained Multidimensional Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 82-98, February.
    2. Yu Yang & Natashia Boland & Martin Savelsbergh, 2021. "Multivariable Branching: A 0-1 Knapsack Problem Case Study," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1354-1367, October.
    3. Bissan Ghaddar & Ignacio Gómez-Casares & Julio González-Díaz & Brais González-Rodríguez & Beatriz Pateiro-López & Sofía Rodríguez-Ballesteros, 2023. "Learning for Spatial Branching: An Algorithm Selection Approach," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1024-1043, September.
    4. Russo, Mauro & Sforza, Antonio & Sterle, Claudio, 2013. "An improvement of the knapsack function based algorithm of Gilmore and Gomory for the unconstrained two-dimensional guillotine cutting problem," International Journal of Production Economics, Elsevier, vol. 145(2), pages 451-462.
    5. Zaretalab, Arash & Sharifi, Mani & Guilani, Pedram Pourkarim & Taghipour, Sharareh & Niaki, Seyed Taghi Akhavan, 2022. "A multi-objective model for optimizing the redundancy allocation, component supplier selection, and reliable activities for multi-state systems," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    6. Hanafi, Said & Freville, Arnaud, 1998. "An efficient tabu search approach for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 659-675, April.
    7. Parada Daza, Victor & Gomes de Alvarenga, Arlindo & de Diego, Jose, 1995. "Exact solutions for constrained two-dimensional cutting problems," European Journal of Operational Research, Elsevier, vol. 84(3), pages 633-644, August.
    8. M Hifi & M Michrafy, 2006. "A reactive local search-based algorithm for the disjunctively constrained knapsack problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(6), pages 718-726, June.
    9. Mazzola, Joseph B. & Neebe, Alan W., 1999. "Lagrangian-relaxation-based solution procedures for a multiproduct capacitated facility location problem with choice of facility type," European Journal of Operational Research, Elsevier, vol. 115(2), pages 285-299, June.
    10. Xian Zhao & Jing Zhang & Xiaoyue Wang, 2019. "Joint optimization of components redundancy, spares inventory and repairmen allocation for a standby series system," Journal of Risk and Reliability, , vol. 233(4), pages 623-638, August.
    11. Sbihi, Abdelkader, 2010. "A cooperative local search-based algorithm for the Multiple-Scenario Max-Min Knapsack Problem," European Journal of Operational Research, Elsevier, vol. 202(2), pages 339-346, April.
    12. Abumoslem Mohammadi & Javad Tayyebi, 2019. "Maximum Capacity Path Interdiction Problem with Fixed Costs," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(04), pages 1-21, August.
    13. Reinaldo Morabito & Vitória Pureza, 2010. "A heuristic approach based on dynamic programming and and/or-graph search for the constrained two-dimensional guillotine cutting problem," Annals of Operations Research, Springer, vol. 179(1), pages 297-315, September.
    14. Becker, Henrique & Buriol, Luciana S., 2019. "An empirical analysis of exact algorithms for the unbounded knapsack problem," European Journal of Operational Research, Elsevier, vol. 277(1), pages 84-99.
    15. Joseph B. Mazzola & Robert H. Schantz, 1997. "Multiple‐facility loading under capacity‐based economies of scope," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(3), pages 229-256, April.
    16. Gomory, Ralph, 2016. "Origin and early evolution of corner polyhedra," European Journal of Operational Research, Elsevier, vol. 253(3), pages 543-556.
    17. M Miman & E Pohl, 2008. "Modelling and analysis of risk and reliability for a contingency logistics supply chain," Journal of Risk and Reliability, , vol. 222(4), pages 477-494, December.
    18. Jakob Puchinger & Günther R. Raidl & Ulrich Pferschy, 2010. "The Multidimensional Knapsack Problem: Structure and Algorithms," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 250-265, May.
    19. Li, Shuai & Chi, Xuefen & Yu, Baozhu, 2022. "An improved particle swarm optimization algorithm for the reliability–redundancy allocation problem with global reliability," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    20. Song, X. & Chu, C.B. & Lewis, R. & Nie, Y.Y. & Thompson, J., 2010. "A worst case analysis of a dynamic programming-based heuristic algorithm for 2D unconstrained guillotine cutting," European Journal of Operational Research, Elsevier, vol. 202(2), pages 368-378, April.

    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:166:y:2009:i:1:p:147-161:10.1007/s10479-008-0408-0. 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.