IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v202y2010i2p339-346.html
   My bibliography  Save this article

A cooperative local search-based algorithm for the Multiple-Scenario Max-Min Knapsack Problem

Author

Listed:
  • Sbihi, Abdelkader

Abstract

The purpose of this article is to present a novel method to approximately solve the Multiple-Scenario Max-Min Knapsack Problem (MSM2KP). This problem models many real world situations, e.g. when for many scenarios noted , the aim is to identify the one offering a better alternative in term of maximizing the worst possible outcome. Herein is presented a cooperative approach based on two local search algorithms: (i) a limited-area local search applied in the elite neighborhood and which accepts the first solution with some deterioration threshold of the current solution, (ii) a wide range local search is applied to perform a sequence of paths exchange to improve the current solution. Results have been analyzed by means state-of-the art methods and via problem instances obtained by a generator code taken from the literature. The tests were executed in compeltely comparable scenarios to those of the literature. The results are promising and the efficiency of the proposed approach is also shown.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:202:y:2010:i:2:p:339-346
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(09)00386-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Luss, Hanan, 1992. "Minimax resource allocation problems: Optimization and parametric analysis," European Journal of Operational Research, Elsevier, vol. 60(1), pages 76-86, July.
    3. Pang, Jong-Shi & Chang-Sung, Yu, 1989. "A min-max resource allocation problem with substitutions," European Journal of Operational Research, Elsevier, vol. 41(2), pages 218-223, July.
    4. P. C. Gilmore & R. E. Gomory, 1966. "The Theory and Computation of Knapsack Functions," Operations Research, INFORMS, vol. 14(6), pages 1045-1074, December.
    5. Yamada, Takeo & Futakawa, Mayumi & Kataoka, Seiji, 1998. "Some exact algorithms for the knapsack sharing problem," European Journal of Operational Research, Elsevier, vol. 106(1), pages 177-183, April.
    6. Hifi, M. & Sadfi, S. & Sbihi, A., 2000. "Efficient Algorithms for the Knapsack Sharing Problem," Papiers d'Economie Mathématique et Applications 2000.122, Université Panthéon-Sorbonne (Paris 1).
    7. Gang Yu, 1996. "On the Max-Min 0-1 Knapsack Problem with Robust Optimization Applications," Operations Research, INFORMS, vol. 44(2), pages 407-415, April.
    8. David Pisinger, 1997. "A Minimal Algorithm for the 0-1 Knapsack Problem," Operations Research, INFORMS, vol. 45(5), pages 758-767, October.
    9. George B. Dantzig, 1957. "Discrete-Variable Extremum Problems," Operations Research, INFORMS, vol. 5(2), pages 266-288, April.
    10. Pisinger, David, 1995. "A minimal algorithm for the multiple-choice knapsack problem," European Journal of Operational Research, Elsevier, vol. 83(2), pages 394-410, June.
    11. Silvano Martello & David Pisinger & Paolo Toth, 1999. "Dynamic Programming and Strong Bounds for the 0-1 Knapsack Problem," Management Science, INFORMS, vol. 45(3), pages 414-424, March.
    12. Martello, Silvano & Pisinger, David & Toth, Paolo, 2000. "New trends in exact algorithms for the 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 123(2), pages 325-332, 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. Fabrice Talla Nobibon & Roel Leus, 2014. "Complexity Results and Exact Algorithms for Robust Knapsack Problems," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 533-552, May.
    2. Schäfer, Luca E. & Dietz, Tobias & Barbati, Maria & Figueira, José Rui & Greco, Salvatore & Ruzika, Stefan, 2021. "The binary knapsack problem with qualitative levels," European Journal of Operational Research, Elsevier, vol. 289(2), pages 508-514.
    3. García-Martínez, C. & Rodriguez, F.J. & Lozano, M., 2014. "Tabu-enhanced iterated greedy algorithm: A case study in the quadratic multiple knapsack problem," European Journal of Operational Research, Elsevier, vol. 232(3), pages 454-463.
    4. Goerigk, Marc & Khosravi, Mohammad, 2023. "Optimal scenario reduction for one- and two-stage robust optimization with discrete uncertainty in the objective," European Journal of Operational Research, Elsevier, vol. 310(2), pages 529-551.

    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. Mhand Hifi & Slim Sadfi & Abdelkader Sbihi, 2004. "An Exact Algorithm for the Multiple-choice Multidimensional Knapsack Problem," Post-Print halshs-03322716, HAL.
    2. 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.
    3. 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.
    4. Wishon, Christopher & Villalobos, J. Rene, 2016. "Robust efficiency measures for linear knapsack problem variants," European Journal of Operational Research, Elsevier, vol. 254(2), pages 398-409.
    5. Mhand Hifi & Hedi Mhalla & Slim Sadfi, 2005. "Sensitivity of the Optimum to Perturbations of the Profit or Weight of an Item in the Binary Knapsack Problem," Journal of Combinatorial Optimization, Springer, vol. 10(3), pages 239-260, November.
    6. 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.
    7. 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.
    8. Toth, Paolo, 2000. "Optimization engineering techniques for the exact solution of NP-hard combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 125(2), pages 222-238, September.
    9. David Pisinger, 2000. "A Minimal Algorithm for the Bounded Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 75-82, February.
    10. Thekra Al-douri & Mhand Hifi & Vassilis Zissimopoulos, 2021. "An iterative algorithm for the Max-Min knapsack problem with multiple scenarios," Operational Research, Springer, vol. 21(2), pages 1355-1392, June.
    11. Furini, Fabio & Ljubić, Ivana & Sinnl, Markus, 2017. "An effective dynamic programming algorithm for the minimum-cost maximal knapsack packing problem," European Journal of Operational Research, Elsevier, vol. 262(2), pages 438-448.
    12. 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.
    13. Ewa M. Bednarczuk & Janusz Miroforidis & Przemysław Pyzel, 2018. "A multi-criteria approach to approximate solution of multiple-choice knapsack problem," Computational Optimization and Applications, Springer, vol. 70(3), pages 889-910, July.
    14. Hanan Luss, 1999. "On Equitable Resource Allocation Problems: A Lexicographic Minimax Approach," Operations Research, INFORMS, vol. 47(3), pages 361-378, June.
    15. Isma Dahmani & Mhand Hifi, 2021. "A modified descent method-based heuristic for binary quadratic knapsack problems with conflict graphs," Annals of Operations Research, Springer, vol. 298(1), pages 125-147, March.
    16. Reilly, Charles H. & Sapkota, Nabin, 2015. "A family of composite discrete bivariate distributions with uniform marginals for simulating realistic and challenging optimization-problem instances," European Journal of Operational Research, Elsevier, vol. 241(3), pages 642-652.
    17. Charles H. Reilly, 2009. "Synthetic Optimization Problem Generation: Show Us the Correlations!," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 458-467, August.
    18. Fujimoto, Masako & Yamada, Takeo, 2006. "An exact algorithm for the knapsack sharing problem with common items," European Journal of Operational Research, Elsevier, vol. 171(2), pages 693-707, June.
    19. B. Golany & N. Goldberg & U. Rothblum, 2015. "Allocating multiple defensive resources in a zero-sum game setting," Annals of Operations Research, Springer, vol. 225(1), pages 91-109, February.
    20. Akinc, Umit, 2006. "Approximate and exact algorithms for the fixed-charge knapsack problem," European Journal of Operational Research, Elsevier, vol. 170(2), pages 363-375, 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:eee:ejores:v:202:y:2010:i:2:p:339-346. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.