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

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  • 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.

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  • 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
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    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. George B. Dantzig, 1957. "Discrete-Variable Extremum Problems," Operations Research, INFORMS, vol. 5(2), pages 266-288, April.
    6. 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.
    7. 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).
    8. 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.
    9. 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.
    10. David Pisinger, 1997. "A Minimal Algorithm for the 0-1 Knapsack Problem," Operations Research, INFORMS, vol. 45(5), pages 758-767, October.
    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.
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    Cited by:

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    4. 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.

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