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A best first search exact algorithm for the Multiple-choice Multidimensional Knapsack Problem

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  • Abdelkader Sbihi

    (Lancaster University Management School, Optimisation Research Centre)

Abstract

In this paper, we propose an optimal algorithm for the Multiple-choice Multidimensional Knapsack Problem MMKP. The main principle of the approach is twofold: (i) to generate an initial feasible solution as a starting lower bound, and (ii) at different levels of the search tree to determine an intermediate upper bound obtained by solving an auxiliary problem called MMKPaux and perform the strategy of fixing items during the exploration. The approach which we develop is of best-first search strategy. The method was able to optimally solve the MMKP. The performance of the exact algorithm is evaluated on a set of small and medium instances, some of them are extracted from the literature and others are randomly generated. This algorithm is parallelizable and it is one of its important feature.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:13:y:2007:i:4:d:10.1007_s10878-006-9035-3
    DOI: 10.1007/s10878-006-9035-3
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    Cited by:

    1. 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.
    2. Diallo, Claver & Venkatadri, Uday & Khatab, Abdelhakim & Liu, Zhuojun, 2018. "Optimal selective maintenance decisions for large serial k-out-of-n: G systems under imperfect maintenance," Reliability Engineering and System Safety, Elsevier, vol. 175(C), pages 234-245.
    3. Sylvain Barde, 2011. "Ignorance is bliss: rationality, information and equilibrium," SciencePo Working papers Main hal-01069478, HAL.
    4. Sylvain Barde, 2012. "Back to the future: economic rationality and maximum entropy prediction," Studies in Economics 1202, School of Economics, University of Kent.
    5. 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.
    6. Caserta, Marco & Voß, Stefan, 2019. "The robust multiple-choice multidimensional knapsack problem," Omega, Elsevier, vol. 86(C), pages 16-27.
    7. 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.
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    9. repec:hal:spmain:info:hdl:2441/5l6uh8ogmqildh09h56484hg0 is not listed on IDEAS
    10. Sylvain Barde, 2015. "Back to the Future: Economic Self-Organisation and Maximum Entropy Prediction," Computational Economics, Springer;Society for Computational Economics, vol. 45(2), pages 337-358, February.
    11. repec:hal:wpspec:info:hdl:2441/5l6uh8ogmqildh09h56484hg0 is not listed on IDEAS
    12. A. Khatab & C. Diallo & E.-H. Aghezzaf & U. Venkatadri, 2022. "Optimization of the integrated fleet-level imperfect selective maintenance and repairpersons assignment problem," Journal of Intelligent Manufacturing, Springer, vol. 33(3), pages 703-718, March.
    13. Chen, Yuning & Hao, Jin-Kao, 2014. "A “reduce and solve” approach for the multiple-choice multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 239(2), pages 313-322.
    14. V. Van Peteghem & M. Vanhoucke, 2009. "An Artificial Immune System for the Multi-Mode Resource-Constrained Project Scheduling Problem," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 09/555, Ghent University, Faculty of Economics and Business Administration.
    15. Gao, Chao & Lu, Guanzhou & Yao, Xin & Li, Jinlong, 2017. "An iterative pseudo-gap enumeration approach for the Multidimensional Multiple-choice Knapsack Problem," European Journal of Operational Research, Elsevier, vol. 260(1), pages 1-11.
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    17. 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.

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