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A two-phase kernel search variant for the multidimensional multiple-choice knapsack problem

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  • Lamanna, Leonardo
  • Mansini, Renata
  • Zanotti, Roberto

Abstract

The Multidimensional Multiple-choice Knapsack Problem (MMKP) is a complex combinatorial optimization problem for which finding high quality feasible solutions is very challenging. Recently, several heuristic approaches and a few exact algorithms have been proposed for its solution. These methods have been able to provide new best-known values for benchmark instances although many of them still remain unclosed to optimality. In this paper, we provide a new variant of the heuristic framework Kernel Search and apply it to the MMKP. The proposed variant keeps the method’s main idea of solving a sequence of restricted mixed-integer subproblems but innovates by partitioning the solution process into two different phases with complementary goals. The first phase strives for feasibility and collects important information to dynamically adapt subproblems’ dimension and solution time in the second phase that is focused on getting high quality solutions. This makes the global approach more scalable and efficient.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:297:y:2022:i:1:p:53-65
    DOI: 10.1016/j.ejor.2021.05.007
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    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Guastaroba, G. & Savelsbergh, M. & Speranza, M.G., 2017. "Adaptive Kernel Search: A heuristic for solving Mixed Integer linear Programs," European Journal of Operational Research, Elsevier, vol. 263(3), pages 789-804.
    7. Voudouris, Christos & Tsang, Edward, 1999. "Guided local search and its application to the traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 113(2), pages 469-499, March.
    8. Renata Mansini & M. Grazia Speranza, 2012. "CORAL: An Exact Algorithm for the Multidimensional Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 399-415, August.
    9. Enrico Angelelli & Renata Mansini & M. Speranza, 2012. "Kernel Search: a new heuristic framework for portfolio selection," Computational Optimization and Applications, Springer, vol. 51(1), pages 345-361, January.
    10. R Mansini & M G Speranza, 2002. "A multidimensional knapsack model for asset-backed securitization," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(8), pages 822-832, August.
    11. 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.
    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. Caserta, Marco & Voß, Stefan, 2019. "The robust multiple-choice multidimensional knapsack problem," Omega, Elsevier, vol. 86(C), pages 16-27.
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