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Strategic oscillation for the quadratic multiple knapsack problem

Author

Listed:
  • Carlos García-Martínez
  • Fred Glover
  • Francisco Rodriguez
  • Manuel Lozano
  • Rafael Martí

Abstract

The quadratic multiple knapsack problem (QMKP) consists in assigning a set of objects, which interact through paired profit values, exclusively to different capacity-constrained knapsacks with the aim of maximising total profit. Its many applications include the assignment of workmen to different tasks when their ability to cooperate may affect the results. Strategic oscillation (SO) is a search strategy that operates in relation to a critical boundary associated with important solution features (such as feasibility). Originally proposed in the context of tabu search, it has become widely applied as an efficient memory-based methodology. We apply strategic oscillation to the quadratic multiple knapsack problem, disclosing that SO effectively exploits domain-specific knowledge, and obtains solutions of particularly high quality compared to those obtained by current state-of-the-art algorithms. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Carlos García-Martínez & Fred Glover & Francisco Rodriguez & Manuel Lozano & Rafael Martí, 2014. "Strategic oscillation for the quadratic multiple knapsack problem," Computational Optimization and Applications, Springer, vol. 58(1), pages 161-185, May.
    • Handle: RePEc:spr:coopap:v:58:y:2014:i:1:p:161-185
    DOI: 10.1007/s10589-013-9623-y
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    References listed on IDEAS

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    1. 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.
    2. Fred Glover & Gary A. Kochenberger & Bahram Alidaee, 1998. "Adaptive Memory Tabu Search for Binary Quadratic Programs," Management Science, INFORMS, vol. 44(3), pages 336-345, March.
    3. Duarte, Abraham & Martí, Rafael & Álvarez, Ada & Ángel-Bello, Francisco, 2012. "Metaheuristics for the linear ordering problem with cumulative costs," European Journal of Operational Research, Elsevier, vol. 216(2), pages 270-277.
    4. M Gallego & M Laguna & R Martí & A Duarte, 2013. "Tabu search with strategic oscillation for the maximally diverse grouping problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(5), pages 724-734, May.
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    Cited by:

    1. Yuning Chen & Jin-Kao Hao, 2015. "Iterated responsive threshold search for the quadratic multiple knapsack problem," Annals of Operations Research, Springer, vol. 226(1), pages 101-131, March.
    2. Wei, Zequn & Hao, Jin-Kao & Ren, Jintong & Glover, Fred, 2023. "Responsive strategic oscillation for solving the disjunctively constrained knapsack problem," European Journal of Operational Research, Elsevier, vol. 309(3), pages 993-1009.
    3. Zheng Wang & Wei Xu & Xiangpei Hu & Yong Wang, 2022. "Inventory allocation to robotic mobile-rack and picker-to-part warehouses at minimum order-splitting and replenishment costs," Annals of Operations Research, Springer, vol. 316(1), pages 467-491, September.

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