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Strategic oscillation for the quadratic multiple knapsack problem

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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.

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Notes

  1. They were obtained by adapting those at http://cedric.cnam.fr/~soutif/QKP/ according to the guidelines in [1].

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Acknowledgements

This work was supported by the research projects TIN2009-07516, TIN2012-35632-C02, TIN2012-37930-C02-01, and P08-TIC-4173.

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Authors and Affiliations

  1. Department of Computing and Numerical Analysis, University of Córdoba, Córdoba, 14071, Spain

    Carlos García-Martínez

  2. OptTek Systems, Boulder, CO, USA

    Fred Glover

  3. Department of Computer Sciences and Artificial Intelligence, University of Granada, Granada, 18071, Spain

    Francisco J. Rodriguez & Manuel Lozano

  4. Department of Statistics and Operations Research, University of Valencia, Valencia, Spain

    Rafael Martí

Authors
  1. Carlos García-Martínez
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  2. Fred Glover
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  3. Francisco J. Rodriguez
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  4. Manuel Lozano
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  5. Rafael Martí
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Corresponding author

Correspondence to Carlos García-Martínez.

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García-Martínez, C., Glover, F., Rodriguez, F.J. et al. Strategic oscillation for the quadratic multiple knapsack problem. Comput Optim Appl 58, 161–185 (2014). https://doi.org/10.1007/s10589-013-9623-y

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