Strategic oscillation for the quadratic multiple knapsack problem

  • Carlos García-Martínez
  • Fred Glover
  • Francisco J. Rodriguez
  • Manuel Lozano
  • Rafael Martí
Article

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.

Keywords

Strategic oscillation Tabu search Quadratic multiple knapsack problem Empirical study 

Notes

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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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Carlos García-Martínez
    • 1
  • Fred Glover
    • 2
  • Francisco J. Rodriguez
    • 3
  • Manuel Lozano
    • 3
  • Rafael Martí
    • 4
  1. 1.Department of Computing and Numerical AnalysisUniversity of CórdobaCórdobaSpain
  2. 2.OptTek SystemsBoulderUSA
  3. 3.Department of Computer Sciences and Artificial IntelligenceUniversity of GranadaGranadaSpain
  4. 4.Department of Statistics and Operations ResearchUniversity of ValenciaValenciaSpain

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