Strategic oscillation for the quadratic multiple knapsack problem

  • Carlos García-MartínezEmail author
  • Fred Glover
  • Francisco J. Rodriguez
  • Manuel Lozano
  • Rafael Martí


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.


Strategic oscillation Tabu search Quadratic multiple knapsack problem Empirical study 



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


  1. 1.
    Hiley, A., Julstrom, B.: The quadratic multiple knapsack problem and three heuristic approaches to it. In: Proc. of the Genetic and Evolutionary Computation Conference (GECCO’06), pp. 547–552 (2006) Google Scholar
  2. 2.
    Julstrom, B.A.: Greedy, genetic, and greedy genetic algorithms for the quadratic knapsack problem. In: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation (GECCO’05), pp. 607–614. ACM, New York (2005) CrossRefGoogle Scholar
  3. 3.
    Sundar, S., Singh, A.: A swarm intelligence approach to the quadratic multiple knapsack problem. In: ICONIP. LNCS, vol. 6443, pp. 626–633 (2010) Google Scholar
  4. 4.
    Saraç, T., Sipahioglu, A.: A genetic algorithm for the quadratic multiple knapsack problem. In: BVAI. LNCS, vol. 4729, pp. 490–498 (2007) Google Scholar
  5. 5.
    Singh, A., Baghel, A.: A new grouping genetic algorithm for the quadratic multiple knapsack problem. In: EvoCOP. LNCS, vol. 4446, pp. 210–218 (2007) Google Scholar
  6. 6.
    García-Martínez, C., Rodríguez-Díaz, F.J., Lozano, M.: A tabu-enhanced iterated greedy for the quadratic multiple knapsack problem. Eur. J. Oper. Res. 232(3), 454–463 (2014) CrossRefGoogle Scholar
  7. 7.
    Glover, F., Laguna, M.: Tabu Search. Kluwer Academic, Dordrecht (1997) CrossRefzbMATHGoogle Scholar
  8. 8.
    Glover, F., Kochenberger, G., Alidaee, B.: Adaptive memory tabu search for binary quadratic programs. Manag. Sci. 44(3), 336–345 (1998) CrossRefzbMATHGoogle Scholar
  9. 9.
    Yagiura, M., Iwasaki, S., Ibaraki, T., Glover, F.: A very large-scale neighborhood search algorithm for the multi-resource generalized assignment problem. Discrete Optim. 1(1), 87–98 (2004) CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Gallego, M., Laguna, M., Martí, R., Duarte, A.: Tabu search with strategic oscillation for the maximally diverse grouping problem. J. Oper. Res. Soc. 64, 724–734 (2013) CrossRefGoogle Scholar
  11. 11.
    Duarte, A., Martí, R., Álvarez, A., Ángel-Bello, F.: Metaheuristics for the linear ordering problem with cumulative costs. Eur. J. Oper. Res. 216, 270–277 (2012) CrossRefGoogle Scholar
  12. 12.
    Glover, F.: Heuristics for integer programming using surrogate constraints. Decis. Sci. 8(1), 156–166 (1977) CrossRefGoogle Scholar
  13. 13.
    Glover, F., Glover, R., McMillan, C.: A heuristic programming approach to the employee scheduling problem and some thoughts on managerial robots. J. Oper. Manag. 4(2), 113–128 (1984) CrossRefGoogle Scholar
  14. 14.
    Glover, F.: Tabu search and adaptive memory programming—advances, applications and challenges. In: Barr, Helgason, Kennington (eds.) Interfaces in Computer Science and Operations Research, pp. 1–75. Kluwer Academic, Dordrecht (1996) Google Scholar
  15. 15.
    Lu, Z., Hao, J.K., Glover, F.: Neighborhood analysis: a case study on curriculum-based course timetabling. J. Heuristics 17(2), 97–119 (2011) CrossRefGoogle Scholar
  16. 16.
    Lozano, M., Glover, F., García-Martínez, C., Rodriguez, F., Martí, R.: Tabu search with strategic oscillation for the quadratic minimum spanning tree. IEE Trans. (2013). doi: 10.1080/0740817X.2013.768785 Google Scholar
  17. 17.
    Garcia, S., Molina, D., Lozano, M., Herrera, F.: A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 special session on real parameter optimization. J. Heuristics 15(6), 617–644 (2009) CrossRefzbMATHGoogle Scholar
  18. 18.
    Zar, J.H.: Biostatistical Analysis. Prentice Hall, New York (1999) Google Scholar
  19. 19.
    Sheskin, D.J.: The Handbook of Parametric and Nonparametric Statistical Procedures. Chapman & Hall/CRC, New York (2003) CrossRefGoogle Scholar
  20. 20.
    Iman, R., Davenport, J.: Approximations of the critical region of the Friedman statistic. In: Commun. Stat., pp. 571–595 (1980) Google Scholar
  21. 21.
    Holm, S.: A simple sequentially rejective multiple test procedure. Scand. J. Stat. 6, 65–70 (1979) zbMATHMathSciNetGoogle Scholar
  22. 22.
    Wilcoxon, F.: Individual comparisons by ranking methods. Biomaterials 1, 80–83 (1945) Google Scholar
  23. 23.
    García-Martínez, C., Lozano, M.: Evaluating a local genetic algorithm as context-independent local search operator for metaheuristics. Soft Comput. 14(10), 1117–1139 (2010) CrossRefGoogle Scholar
  24. 24.
    Molina, D., Lozano, M., García-Martínez, C., Herrera, F.: Memetic algorithms for continuous optimization based on local search chains. Evol. Comput. 18(1), 27–63 (2010) CrossRefGoogle Scholar
  25. 25.
    García-Martínez, C., Lozano, M., Rodriguez, F.J.: Arbitrary function optimization. No free lunch and real-world problems. Soft Comput. 16(12), 2115–2133 (2012) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Carlos García-Martínez
    • 1
    Email author
  • 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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