Solving the Quadratic Assignment Problem with Cooperative Parallel Extremal Optimization

  • Danny Munera
  • Daniel Diaz
  • Salvador AbreuEmail author
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9595)


Several real-life applications can be stated in terms of the Quadratic Assignment Problem. Finding an optimal assignment is computationally very difficult, for many useful instances. We address this problem using a local search technique, based on Extremal Optimization and present experimental evidence that this approach is competitive. Moreover, cooperative parallel versions of our solver improve performance so much that large and hard instances can be solved quickly.


QAP Extremal optimization Heuristics Parallelism Cooperation 



The authors wish to acknowledge Stefan Boettcher (Emory University) for his explanations about the Extremal Optimization method. The experimentation used the cluster of the University of Évora, which was partly funded by grants ALENT-07-0262-FEDER-001872 and ALENT-07-0262-FEDER-001876.


  1. 1.
    Koopmans, T.C., Beckmann, M.: Assignment problems and the location of economic activities. Econometrica 25(1), 53–76 (1957)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Commander, C.W.: A survey of the quadratic assignment problem, with applications. Morehead Electron. J. Appl. Math. 4, 1–15 (2005). MATH-2005-01Google Scholar
  3. 3.
    Bhati, R.K., Rasool, A.: Quadratic assignment problem and its relevance to the real world: a survey. Int. J. Comput. Appl. 96(9), 42–47 (2014)Google Scholar
  4. 4.
    Sahni, S., Gonzalez, T.: P-complete approximation problems. J. ACM 23(3), 555–565 (1976)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Boettcher, S., Percus, A.: Nature’s way of optimizing. Artif. Intell. 119(1–2), 275–286 (2000)zbMATHCrossRefGoogle Scholar
  6. 6.
    Randall, M., Lewis, A.: Intensification strategies for extremal optimisation. In: Deb, K., et al. (eds.) SEAL 2010. LNCS, vol. 6457, pp. 115–124. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Munera, D., Diaz, D., Abreu, S., Codognet, P.: A parametric framework for cooperative parallel local search. In: Blum, C., Ochoa, G. (eds.) EvoCOP 2014. LNCS, vol. 8600, pp. 13–24. Springer, Heidelberg (2014)Google Scholar
  8. 8.
    Charles, P., Grothoff, C., Saraswat, V., Donawa, C., Kielstra, A., Ebcioglu, K., Von Praun, C., Sarkar, V.: X10: an object-oriented approach to non-uniform cluster computing. In: SIGPLAN Conference on Object-oriented Programming, Systems, Languages, and Applications, pp. 519–538. ACM, San Diego (2005)Google Scholar
  9. 9.
    Saraswat, V., Tardieu, O., Grove, D., Cunningham, D., Takeuchi, M., Herta, B.:A Brief Introduction to X10 (for the High Performance Programmer). Technical report (2012)Google Scholar
  10. 10.
    Burkard, R.E.: Quadratic assignment problems. In: Pardalos, P.M., Du, D.Z., Graham, R.L. (eds.) Handbook of Combinatorial Optimization, 2nd edn, pp. 2741–2814. Springer, New York (2013)CrossRefGoogle Scholar
  11. 11.
    Loiola, E.M., de Abreu, N.M.M., Netto, P.O.B., Hahn, P., Querido, T.M.: A survey for the quadratic assignment problem. Eur. J. Oper. Res. 176(2), 657–690 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Zaied, A.N.H., Shawky, LAE-f: A survey of quadratic assignment problems. Int. J. Comput. Appl. 101(6), 28–36 (2014)Google Scholar
  13. 13.
    Said, G., Mahmoud, A.M., El-Horbaty, E.S.M.: A comparative study of meta-heuristic algorithms for solving quadratic assignment problem. Int. J. Adv. Comput. Sci. Appl. (IJACSA) 5(1), 1–6 (2014)Google Scholar
  14. 14.
    Boettcher, S., Percus, A.G.: Extremal optimization: an evolutionary local-search algorithm. In: Bhargava, H.K., Ye, N. (eds.) Computational Modeling and Problem Solving in the Networked World, vol. 21, pp. 61–77. Springer, US (2003)CrossRefGoogle Scholar
  15. 15.
    Boettcher, S.: Extremal optimization. In: Hartmann, A.K., Rieger, H. (eds.) New Optimization Algorithms to Physics, pp. 227–251. Wiley-VCH Verlag, Berlin (2004)Google Scholar
  16. 16.
    Bak, P., Tang, C., Wiesenfeld, K.: Self-organized crtiticality: an explenation of 1/f noise. Phys. Rev. Lett. 59(4), 381–384 (1987)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Bak, P.: How Nature Works: The Science of Self-organized Criticality, 1st edn. Copernicus (Springer), New York (1996)zbMATHCrossRefGoogle Scholar
  18. 18.
    Bak, P., Sneppen, K.: Punctuated equilibrium and criticality in a simple model of evolution. Phys. Rev. Lett. 71(24), 4083–4086 (1993)CrossRefGoogle Scholar
  19. 19.
    Boettcher, S., Percus, A.G.: Optimization with extremal dynamics. Phys. Rev. Lett. 86(23), 5211–5214 (2001)zbMATHCrossRefGoogle Scholar
  20. 20.
    De Sousa, F.L., Ramos, F.M.: Function optimization using extremal dynamics. In: International Conference on Inverse Problems in Engineering Rio de Janeiro, Brazil (2002)Google Scholar
  21. 21.
    De Sousa, F.L., Vlassov, V., Ramos, F.M.: Generalized extremal optimization for solving complex optimal design problems. In: International Conference on Genetic and Evolutionary Computation, pp. 375–376 (2003)Google Scholar
  22. 22.
    Zhou, T., Bai, W.J., Cheng, L.J., Wang, B.H.: Continuous extremal optimization for Lennard-Jones clusters. Phys. Rev. E 72(1), 016702 (2005)CrossRefGoogle Scholar
  23. 23.
    Alba, E.: Parallel Metaheuristics: A New Class of Algorithms. Wiley-Interscience, New York (2005)zbMATHCrossRefGoogle Scholar
  24. 24.
    Alba, E., Luque, G., Nesmachnow, S.: Parallel metaheuristics: recent advances and new trends. Int. Trans. Oper. Res. 20(1), 1–48 (2013)zbMATHCrossRefGoogle Scholar
  25. 25.
    Diaz, D., Abreu, S., Codognet, P.: Parallel constraint-based local search on the Cell/BE multicore architecture. In: Essaaidi, M., Malgeri, M., Badica, C. (eds.) Intelligent Distributed Computing IV. SCI, vol. 315, pp. 265–274. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  26. 26.
    Verhoeven, M., Aarts, E.: Parallel local search. J. heuristics 1(1), 43–65 (1995)zbMATHCrossRefGoogle Scholar
  27. 27.
    Caniou, Y., Codognet, P., Richoux, F., Diaz, D., Abreu, S.: Large-scale parallelism for constraint-based local search: the costas array case study. Constraints 20(1), 1–27 (2014)zbMATHGoogle Scholar
  28. 28.
    Toulouse, M., Crainic, T., Sansó, B.: Systemic behavior of cooperative search algorithms. Parallel Comput. 30, 57–79 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    Munera, D., Diaz, D., Abreu, S., Codognet, P.: Flexible cooperation in parallel local search. In: Symposium on Applied Computing (SAC), pp. 1360–1361. ACM Press, New York (2014)Google Scholar
  30. 30.
    Minton, S., Philips, A., Johnston, M.D., Laird, P.: Minimizing conflicts: a heuristic repair method for constraint-satisfaction and scheduling problems. J. Artif. Intell. Res. 58, 161–205 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  31. 31.
    Taillard, É.D.: Comparison of iterative searches for the quadratic assignment problem. Location Sci. 3(2), 87–105 (1995)zbMATHCrossRefGoogle Scholar
  32. 32.
    James, T., Rego, C., Glover, F.: A cooperative parallel tabu search algorithm for the quadratic assignment problem. Eur. J. Oper. Res. 195, 810–826 (2009)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.University of Paris 1-Sorbonne/CRIParisFrance
  2. 2.Universidade de Évora/LISPÉvoraPortugal

Personalised recommendations