Skip to main content
SpringerLink
Log in

Solving the Quadratic Assignment Problem with Cooperative Parallel Extremal Optimization

  • Conference paper
Evolutionary Computation in Combinatorial Optimization (EvoCOP 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9595))

Included in the following conference series:

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Source code and instances are available from http://cri-hpc1.univ-paris1.fr/qap/.

  2. 2.

    With a probability pAdopt.

References

  1. Koopmans, T.C., Beckmann, M.: Assignment problems and the location of economic activities. Econometrica 25(1), 53–76 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  2. Commander, C.W.: A survey of the quadratic assignment problem, with applications. Morehead Electron. J. Appl. Math. 4, 1–15 (2005). MATH-2005-01

    Google Scholar 

  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. Sahni, S., Gonzalez, T.: P-complete approximation problems. J. ACM 23(3), 555–565 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  5. Boettcher, S., Percus, A.: Nature’s way of optimizing. Artif. Intell. 119(1–2), 275–286 (2000)

    Article  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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. 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. 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)

    Chapter  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. 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)

    Chapter  Google Scholar 

  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. Bak, P., Tang, C., Wiesenfeld, K.: Self-organized crtiticality: an explenation of 1/f noise. Phys. Rev. Lett. 59(4), 381–384 (1987)

    Article  MathSciNet  Google Scholar 

  17. Bak, P.: How Nature Works: The Science of Self-organized Criticality, 1st edn. Copernicus (Springer), New York (1996)

    Book  MATH  Google Scholar 

  18. Bak, P., Sneppen, K.: Punctuated equilibrium and criticality in a simple model of evolution. Phys. Rev. Lett. 71(24), 4083–4086 (1993)

    Article  Google Scholar 

  19. Boettcher, S., Percus, A.G.: Optimization with extremal dynamics. Phys. Rev. Lett. 86(23), 5211–5214 (2001)

    Article  MATH  Google Scholar 

  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. 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. 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)

    Article  Google Scholar 

  23. Alba, E.: Parallel Metaheuristics: A New Class of Algorithms. Wiley-Interscience, New York (2005)

    Book  MATH  Google Scholar 

  24. Alba, E., Luque, G., Nesmachnow, S.: Parallel metaheuristics: recent advances and new trends. Int. Trans. Oper. Res. 20(1), 1–48 (2013)

    Article  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  26. Verhoeven, M., Aarts, E.: Parallel local search. J. heuristics 1(1), 43–65 (1995)

    Article  MATH  Google Scholar 

  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)

    MATH  Google Scholar 

  28. Toulouse, M., Crainic, T., Sansó, B.: Systemic behavior of cooperative search algorithms. Parallel Comput. 30, 57–79 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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)

    Article  MathSciNet  MATH  Google Scholar 

  31. Taillard, É.D.: Comparison of iterative searches for the quadratic assignment problem. Location Sci. 3(2), 87–105 (1995)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

Download references

Acknowledgments

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.

Author information

Authors and Affiliations

  1. University of Paris 1-Sorbonne/CRI, Paris, France

    Danny Munera, Daniel Diaz & Salvador Abreu

  2. Universidade de Évora/LISP, Évora, Portugal

    Salvador Abreu

Authors
  1. Danny Munera
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Diaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Salvador Abreu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Salvador Abreu .

Editor information

Editors and Affiliations

  1. University of Málaga, Málaga, Spain

    Francisco Chicano

  2. Austrian Insttitute of Technology, Vienna, Austria

    Bin Hu

  3. University of Granada, Granada, Spain

    Pablo García-Sánchez

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Munera, D., Diaz, D., Abreu, S. (2016). Solving the Quadratic Assignment Problem with Cooperative Parallel Extremal Optimization. In: Chicano, F., Hu, B., García-Sánchez, P. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2016. Lecture Notes in Computer Science(), vol 9595. Springer, Cham. https://doi.org/10.1007/978-3-319-30698-8_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-30698-8_17

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30697-1

  • Online ISBN: 978-3-319-30698-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation