Solving Quadratic Assignment Problems Using the Reverse Elimination Method

  • Stefan Voß
Part of the Operations Research/Computer Science Interfaces Series book series (ORCS, volume 4)


The quadratic assignment problem (QAP) is among the most commonly encountered combinatorial optimization problems. Recently, various tabu search implementations have been proposed to solve the QAP efficiently. These approaches mainly investigate tabu list management ideas that do not take account of logical interdependencies deriving from the sequence in which solutions are generated. Here we apply different versions of the reverse elimination method (REM), a dynamic strategy that explicitly incorporates logical interdependencies. We also introduce a new type of intensification strategy based on a clustering approach and combine it with some diversification ideas. Computational results are reported for a large number of benchmark problems up to the dimension of 128. Our version of REM improves on some of the best known results and matches them for most of the remaining problems.


Tabu Search Cluster Approach Tabu List Quadratic Assignment Problem Dynamic Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    R. Battiti and G. Tecchiolli, 1992. Parallel biased search for combinato rial optimization:genetic algorithms and tabu search. Microprocessors and Microsystems, 16, 351–367.CrossRefGoogle Scholar
  2. [2]
    R. Battiti and G. Tecchiolli, 1992. The reactive tabu search. Preprint, Department of Mathematics, University of TrentoGoogle Scholar
  3. [3]
    E.C. Buffa, G.C. Armour and T.E. Vollmann, 1962. Allocating facilities with CRAFT. Harvard Business Review, 42, 136–158.Google Scholar
  4. [4]
    R.E. Burkard, S. Karisch and F. Rendl, 1991. QAPLIB—a quadratic as signment problem library. European Journal of Operational Research, 55, 115–119.CrossRefGoogle Scholar
  5. [5]
    J. Chakrapani and J. Skorin-Kapov, 1992. A connectionist approach to the quadratic assignment problem. Computers & Operations Research, 19, 287–295.Google Scholar
  6. [6]
    J. Chakrapani and J. Skorin-Kapov, 1993. Massively parallel tabu search for the quadratic assignment problem. Annals of Operations Research, 41, 327–341.Google Scholar
  7. [7]
    F. Dammeyer, P. Forst and S. Voß, 1991. On the cancellation sequence method of tabu search. ORS A Journal on Computing, 3, 262–265.Google Scholar
  8. [8]
    F. Dammeyer and S. Voß, 1993. Dynamic tabu list management using the reverse elimination method. Annals of Operations Research, 41, 31–46.Google Scholar
  9. [9]
    W. Domschke, P. Forst and S. Voß, 1992. Tabu search techniques for the quadratic semi-assignment problem. In:G. Fandel, T. Gulledge and A. Jones (eds.), New Directions for Operations Research in Manufacturing (Springer, Berlin), pp. 389–405.Google Scholar
  10. [10]
    C.N. Fiechter, A. Rogger and D. de Werra, 1992. Basic ideas of tabu search with an application to traveling salesman and quadratic assign ment. Ricerca Operativa, 62, 5–28.Google Scholar
  11. [11]
    G. Finke, R.E. Burkard and F. Rendl, 1987. Quadratic assignment prob lems. Annals of Discrete Mathematics, 31, 61–82.Google Scholar
  12. [12]
    F. Glover, 1990. Tabu search—part II. ORSA Journal on Computing, 2, 4–32.Google Scholar
  13. [13]
    F. Glover and M. Laguna, 1993. Tabu search. In:C.R. Reeves (ed.), Modern Heuristic Techniques for Combinatorial Problems (Blackwell, Oxford), pp. 70–150.Google Scholar
  14. [14]
    V. Nissen, 1993. A new efficient evolutionary algorithm for the quadratic assignment problem. In:K.-W. Hansmann, A. Bachern, M. Jarke, W.E. Katzenberger and A. Marusev (eds.), Operations Research Proceedings 1992 (Springer, Berlin), pp. 259–267.Google Scholar
  15. [15]
    J. Skorin-Kapov, 1990. Tabu search applied to the quadratic assignment problem. ORSA Journal on Computing, 2, 33–45.Google Scholar
  16. [16]
    E. Taillard, 1991. Robust taboo search for the quadratic assignment prob lem. Parallel Computing, 17, 443–455.Google Scholar
  17. [17]
    K.Y. Tarn, 1992. Genetic algorithms, function optimization, and facility layout design. European Journal of Operational Research, 63, 322–346.Google Scholar
  18. [18]
    S. Voß, 1993. Tabu search:applications and prospects. In:D.-Z. Du and P.M. Pardalos (eds.), Network Optimization Problems:Algorithms, Appli cations and Complexity (World Scientific, Singapore), pp. 333–353.Google Scholar
  19. [19]
    M.R. William and T.L. Ward, 1987. Solving quadratic assignment prob lems by’ simulated annealing’. HE Transactions, 19, 107–119.Google Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Stefan Voß
    • 1
  1. 1.FB 1 / FG Operations ResearchTechnische Hochschule DarmstadtDarmstadtGermany

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