Skip to main content
SpringerLink
Log in

An implementation of the iterated tabu search algorithm for the quadratic assignment problem

  • Regular Article
  • Published:
OR Spectrum Aims and scope Submit manuscript

Abstract

In this paper, we describe an implementation of the iterated tabu search (ITS) algorithm for the quadratic assignment problem (QAP), which is one of the well-known problems in combinatorial optimization. The medium- and large-scale QAPs are not, to this date, practically solvable to optimality, therefore heuristic algorithms are widely used. In the proposed ITS approach, intensification and diversification mechanisms are combined in a proper way. The goal of intensification is to search for good solutions in the neighbourhood of a given solution, while diversification is responsible for escaping from local optima and moving towards new regions of the search space. In particular, the following enhancements were implemented: new formula for fast evaluation of the objective function and efficient data structure; extended intensification mechanisms (including randomized tabu criterion, combination of tabu search and local search, dynamic tabu list maintaining); enhanced diversification strategy using periodic tabu tenure and special mutation procedure. The ITS algorithm is tested on the different instances taken from the QAP library QAPLIB. The results from the experiments demonstrate promising efficiency of the proposed algorithm, especially for the random QAP instances.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ahuja RK, Jha KC, Orlin JB, Sharma D (2007) Very large-scale neighborhood search for the quadratic assignment problem. INFORMS J Comput 19: 646–657

    Article  Google Scholar 

  • Angel E, Zissimopoulos V (2002) On the hardness of the quadratic assignment problem with metaheuristics. J Heurist 8: 399–414

    Article  Google Scholar 

  • Battiti R, Tecchiolli G (1994) The reactive tabu search. ORSA J Comput 6: 126–140

    Article  Google Scholar 

  • Blum C, Roli A (2003) Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Comput Surv 35: 268–308

    Article  Google Scholar 

  • Bölte A, Thonemann UW (1996) Optimizing simulated annealing schedules with genetic programming. Eur J Oper Res 92: 402–416

    Article  Google Scholar 

  • Burkard RE, Çela E, Pardalos PM, Pitsoulis L (1998) The quadratic assignment problem. In: Du DZ, Pardalos PM (eds) Handbook of Combinatorial Optimization, vol 3. Kluwer, Dordrecht, pp 241–337

    Google Scholar 

  • Burkard RE, Karisch S, Rendl F (1997) QAPLIB—a quadratic assignment problem library. J Glob Optim 10:391–403. http://www.seas.upenn.edu/qaplib/

    Google Scholar 

  • Drezner Z (2003) A new genetic algorithm for the quadratic assignment problem. INFORMS J Comput 15: 320–330

    Article  Google Scholar 

  • Drezner Z (2005) The extended concentric tabu for the quadratic assignment problem. Eur J Oper Res 160: 416–422

    Article  Google Scholar 

  • Drezner Z (2008) Extensive experiments with hybrid genetic algorithms for the solution of the quadratic assignment problem. Comput Oper Res 35: 717–736

    Article  Google Scholar 

  • Drezner Z, Hahn PM, Taillard ED (2005) Recent advances for the quadratic assignment problem with special emphasis on instances that are difficult for meta-heuristic methods. Ann Oper Res 139: 65–94

    Article  Google Scholar 

  • Fleurent C, Ferland JA (1994) Genetic hybrids for the quadratic assignment problem. In: Pardalos PM, Wolkowicz H (eds) Quadratic Assignment and Related Problems. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol 16. AMS, Providence, pp 173–188

    Google Scholar 

  • Frieze AM, Yadegar J, El-Horbaty S, Parkinson D (1989) Algorithms for assignment problems on an array processor. Parallel Comput 11: 151–162

    Article  Google Scholar 

  • Gambardella LM, Taillard ED, Dorigo M (1999) Ant colonies for the quadratic assignment problems. J Oper Res Soc 50: 167–176

    Google Scholar 

  • Glover F (1989) Tabu search: part I. ORSA J Comput 1: 190–206

    Article  Google Scholar 

  • Glover F (1990) Tabu search: part II. ORSA J Comput 2: 4–32

    Article  Google Scholar 

  • Glover F, Laguna M (1997) Tabu Search. Kluwer, Dordrecht

    Book  Google Scholar 

  • James T, Rego C, Glover F (2009) A cooperative parallel tabu search algorithm for the quadratic assignment problem. Eur J Oper Res 195: 810–826

    Article  Google Scholar 

  • Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the 4th IEEE international conference on neural networks, Perth, Australia, pp 1942–1948

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

    Article  Google Scholar 

  • Li Y, Pardalos PM, Resende MGC (1994) A greedy randomized adaptive search procedure for the quadratic assignment problem. In: Pardalos PM, Wolkowicz H (eds) Quadratic Assignment and Related Problems. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol 16. AMS, Providence, pp 237–261

    Google Scholar 

  • Loiola EM, de Abreu NMM, Boaventura-Netto PO, Hahn P, Querido T (2007) A survey for the quadratic assignment problem. Eur J Oper Res 176: 657–690

    Article  Google Scholar 

  • Lourenco HR, Martin O, Stützle T (2002) Iterated local search. In: Glover F, Kochenberger G (eds) Handbook of Metaheuristics. Kluwer, Norwell, pp 321–353

    Google Scholar 

  • Martin O, Otto SW (1996) Combining simulated annealing with local search heuristics. Ann Oper Res 63: 57–75

    Article  Google Scholar 

  • Martin O, Otto SW, Felten EW (1991) Large-step Markov chains for the traveling salesman problem. Complex Syst 5: 299–326

    Google Scholar 

  • McLoughlin JF III, Cedeño W (2005) The enhanced evolutionary tabu search and its application to the quadratic assignment problem. In: Beyer H-G, O’Reilly U-M (eds) Proceedings of the genetic and evolutionary computation conference—GECCO 2005. ACM Press, New York, pp 975–982

  • Merz P, Freisleben B (2000) Fitness landscape analysis and memetic algorithms for the quadratic assignment problem. IEEE Trans Evolut Comput 4: 337–352

    Article  Google Scholar 

  • Misevicius A (2004) An improved hybrid genetic algorithm: new results for the quadratic assignment problem. Knowl Based Syst 17: 65–73

    Article  Google Scholar 

  • Misevicius A (2005) A tabu search algorithm for the quadratic assignment problem. Comput Optim Appl 30: 95–111

    Article  Google Scholar 

  • Misevicius A, Ostreika A (2007) Defining tabu tenure for the quadratic assignment problem. Inform Technol Control 36: 341–347

    Google Scholar 

  • Nissen V (1994) Solving the quadratic assignment problem with clues from nature. IEEE Trans Neural Netw 5: 66–72

    Article  Google Scholar 

  • Nolle L (2008) On a control parameter free optimization algorithm. In: Bramer M, Coenen F, Petridis M (eds) Research and development in intelligent systems XXV, Proceedings of AI-2008, the twenty-eighth SGAI international conference on innovative techniques and applications of artificial intelligence. Springer, London, pp 119–130

  • Rechenberg I (1994) Evolutionsstrategie ’94. Frommann-Holzboog, Stuttgart

    Google Scholar 

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

    Article  Google Scholar 

  • Schrimpf G, Schneider J, Stamm-Wilbrandt H, Dueck G (2000) Record breaking optimization results using the ruin and recreate principle. J Comput Phys 159: 139–171

    Article  Google Scholar 

  • Schwefel H-P (1995) Evolution and Optimum Seeking. Wiley, New York

    Google Scholar 

  • Smyth K, Hoos HH, Stützle T (2003) Iterated robust tabu search for MAX-SAT. In: Xiang Y, Chaib-draa B (eds) Advances in artificial intelligence: Proceedings of the 16th conference of the Canadian society for computational studies of intelligence. Lecture notes in artificial intelligence, vol 2671. Springer, Berlin, pp 129–144

  • Stützle T (2006) Iterated local search for the quadratic assignment problem. Eur J Oper Res 174: 1519–1539

    Article  Google Scholar 

  • Taillard ED (1991) Robust taboo search for the QAP. Parallel Comput 17: 443–455

    Article  Google Scholar 

  • Taillard ED (1995) Comparison of iterative searches for the quadratic assignment problem. Locat Sci 3: 87–105

    Article  Google Scholar 

  • Tseng L, Liang S (2005) A hybrid metaheuristic for the quadratic assignment problem. Comput Optim Appl 34: 85–113

    Article  Google Scholar 

  • Voß S (1995) Solving quadratic assignment problems using the reverse elimination method. In: Nash SG, Sofer A (eds) The Impact of Emerging Technologies on Computer Science and Operations Research. Kluwer, Dordrecht, pp 281–296

    Chapter  Google Scholar 

  • Voß S (2000) Heuristics for nonlinear assignment problems. In: Pardalos PM, Pitsoulis L (eds) Nonlinear Assignment Problems. Kluwer, Boston, pp 175–215

    Google Scholar 

  • Xu Y-L, Lim MH, Ong YS, Tang J (2006) A GA-ACO-local search hybrid algorithm for solving quadratic assignment problem. In: Keijzer M et al (eds) Proceedings of the genetic and evolutionary computation conference-GECCO 2006, vol 1. ACM Press, New York, pp 599–605

Download references

Author information

Authors and Affiliations

  1. Department of Multimedia Engineering, Kaunas University of Technology, Studentu st. 50-400a/416a, 51368, Kaunas, Lithuania

    Alfonsas Misevicius

Authors
  1. Alfonsas Misevicius
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alfonsas Misevicius.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Misevicius, A. An implementation of the iterated tabu search algorithm for the quadratic assignment problem. OR Spectrum 34, 665–690 (2012). https://doi.org/10.1007/s00291-011-0274-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00291-011-0274-z

Keywords

Search

Navigation