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A Self-adaptive Nature-Inspired Procedure for Solving the Quadratic Assignment Problem

  • Reza Zamani
  • Mehrdad AmirghasemiEmail author
Chapter
  • 20 Downloads
Part of the Springer Tracts in Nature-Inspired Computing book series (STNIC)

Abstract

The quadratic assignment problem has been traditionally introduced as a mathematical model related to economic activities, modeling many real-world problems from making optimal arrangement of machines in factories to finding the best location of departments within plants. The biological systems consist of self-adaptive mechanisms, and such self-adaptivity can inspire computer scientists to use the same mechanism in their algorithms. In this paper, a self-adaptive search procedure is presented for solving the quadratic assignment problem, exploring the structure of the problem through regular interchanges of facilities made by a linear assignment technique. The relationship between different aspects of the quadratic assignment problem and the proposed self-adaptive mechanism is mainly related to the intelligence needed to change the location of facilities based on the feedback received from the system. In the employed local search procedure, whenever the number of suggested interchanges is high, some facilities are enforced not to participate in swaps. A key point with making such enforcement is that the employed linear assignment uses all previous information and prevents recalculation. By using a simple mathematical concept in linear programming, the length of the cycles in an interchange is adaptively decreased until the cycle consists of only two facilities. The result of computational experiments on the benchmark instances indicates that the procedure performs in the level of current state-of-the-art procedures.

References

  1. 1.
    Ahuja R, Jha K, Orlin J, Sharma D (2007) Very large-scale neighborhood search for the quadratic assignment problem. INFORMS Journal on Computing 19(4):646–657CrossRefMathSciNetzbMATHGoogle Scholar
  2. 2.
    Ahuja R, Orlin J, Tiwari A (2000) A greedy genetic algorithm for the quadratic assignment problem. Computers & Operations Research 27(10):917–934CrossRefMathSciNetzbMATHGoogle Scholar
  3. 3.
    Amirghasemi M, Zamani R (2018) An effective structural iterative refinement technique for solving the quadratic assignment problem. In: Cerulli R, Raiconi A, Voß S (eds) Computational Logistics. Springer International Publishing, Cham, pp 446–460CrossRefGoogle Scholar
  4. 4.
    Amirghasemi, M., Zamani, R.: Developing an effective decomposition-based procedure for solving the quadratic assignment problem. In: Paternina-Arboleda, C., Voß, S. (eds.) Computational logistics. Springer International Publishing, Cham, pp 297–316Google Scholar
  5. 5.
    Arkin E, Hassin R, Sviridenko M (2001) Approximating the maximum quadratic assignment problem. Information Processing Letters 77(1):13–16CrossRefMathSciNetzbMATHGoogle Scholar
  6. 6.
    Baykasoǧlu A (2004) A meta-heuristic algorithm to solve quadratic assignment formulations of cell formation problems without presetting number of cells. Journal of Intelligent Manufacturing 15(6):753–759CrossRefGoogle Scholar
  7. 7.
    Benlic U, Hao JK (2015) Memetic search for the quadratic assignment problem. Expert Systems with Applications 42(1):584–595.  https://doi.org/10.1016/j.eswa.2014.08.011CrossRefGoogle Scholar
  8. 8.
    Burkard RE, Karisch SE, Rendl F (1997) Qaplib-a quadratic assignment problem library. Journal of Global Optimization 10(4):391–403CrossRefMathSciNetzbMATHGoogle Scholar
  9. 9.
    Cartwright, H.M., Mott, G.F.: Looking around: Using clues from the data space to guide genetic algorithm searches. In: Proceedings of the Fourth International Conference on Genetic Algorithms. pp. 108–114 (1991)Google Scholar
  10. 10.
    Connolly D (1990) An improved annealing scheme for the qap. European Journal of Operational Research 46(1):93–100CrossRefMathSciNetzbMATHGoogle Scholar
  11. 11.
    De Abreu N, Querido TM, Boaventura-Netto P (1999) Redinv-sa: la simulated annealing for the quadratic assignment problem. RAIRO-Operations Research 33(03):249–273CrossRefMathSciNetzbMATHGoogle Scholar
  12. 12.
    Demirel N, Toksarı M (2006) Optimization of the quadratic assignment problem using an ant colony algorithm. Applied Mathematics and Computation 183(1):427–435CrossRefMathSciNetzbMATHGoogle Scholar
  13. 13.
    Dokeroglu T, Cosar A (2016) A novel multistart hyper-heuristic algorithm on the grid for the quadratic assignment problem. Engineering Applications of Artificial Intelligence 52:10–25.  https://doi.org/10.1016/j.engappai.2016.02.004CrossRefGoogle Scholar
  14. 14.
    Dorigo M, Gambardella LM (1997) Ant colony system: A cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation 1(1):53–66CrossRefGoogle Scholar
  15. 15.
    Drezner Z (2002) Heuristic algorithms for the solution of the quadratic assignment problem. Journal of Applied Mathematics and Decision Sciences 6:163–173CrossRefGoogle Scholar
  16. 16.
    Drezner Z (2003) A new genetic algorithm for the quadratic assignment problem. Informs Journal on Computing 15(3):320–330CrossRefMathSciNetzbMATHGoogle Scholar
  17. 17.
    Drezner Z (2005) Compounded genetic algorithms for the quadratic assignment problem. Operations Research Letters 33(5):475–480CrossRefMathSciNetzbMATHGoogle Scholar
  18. 18.
    Feo TA, Resende MGC (1995) Greedy randomized adaptive search procedures. Journal of Global Optimization 6(2):109–133CrossRefMathSciNetzbMATHGoogle Scholar
  19. 19.
    Gambardella L, Taillard E, Dorigo M (1999) Ant colonies for the quadratic assignment problem. Journal of the Operational Research Society 50(2):167–176CrossRefzbMATHGoogle Scholar
  20. 20.
    Gilmore PC (1962) Optimal and suboptimal algorithms for the quadratic assignment problem. Journal of the Society for Industrial & Applied Mathematics 10(2):305–313CrossRefMathSciNetzbMATHGoogle Scholar
  21. 21.
    Glover F (1989) Tabu search - part i. ORSA journal on computing 1(3):190–206CrossRefMathSciNetzbMATHGoogle Scholar
  22. 22.
    Glover F (1990) Tabu search - part ii. ORSA journal on computing 2(1):4–32CrossRefMathSciNetzbMATHGoogle Scholar
  23. 23.
    Gutin G, Yeo A (2002) Polynomial approximation algorithms for the tsp and the qap with a factorial domination number. Discrete Applied Mathematics 119(1):107–116CrossRefMathSciNetzbMATHGoogle Scholar
  24. 24.
    Haghani A, Chen MC (1998) Optimizing gate assignments at airport terminals. Transportation Research Part A: Policy and Practice 32(6):437–454.  https://doi.org/10.1016/S0965-8564(98)00005-6CrossRefGoogle Scholar
  25. 25.
    Jagatheesan K, Anand B, Samanta S, Dey N, Ashour AS, Balas VE (2017) Particle swarm optimisation-based parameters optimisation of pid controller for load frequency control of multi-area reheat thermal power systems. International Journal of Advanced Intelligence Paradigms 9(5–6):464–489.  https://doi.org/10.1504/IJAIP.2017.088143CrossRefGoogle Scholar
  26. 26.
    James T, Rego C, Glover F (2009) A cooperative parallel tabu search algorithm for the quadratic assignment problem. European Journal of Operational Research 195(3):810–826.  https://doi.org/10.1016/j.ejor.2007.06.061CrossRefzbMATHGoogle Scholar
  27. 27.
    James T, Rego C, Glover F (2009) Multistart tabu search and diversification strategies for the quadratic assignment problem. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans 39(3):579–596CrossRefGoogle Scholar
  28. 28.
    Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680CrossRefMathSciNetzbMATHGoogle Scholar
  29. 29.
    Koopmans, T., Beckmann, M.: Assignment problems and the location of economic activities. Econometrica: Journal of the Econometric Society pp. 53–76 (1957)Google Scholar
  30. 30.
    Lee, Y., Orlin, J.: Quickmatch: a very fast algorithm for the assignment problem. Report, Massachusetts Institute of Technology, Sloan School of Management (Report number: WP#3547-93) (1993)Google Scholar
  31. 31.
    Li Y, Pardalos P, Resende M (1994) A greedy randomized adaptive search procedure for the quadratic assignment problem. Quadratic assignment and related problems 16:237–261CrossRefMathSciNetzbMATHGoogle Scholar
  32. 32.
    Lin S, Kernighan B (1973) An effective heuristic algorithm for the traveling salesman problem. Operations Research 21:443–452CrossRefMathSciNetzbMATHGoogle Scholar
  33. 33.
    Loiola EM, de Abreu NMM, Boaventura-Netto PO, Hahn P, Querido T (2007) A survey for the quadratic assignment problem. European Journal of Operational Research 176(2):657–690.  https://doi.org/10.1016/j.ejor.2005.09.032MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Lourenco, H., Martin, O., Stützle, T.: Iterated local search. Handbook of metaheuristics pp. 320–353 (2003)Google Scholar
  35. 35.
    Maniezzo V, Colorni A (1999) The ant system applied to the quadratic assignment problem. IEEE Transactions on Knowledge and Data Engineering 11(5):769–778CrossRefGoogle Scholar
  36. 36.
    Martin O, Otto S (1996) Combining simulated annealing with local search heuristics. Annals of Operations Research 63(1):57–75CrossRefMathSciNetzbMATHGoogle Scholar
  37. 37.
    Martin OC, Otto SW, Felten EW (1991) Large-step markov chains for the traveling salesman problem. Complex Systems 5:219–224MathSciNetzbMATHGoogle Scholar
  38. 38.
    Mavridou T, Pardalos P (1997) Simulated annealing and genetic algorithms for the facility layout problem: A survey. Computational optimization and Applications 7(1):111–126CrossRefMathSciNetzbMATHGoogle Scholar
  39. 39.
    Misevicius A (2005) A tabu search algorithm for the quadratic assignment problem. Computational optimization and Applications 30(1):95–111CrossRefMathSciNetzbMATHGoogle Scholar
  40. 40.
    Moscato, P.: On evolution, search, optimization, genetic algorithms and martial arts: Towards memetic algorithms. Caltech Concurrent Computation Program, C3P Report 826,  1989 (1989)Google Scholar
  41. 41.
    Nugent C, Vollmann T, Ruml J (1968) An experimental comparison of techniques for the assignment of facilities to locations. Operations Research 16(1):150–173CrossRefGoogle Scholar
  42. 42.
    Oliveira, C., Pardalos, P., Resende, M.: Grasp with path-relinking for the quadratic assignment problem. Experimental and Efficient Algorithms pp. 356–368 (2004)Google Scholar
  43. 43.
    Pardalos, P., Pitsoulis, L., Resende, M.: A parallel grasp implementation for the quadratic assignment problem. In: Ferreira, A., Rolim, J.D. (eds.) Parallel Algorithms for Irregular Problems: State of the Art, pp. 115–133. Springer US (1995). 10.1007/978-1-4757-6130-6-6Google Scholar
  44. 44.
    Rego C, James T, Glover F (2010) An ejection chain algorithm for the quadratic assignment problem. Networks 56(3):188–206CrossRefMathSciNetzbMATHGoogle Scholar
  45. 45.
    Sahni S, Gonzalez T (1976) P-complete approximation problems. Journal of the ACM (JACM) 23(3):555–565CrossRefMathSciNetzbMATHGoogle Scholar
  46. 46.
    Sarker B, Wilhelm W, Hogg G (1998) One-dimensional machine location problems in a multi-product flowline with equidistant locations. European Journal of Operational Research 105(3):401–426CrossRefzbMATHGoogle Scholar
  47. 47.
    Satapathy, S.C., Sri Madhava Raja, N., Rajinikanth, V., Ashour, A.S., Dey, N.: Multi-level image thresholding using otsu and chaotic bat algorithm. Neural Computing and Applications 29(12), 1285–1307 (Jun 2018). 10.1007/s00521-016-2645-5Google Scholar
  48. 48.
    Solimanpur M, Vrat P, Shankar R (2004) Ant colony optimization algorithm to the inter-cell layout problem in cellular manufacturing. European Journal of Operational Research 157(3):592–606CrossRefMathSciNetzbMATHGoogle Scholar
  49. 49.
    Steinberg L (1961) The backboard wiring problem: A placement algorithm. Siam Review 3(1):37–50CrossRefMathSciNetzbMATHGoogle Scholar
  50. 50.
    Stützle, T.: Iterated local search for the quadratic assignment problem. European Journal of Operational Research 174(3), 1519–1539 (2006)Google Scholar
  51. 51.
    Taillard E (1991) Robust taboo search for the quadratic assignment problem. Parallel Computing 17(4–5):443–455.  https://doi.org/10.1016/S0167-8191(05)80147-4MathSciNetCrossRefGoogle Scholar
  52. 52.
    Talbi EG, Roux O, Fonlupt C, Robillard D (2001) Parallel ant colonies for the quadratic assignment problem. Future Generation Computer Systems 17(4):441–449.  https://doi.org/10.1016/S0167-739X(99)00124-7CrossRefzbMATHGoogle Scholar
  53. 53.
    Tate D, Smith A (1995) A genetic approach to the quadratic assignment problem. Computers & Operations Research 22(1):73–83CrossRefzbMATHGoogle Scholar
  54. 54.
    Tseng LY, Chen SC (2006) A hybrid metaheuristic for the resource-constrained project scheduling problem. European Journal of Operational Research 175(2):707–721CrossRefMathSciNetzbMATHGoogle Scholar
  55. 55.
    Yang, X.S.: Nature-inspired metaheuristic algorithms. Luniver press (2010)Google Scholar
  56. 56.
    Yu J, Sarker B (2003) Directional decomposition heuristic for a linear machine-cell location problem. European Journal of Operational Research 149(1):142–184CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.School of Computing and Information TechnologyUniversity of WollongongWollongongAustralia
  2. 2.SMART Infrastructure FacilityUniversity of WollongongWolllongongAustralia

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