Skip to main content

Advertisement

SpringerLink
Log in

A multi-parent genetic algorithm for the quadratic assignment problem

  • Application Article
  • Published:
OPSEARCH Aims and scope Submit manuscript

Abstract

Instead of using traditional (two-parent) crossover operator, multi-parent crossover operator is used in genetic algorithms to improve solution quality for many numerical optimization problems. However, very few literatures are available on multi-parent crossover operator for combinatorial optimization problems, especially, quadratic assignment problem (QAP). This paper proposes a multi-parent extension of the sequential constructive crossover (MPSCX), which is a generalization of the traditional sequential constructive crossover (SCX), for the QAP. Then a multi-parent genetic algorithm (MPGA) using MPSCX is developed. Experimental results on ten QAPLIB instances show that our MPGA significantly improves GA using SCX by up to 1.75 % in average assignment cost with maximum of 2.79 % away from the best known solution value. Finally, the efficiency of our MPGA is compared against MPGA using an existing multi-parent crossover for the problem. Experimental results show that our MPGA is better.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Pardalos, P.M., Resende, M.G.C.: Handbook of Applied Optimization”. Oxford University Press, New York (2002)

    Book  Google Scholar 

  2. Goldberg, D.E.: Genetic Algorithms In Search, Optimization, And Machine Learning”. Addison-Wesley, New York (1989)

    Google Scholar 

  3. Eiben, A., van Kemenade, C.: Diagonal crossover in genetic algorithms for numerical optimization’. J. Control Cybern. 26(3), 447–465 (1997)

    Google Scholar 

  4. Ahuja, R., Orlin, J.B., Tiwari, A.: A greedy genetic algorithm for the quadratic assignment problem”. Comput. Oper. Res. 27(10), 917–934 (2000)

    Article  Google Scholar 

  5. Ahmed, Z.H.: Genetic algorithm for the traveling salesman problem using sequential constructive crossover operator. Int. J. Biom. Bioinforma. 3(6), 96–105 (2010)

    Google Scholar 

  6. Holland, J.: ‘Adaptation in natural and artificial systems’, University of Michigan Press (1975)

  7. Eiben, A., Rouě, P.-E. andRuttkay, Z.: ‘Genetic algorithms with multi-parent recombination’, Parallel problem solving from nature – PPSN III. LNCS, pp. 78–87. Springer, 866, (1994)

  8. Eiben, A.: ‘Multi-parent recombination in evolutionary computing’, Advances in Evolutionary Computing, pp. 175–192. Springer (2002)

  9. Wang, H., Wu, Z. and Liu, Y.: ‘Particle swarm optimization with a novel multi-parent crossover operator’, Proceedings of 4th International Conference on Natural Computation, pp. 664–668 (2008).

  10. Wu, A., Tsang, P.W.M., Yuen, T.Y.F., Yeung, L.F.: Affine invariant object shape matching using genetic algorithm with multi-parent orthogonal recombination and migrant principle’. Appl. Soft Comput. 9, 282–289 (2009)

    Article  Google Scholar 

  11. Porumbel, D.C., Hao, J.-K., Kunz, P.: An evolutionary approach with diversity guarantee and well-informed grouping recombination for graph coloring’. Comput. Oper. Res. 37(10), 1822–1832 (2010)

    Article  Google Scholar 

  12. Ting, C.-K.: ‘Design and analysis of multi-parent genetic algorithms’, Ph.D. thesis, University of Paderborn, Germany (2005).

  13. Ting, C.-K., Su, C.-H., Lee, C.-N.: Multi-parent extension of partially mapped crossover for combinatorial optimization problems’. Exp. Syst. Appl. 37, 1879–1886 (2010)

    Article  Google Scholar 

  14. Ahmed, Z.H.: Multi-parent extension of sequential constructive crossover for the traveling salesman problem. Int. J. Oper. Res. 11(3), 331–342 (2011)

    Article  Google Scholar 

  15. Chen, S.-H., Chen, M.-C., Chang, P.-C., Mani, V.: Multiple parents crossover operators: A new approach removes the overlapping solutions for sequencing problems. Appl. Math. Model. 37, 2737–2746 (2013)

    Article  Google Scholar 

  16. Sahni, S., Gonzales, T.: P-complete approximation problems. J. Assoc. Comput. Mach. 23, 555–565 (1976)

    Article  Google Scholar 

  17. Misevicius, A., Rubliauskas, D.: Performance of hybrid genetic algorithm for the grey pattern problem”. J. Inf. Technol. Constr. 34(1), 15–24 (2005)

    Google Scholar 

  18. Ahmed, Z.H.: A simple genetic algorithm using sequential constructive crossover for the quadratic assignment problem. J. Sci. Ind. Res. 73(12), 763–766 (2014)

    Google Scholar 

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

    Article  Google Scholar 

  20. Steinberg, L.: The backboard wiring problem: A placement algorithm. SIAM Rev. 3, 37–50 (1961)

    Article  Google Scholar 

  21. Geoffrion, A.M., Graves, G.W.: Scheduling parallel production lines with changeover costs: Practical applications of a quadratic assignment/LP approach. Oper. Res. 24, 595–610 (1976)

    Article  Google Scholar 

  22. Pollatschek, M.A., Gershoni, N., Radday, Y.T.: Optimization of the typewriter keyboard by simulation. AngewandteInformatik 17, 438–439 (1976)

    Google Scholar 

  23. Elshafei, A.N.: Hospital layout as a quadratic assignment problem. Oper. Res. Q. 28(1), 167–179 (1977)

    Article  Google Scholar 

  24. Krarup, J., Pruzan, P.M.: Computer-aided layout design. Math. Prog. Stud. 9, 75–94 (1978)

    Article  Google Scholar 

  25. Heffley, D.R.: Decomposition of the Koopmans–Beckmann problem. Reg. Sci. Urban Econ. 10(4), 571–580 (1980)

    Article  Google Scholar 

  26. Hubert, L.: "Assignment methods in combinatorial data analysis". Statistics: Textbooks and Monographs Series, 73. Marcel Dekker (1987).

  27. Bos, J.: A quadratic assignment problem solved by simulated annealing. J. Environ. Manag. 37(2), 127–145 (1993)

    Article  Google Scholar 

  28. Forsberg, J.H., Delaney, R.M., Zhao, Q., Harakas, G., Chandran, R.: Analyzing lanthanide-included shifts in the NMR spectra of lanthanide (III) complexes derived from 1,4,7,10-tetrakis (N, N-diethylacetamido)-1,4,7,10-tetraazacyclododecane. Inorg. Chem. 34, 3705–3715 (1994)

    Article  Google Scholar 

  29. Brusco, M.J., Stahl, S.: Using quadratic assignment methods to generate initial permutations for least-squares unidimensional scaling of symmetric proximity matrices. J. Classif. 17(2), 197–223 (2000)

    Article  Google Scholar 

  30. Miranda, G., Luna, H.P.L., Mateus, G.R., Ferreira, R.P.M.: A performance guarantee heuristic for electronic components placement problems including thermal effects. Comput. Oper. Res. 32, 2937–2957 (2005)

    Article  Google Scholar 

  31. Duman, E., Ilhan, O.: The quadratic assignment problem in the context of the printed circuit board assembly process. Comput. Oper. Res. 34, 163–179 (2007)

    Article  Google Scholar 

  32. Tsutsui, S. and Ghosh, A.: ‘A study on the effect of multi-parent recombination in real coded genetic algorithms’, Proceedings of International Conference on Evolutionary Computation, pp. 828–833 (1998)

  33. Lin, G., Kang, L., Chen, Y., McKay, B., Sarker, R.: A self-adaptive mutations with multi-parent crossover evolutionary algorithm for solving function optimization problems’. Lect. Notes Comput. Sci 4683, 157–168 (2007)

    Article  Google Scholar 

  34. Li, Y. and Chen, S.: ‘A multi-stage evolutionary algorithm for solving complex function optimization problems’, Second International Conference on Computer and Electrical Engineering, pp. 516–519. (2009)

  35. Binh, H.T.T. and Nghia, N.D. ‘New multi-parent recombination in genetic algorithm for solving bounded diameter minimum spanning tree problem’. Proceedings of 1st Asian Conference on Intelligence Information and Database Systems, pp. 283–288. (2009)

  36. Misevicius, A., Kilda, B.: Comparison of crossover operators for the quadratic assignment problem”. J. Inf. Technol. Constr. 34(2), 109–119 (2005)

  37. Ting, C.-K.: ‘Multi-parent extension of edge recombination’, GECCO'07, pp. 1535. London, England (2007).

  38. Drezner, Z.: (2003) “Extensive experiments with hybrid genetic algorithms for the solution of the quadratic assignment problem”. Comput. Oper. Res. 35, 717–736 (2008)

  39. Misevicius, A.: An improved hybrid optimization algorithm for the quadratic assignment problem”. Math. Model. Anal. 9(2), 149–168 (2004)

    Google Scholar 

  40. Misevicius, A., Guogis, E.: Computational study of four genetic algorithm variants for solving the quadratic assignment problem, ICIST 2012. CCIS 319, 24–37 (2012)

    Google Scholar 

  41. Drezner, Z., Misevicius, A.: Enhancing the performance of hybrid genetic algorithms by differential improvement. Comput. Oper. Res. 40, 1038–1046 (2013)

    Article  Google Scholar 

  42. Ahmed, Z.H.: “An improved genetic algorithm using adaptive mutation operator for the quadratic assignment problem,” In: 37th International Conference on Telecommunications and Signal Processing 2014 (TSP 2014), pp. 616–620. Berlin, Germany (2014d)

  43. Ahmed, Z.H., Bennaceur, H., Habib Vulla, M., and Altukhaim, F.: A hybrid genetic algorithm for the quadratic assignment problem. In: Proceedings of Second International Conference on Emerging Research in Computing, Information, Communication and Applications (ERCICA 2014), vol. 3, pp. 916–922. Bangalore, India (2014)

  44. Li Y, Pardalos PM, and Resende MGC: “A greedy randomized adaptive search procedure for the quadratic assignment problem”. In: Pardalos PM, Wolkowicz H, editors. Quadratic assignment and related problems. DIMACS series in discrete mathematics and theoretical computer science, vol. 16, pp. 237–261. American Mathematical Society (1994).

  45. Oliveira, CAS, Pardalos, PM, Resende, MGC: “GRASP with path-relinking for the quadratic assignment problem”. In: Ribeiro CC, Martins SL. (eds.) Efficient and experimental algorithms, pp. 237–261. Springer-Verlag (2004)

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

    Article  Google Scholar 

  47. Rodriguez, J.M., MacPhee, F.C., Bonham, D.J., Horton, J.D., Bhavsar, V.C.: Best permuta- tions for the dynamic plant layout problem”. In: Dasgupta, A.R., Iyengar, S.S., Bhatt, H.S. (eds.) Efficient and experimental algorithms: proceedings of the 12th international conference on advances in computing and communications (ADCOM 2004), pp. 173–178. Allied Publishers Pvt. Ltd, New Delhi (2004)

    Google Scholar 

  48. Pelikan M, Tsutsui S, and Kalapala R: “Dependency trees permutations, and quadratic assignment problem”. Technical Report No. 2007003. Missouiri Estimation of Distribution Algorithms Laboratory (MEDAL) (2007)

  49. Deb, K.: “Optimization for engineering design: algorithms and examples”, Prentice Hall of India Pvt. Ltd., New Delhi, India (1995)

  50. Ahmed, Z.H.: Improved genetic algorithms for the traveling salesman problem. Int. J. Process. Manag. Benchmark 4(1), 109–124 (2014)

    Article  Google Scholar 

  51. Ahmed, Z.H.: “A hybrid genetic algorithm for the bottleneck traveling salesman problem”. ACM Trans. Embed. Comput. Syst. 12(1), Art. 9 (2013a)

  52. Ahmed, Z.H.: An experimental study of a hybrid genetic algorithm for the maximum travelling salesman problem”. Math. Sci. 7(1), 1–7 (2013)

    Article  Google Scholar 

  53. Ahmed, Z.H.: “The ordered clustered travelling salesman problem: a hybrid genetic algorithm”. Sci. World J. 2014, Article ID 258207, 13 pages (2014a). doi:10.1155/2014/258207

  54. Lim, M.H., Yuan, Y., Omatu, S.: Efficient genetic algorithms using simple genes exchange local search policy for the quadratic assignment problem. Comput. Optim. Appl. 15, 249–268 (2000)

    Article  Google Scholar 

  55. Taillard, E.: Comparison of iterative searches for the quadratic assignment problem”. Loc. Sci. 3, 87–105 (1995)

    Article  Google Scholar 

  56. Burkard, R.E., Cela, E., Karisch, S.E., Rendl, F.: QAPLIB - a quadratic assignment problem library”. J. Glob. Optim. 10(4), 391–403 (1997). http://www.seas.upenn.edu/qaplib/

    Article  Google Scholar 

Download references

Acknowledgments

The author is thankful to the honorable anonymous reviewer for his constructive comments and suggestions. This research was supported by the NSTIP strategic technologies program number (10) in the Kingdom of Saudi Arabia vide Award No.11-INF1788-08.The author is very much thankful to the NSTIP for its financial and technical supports.

Author information

Authors and Affiliations

  1. Department of Computer Science, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box No. 5701, Riyadh, 11432, Kingdom of Saudi Arabia

    Zakir Hussain Ahmed

Authors
  1. Zakir Hussain Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zakir Hussain Ahmed.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ahmed, Z.H. A multi-parent genetic algorithm for the quadratic assignment problem. OPSEARCH 52, 714–732 (2015). https://doi.org/10.1007/s12597-015-0208-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12597-015-0208-7

Keywords

Search

Navigation