Abstract
A robust search algorithm should ideally exhibit reasonable performance on a diverse and varied set of problems. In an earlier paper Lim et al. (Computational Optimization and Applications, vol. 15, no. 3, 2000), we outlined a class of hybrid genetic algorithms based on the k-gene exchange local search for solving the quadratic assignment problem (QAP). We follow up on our development of the algorithms by reporting in this paper the results of comprehensive testing of the hybrid genetic algorithms (GA) in solving QAP. Over a hundred instances of QAP benchmarks were tested using a standard set of parameters setting and the results are presented along with the results obtained using simple GA for comparisons. Results of our testing on all the benchmarks show that the hybrid GA can obtain good quality solutions of within 2.5% above the best-known solution for 98% of the instances of QAP benchmarks tested. The computation time is also reasonable. For all the instances tested, all except for one require computation time not exceeding one hour. The results will serve as a useful baseline for performance comparison against other algorithms using the QAP benchmarks as a basis for testing.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D.E. Brown, C.L. Huntley, and A.R. Spillane, “A parallel genetic heuristic for the quadratic assignment problem,” ICGA'89, pp. 406–415.
R. Burkard, E. Cela, P. Pardalos, and L. Pitsoulis, “The quadratic assignment problem,” in Handbook of Combinatorial Optimization. P. Pardalos and D.Z. Du (Eds.), Kluwer: Boston, 1998, pp. 241–338.
R.E. Burkard, S.E. Karisch, and F. Rendl, “QAPLIB-A quadratic assignment problem library,” Journal of Global Optimization, vol. 10, pp. 391–403, 1997. [URL: http://fmatbhp1.tu-graz.ac.at/~karisch/qaplib/]
C. Fleurent and J. Ferland, “Genetic hybrids for the quadratic assignment problem,” in Quadratic Assignment and Related Problems. P. Pardalos and H. Wolkowicz (Eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 16, American Math. Soc., 1994, pp. 173–187.
D.E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley: Reading, MA, 1989.
T.C. Koopmans and M.J. Beckmann, “Assignment problems and the location of economic activities,” Econometrica, vol. 25, pp. 53–76, 1957.
Y. Li and P. Pardalos, “Generating quadratic assignment test problems with known optimal permutations,” Computational Optimization and Applications, vol. 1, pp. 163–184, 1992.
Y. Li, P. Pardalos, and M. Resende, “A greedy randomized adaptive search procedure for the quadratic assignment problem,” in Quadratic Assignment and Related Problems. P. Pardalos and H. Wolkowicz (Eds.), DIMACS Series, American Math. Soc., 1994, pp. 237–261.
M.H. Lim, Y. Yuan, and S. Omatu, “Efficient genetic algorithms using simple genes exchange local search policy for the quadratic assignment problem,” Computational Optimization and Applications, vol. 15, no. 3, 2000.
P. Merz and B. Freisleben, “A genetic local search approach to the quadratic assignment problem,” in Proc. of Int'l Conf. on Genetic Algorithms (ICGA'97), Morgan Kaufmann: San Mateo, CA, pp. 465–472.
H. Muhlenbein, “Parallel genetic algorithms, population genetics and combinatorial optimization,” in Proc. of Int'l Conf. on Genetic Algorithms (ICGA'89), pp. 416–421.
C.E. Nugent, T.E. Vollman, and J. Ruml, “An experimental comparison of techniques for the assignment of facilities to locations,” Operations Research, vol. 16, pp. 150–173, 1968.
P. Pardalos and L. Pitsoulis (Eds.), Nonlinear Assignment Problems-Algorithms and Applications, Kluwer Academic: Dordrecht, 2000.
P. Pardalos, L. Pitsoulis, and M. Resende, “Algorithm 769: Fortran subroutines for approximate solution of sparse quadratic assignment problems using GRASP,” ACMTrans. on Mathematical Software, vol. 23, no. 2, pp. 196–208, 1997.
P. Pardalos and H. Wolkowicz (Eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 16, American Math. Soc., 1994.
M. Resende, P. Pardalos, and Y. Li, “Algorithm 754: Fortran subroutines for approximate solution of dense quadratic assignment problems using GRASP,” ACM Trans. on Mathematical Software, vol. 22, no. 1, pp. 104–118, 1996.
D.M. Tate and A.E. Smith, “Agenetic approach to the quadratic assignment problem,” Computers&Operations Research, vol. 22, no. 1, pp. 73–83, 1995.
M. Vazquez and L.D. Whitley, “A hybrid genetic algorithm for the quadratic assignment problem,” Genetic and Evolutionary Computation Conf. (GECCO 2000), Morgan Kaufmann: San Mateo, CA, pp. 135–142.
Y. Yuan, “Genetic algorithm based approaches for the quadratic assignment problem,” Master's Thesis, Nanyang Technological University, Singapore, 1999.
Y. Yuan and M.H. Lim, “Studies on GA embedded with k-gene exchange local search for the QAP,” in ICARCV'98, Fifth International Conference on Control, Automation, Robotics and Vision, Singapore, 1998.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lim, MH., Yuan, Y. & Omatu, S. Extensive Testing of a Hybrid Genetic Algorithm for Solving Quadratic Assignment Problems. Computational Optimization and Applications 23, 47–64 (2002). https://doi.org/10.1023/A:1019972523847
Issue Date:
DOI: https://doi.org/10.1023/A:1019972523847