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Volume 2006 |Article ID 070240 | https://doi.org/10.1155/JAMDS/2006/70240

Zvi Drezner, George A. Marcoulides, "Mapping the convergence of genetic algorithms", Advances in Decision Sciences, vol. 2006, Article ID 070240, 16 pages, 2006. https://doi.org/10.1155/JAMDS/2006/70240

Mapping the convergence of genetic algorithms

Received29 Aug 2005
Revised25 Apr 2006
Accepted06 Jun 2006
Published03 Sep 2006

Abstract

This paper examines the convergence of genetic algorithms using a cluster-analytic-type procedure. The procedure is illustrated with a hybrid genetic algorithm applied to the quadratic assignment problem. Results provide valuable insight into how population members are selected as the number of generations increases and how genetic algorithms approach stagnation after many generations.

References

  1. R. K. Ahuja, J. B. Orlin, and A. Tiwari, “A greedy genetic algorithm for the quadratic assignment problem,” Computers & Operations Research, vol. 27, no. 10, pp. 917–934, 2000. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  2. K. M. Anstreicher and N. W. Brixius, “A new bound for the quadratic assignment problem based on convex quadratic programming,” Mathematical Programming, vol. 89, no. 3, pp. 341–357, 2001. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  3. K. M. Anstreicher, N. W. Brixius, J.-P. Goux, and J. Linderoth, “Solving large quadratic assignment problems on computational grids,” Mathematical Programming, vol. 91, no. 3, pp. 563–588, 2002. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  4. G. C. Armour and E. S. Buffa, “A heuristic algorithm and simulation approach to relative location of facilities,” Management Science, vol. 9, pp. 294–309, 1963. View at: Google Scholar
  5. R. Battiti and G. Tecchiolli, “The reactive tabu search,” ORSA Journal on Computing, vol. 6, pp. 126–140, 1994. View at: Google Scholar | Zentralblatt MATH
  6. J. E. Beasley, “Population heuristics,” in Handbook of Applied Optimization, P. M. Pardalos and M. G. C. Resende, Eds., pp. 138–157, Oxford University Press, Oxford, 2002. View at: Google Scholar
  7. R. E. Burkard, “Locations with spatial interactions: the quadratic assignment problem,” in Discrete Location Theory, P. B. Mirchandani and R. L. Francis, Eds., Wiley-Intersci. Ser. Discrete Math. Optim., pp. 387–437, Wiley, New York, 1990. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  8. R. E. Burkard and F. Rendl, “A thermodynamically motivated simulation procedure for combinatorial optimization problems,” European Journal of Operational Research, vol. 17, no. 2, pp. 169–174, 1984. View at: Publisher Site | Google Scholar | Zentralblatt MATH
  9. E. Çela, The Quadratic Assignment Problem: Theory and Algorithms, vol. 1 of Combinatorial Optimization, Kluwer Academic, Dordrecht, 1998. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  10. D. T. Connolly, “An improved annealing scheme for the QAP,” European Journal of Operational Research, vol. 46, no. 1, pp. 93–100, 1990. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  11. Z. Drezner, “DISCON: a new method for the layout problem,” Operations Research, vol. 28, pp. 1375–1384, 1980. View at: Google Scholar | Zentralblatt MATH
  12. Z. Drezner, “A heuristic procedure for the layout of a large number of facilities,” Management Science, vol. 33, pp. 909–915, 1987. View at: Google Scholar | Zentralblatt MATH
  13. Z. Drezner, “Lower bounds based on linear programming for the quadratic assignment problem,” Computational Optimization & Applications, vol. 4, no. 2, pp. 159–165, 1995. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  14. Z. Drezner, “Heuristic algorithms for the solution of the quadratic assignment problem,” Journal of Applied Mathematics and Decision Sciences, vol. 6, no. 3, pp. 163–173, 2002. View at: Google Scholar
  15. Z. Drezner, “A new genetic algorithm for the quadratic assignment problem,” INFORMS Journal on Computing, vol. 15, no. 3, pp. 320–330, 2003. View at: Publisher Site | Google Scholar | MathSciNet
  16. Z. Drezner, “Compounded genetic algorithms for the quadratic assignment problem,” Operations Research Letters, vol. 33, no. 5, pp. 475–480, 2005. View at: Publisher Site | Google Scholar | MathSciNet
  17. Z. Drezner, “The extended concentric tabu for the quadratic assignment problem,” European Journal of Operational Research, vol. 160, no. 2, pp. 416–422, 2005. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  18. C. Fleurent and J. Ferland, “Genetic hybrids for the quadratic assignment problem,” in Quadratic Assignment and Related Problems (New Brunswick, NJ, 1993), vol. 16 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 173–187, American Mathematical Society, Rhode Island, 1994. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  19. L. M. Gambardella, E. D. Taillard, and M. Dorigo, “Ant colonies for the quadratic assignment problem,” Journal of the Operational Research Society, vol. 50, no. 2, pp. 167–176, 1999. View at: Google Scholar | Zentralblatt MATH
  20. P. C. Gilmore, “Optimal and suboptimal algorithms for the quadratic assignment problem,” Journal of the Society of Industrial and Applied Mathematics, vol. 10, no. 2, pp. 305–313, 1962. View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
  21. P. M. Hahn and T. L. Grant, “Lower bounds for the quadratic assignment problem based upon a dual formulation,” Operations Research, vol. 46, no. 6, pp. 912–922, 1998. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  22. P. M. Hahn, W. L. Hightower, W. P. Adams, and M. Guignard-Spielberg, “A level-2 reformulation-linearization technique bound for the quadratic assignment problem,” to appear in European Journal of Operational Research. View at: Google Scholar
  23. P. M. Hahn and J. Krarup, “A hospital facility problem finally solved,” Journal of Intelligent Manufacturing, vol. 12, no. 5-6, pp. 487–496, 2001. View at: Publisher Site | Google Scholar
  24. E. L. Lawler, “The quadratic assignment problem,” Management Science, vol. 9, pp. 586–599, 1963. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  25. Y. Li, P. M. Pardalos, and M. G. C. Resende, “A greedy randomized adaptive search procedure for the quadratic assignment problem,” in Quadratic Assignment and Related Problems, P. M. Pardalos and H. Wolkowicz, Eds., vol. 16 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 237–261, American Mathematical Society, Rhode Island, 1994. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  26. G. A. Marcoulides and Z. Drezner, “A procedure for transforming points in multi-dimensional space to two-dimensional,” Educational and Psychological Measurement, vol. 53, pp. 933–940, 1993. View at: Google Scholar
  27. G. A. Marcoulides and Z. Drezner, “A procedure for detecting pattern clustering in measurement designs,” in Objective Measurement: Theory into Practice, M. Wilson, K. Draney, and G. Engelhard, Jr., Eds., vol. 5, pp. 287–302, Ablex, New Jersey, 2000. View at: Google Scholar
  28. P. Moscato, “Memetic algorithms,” in Handbook of Applied Optimization, P. M. Pardalos and M. G. C. Resende, Eds., Oxford University Press, Oxford, 2002. View at: Google Scholar
  29. 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. View at: Google Scholar
  30. M. Nystrom, “Solving certain large instances of the quadratic assignment problem: Steinberg's examples,” Working paper, California Institute of Technology, California, 1999. View at: Google Scholar
  31. F. Rendl, “The quadratic assignment problem,” in Facility Location: Applications and Theory, Z. Drezner and H. Hamacher, Eds., pp. 439–457, Springer, Berlin, 2002. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  32. M. G. C. Resende, K. G. Ramakrishnan, and Z. Drezner, “Computing lower bounds for the quadratic assignment problem with an interior point algorithm for linear programming,” Operations Research, vol. 43, no. 5, pp. 781–791, 1995. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  33. S. Salhi, “Heuristic search methods,” in Modern Methods for Business Research, G. A. Marcoulides, Ed., Lawrence Erlbaum Associates, New Jersey, 1998. View at: Google Scholar
  34. J. Skorin-Kapov, “Tabu search applied to the quadratic assignment problem,” ORSA Journal on Computing, vol. 2, no. 1, pp. 33–45, 1990. View at: Google Scholar | Zentralblatt MATH
  35. E. D. Taillard, “Robust taboo search for the quadratic assignment problem,” Parallel Computing, vol. 17, no. 4-5, pp. 443–455, 1991. View at: Publisher Site | Google Scholar | MathSciNet
  36. E. D. Taillard, “Comparison of iterative searches for the quadratic assignment problem,” Location Science, vol. 3, no. 2, pp. 87–105, 1995. View at: Publisher Site | Google Scholar | Zentralblatt MATH
  37. D. M. Tate and A. E. Smith, “A genetic approach to the quadratic assignment problem,” Computers & Operations Research, vol. 22, no. 1, pp. 73–83, 1995. View at: Publisher Site | Google Scholar | Zentralblatt MATH
  38. M. R. Wilhelm and T. L. Ward, “Solving quadratic assignment problems by simulated annealing,” IIE Transactions, vol. 19, pp. 107–119, 1987. View at: Google Scholar

Copyright © 2006 Zvi Drezner and George A. Marcoulides. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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