On the Global Convergence of Univariate Dynamic Encoding Algorithm for Searches (uDEAS)

  • Kim, Jong-Wook (Department of Electronics Engineering, Dang-A University) ;
  • Kim, Tae-Gyu (Department of Electronics Engineering, Dang-A University) ;
  • Choi, Joon-Young (Department of Electronic Engineering, Pusan National University) ;
  • Kim, Sang-Woo (Electrical and Computer Engineering Division, Pohang University of Science and Technology)
  • Published : 2008.08.31

Abstract

This paper analyzes global convergence of the univariate dynamic encoding algorithm for searches (uDEAS) and provides an application result to function optimization. uDEAS is a more advanced optimization method than its predecessor in terms of the number of neighborhood points. This improvement should be validated through mathematical analysis for further research and application. Since uDEAS can be categorized into the generating set search method also established recently, the global convergence property of uDEAS is proved in the context of the direct search method. To show the strong performance of uDEAS, the global minima of four 30 dimensional benchmark functions are attempted to be located by uDEAS and the other direct search methods. The proof of global convergence and the successful optimization result guarantee that uDEAS is a reliable and effective global optimization method.

Keywords

References

  1. R. Hooke and T. A. Jeeves, "Direct search solution of numerical and statistical problems," Journal of the ACM, vol. 8, no. 2, pp. 212-229, 1961 https://doi.org/10.1145/321062.321069
  2. V. Torczon, "On the convergence of pattern search algorithms," SIAM Journal on Optimization, vol. 7, no. 1, pp. 1-25, 1997 https://doi.org/10.1137/S1052623493250780
  3. J. A. Nelder and R. Mead, "A simplex method for function minimization," Computer Journal, vol. 7, pp. 308-313, 1965 https://doi.org/10.1093/comjnl/7.4.308
  4. D. E. Goldberg, Genetic Algorithm in Search, Optimization and Machine Learning, Addison Wesley, 1989
  5. Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer, 1996
  6. J.-W. Kim and S. W. Kim, "New encoding/ converting methods of binary GA/real-coded GA," IEICE Trans. on Fundamentals, vol. E88-A, no. 6, pp. 1554-1564, June 2005 https://doi.org/10.1093/ietfec/e88-a.6.1554
  7. J.-W. Kim and S. W. Kim, "Parameter identification of induction motors using dynamic encoding algorithm for searches (DEAS)," IEEE Trans. on Energy Conversion, vol. 20, no. 1, pp. 16-24, March 2005 https://doi.org/10.1109/TEC.2004.837287
  8. Y. S. Park, Y. Lee, J.-W. Kim, and S. W. Kim, "Parameter optimization for SVM using dynamic encoding algorithm," Proc. of International Conference on Control, Automation, and Systems, KINTEX, Korea, pp. 2542-2547, June 2005
  9. T. Kim and J.-W. Kim, "Optimal design of a transformer core using DEAS," Trans. KIEE, vol. 56, no. 6, pp. 1055-1063, June 2007
  10. J.-W. Kim and S. W. Kim, "PID control design with exhaustive dynamic encoding algorithm for searches (eDEAS)," International Journal of Control, Automation, and Systems, vol. 5, no. 6, pp. 691-700, Dec. 2007
  11. J.-W. Kim and S. W. Kim, "Numerical method for global optimization: Dynamic encoding algorithm for searches," IEE Proc.-Control Theory Appl., vol. 151, no. 5, pp. 661-668, Sept. 2004 https://doi.org/10.1049/ip-cta:20040901
  12. F. Glover, "Tabu search methods in artificial intelligence and operations research," ORSA Artificial Intelligence, vol. 1, no. 2, p. 6, 1987
  13. S. S. Rao, Engineering Optimization, John Wiley & Sons Inc., 1996
  14. J.-W. Kim, N. G. Kim, S.-C. Choi, and S. W. Kim, "On-load parameter identification of an induction motor using univariate dynamic encoding algorithm for searches," Proc. of International Conference on Control, Automation and Systems, Bangkok, Thailand, pp. 852-856, August, 2004
  15. Y. J. Jang and S. W. Kim, "Estimation of a billet temperature during reheating furnace operation," International Journal of Control, Automation, and Systems, vol. 5, no. 1, pp. 43-50, Feb. 2007
  16. T. G. Kolda, R. M. Lewis, and V. Torczon, "Optimization by direct search: New perspectives on some classical and modern methods," SIAM Review, vol. 45, no. 3, pp. 385- 482, 2003 https://doi.org/10.1137/S003614450242889
  17. V. Torczon, "On the convergence of the multidirectional search algorithm," SIAM Journal on Optimization, vol. 1, no. 1, pp. 123- 145, 1991 https://doi.org/10.1137/0801010
  18. C. Davis, "Theory of positive linear dependence," Amer. J. Math., vol. 76, pp. 733- 746, 1954 https://doi.org/10.2307/2372648
  19. N. G. Kim, J.-W. Kim, and S. W. Kim, "A study for global optimization using dynamic encoding algorithm for searches," Proc. of International Conference on Control, Automation and Systems, Bangkok, Thailand, pp. 857-862, Aug. 2004
  20. G. Berman, "Lattice approximations to the minimum of functions of several variables," Journal of the ACM, vol. 16, pp. 286-294, 1969 https://doi.org/10.1145/321510.321520
  21. J.-W. Kim and S. W. Kim, "A fast computational optimization method: Univariate dynamic encoding algorithm for searches (uDEAS)," IEICE Trans. on Fundamentals, vol. E90-A, no. 8, pp. 1679-1689, Aug. 2007 https://doi.org/10.1093/ietfec/e90-a.8.1679
  22. C. Audet and J. E. Dennis JR, "Mesh adaptive direct search algorithms for constrained optimization," SIAM Journal on Optimization, vol. 17, no. 1, pp. 188-217, 2006 https://doi.org/10.1137/040603371
  23. X. Yao, Y. Liu, and G. Lin, "Evolutionary programming made faster," IEEE Trans. on Evolutionary Computation, vol. 3, no. 2, pp. 82- 102, July, 1999 https://doi.org/10.1109/4235.771163