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A New Filled Function Method for Global Optimization

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Abstract

A novel filled function is suggested in this paper for identifying a global minimum point for a general class of nonlinear programming problems with a closed bounded domain. Theoretical and numerical properties of the proposed filled function are investigated and a solution algorithm is proposed. The implementation of the algorithm on several test problems is reported with satisfactory numerical results.

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References

  1. Barhen, J., Protopopescu, V. and Reister, D. (1997), TRUST: a deterministic algorithm for global optimization, Science 276, 1094–1097.

    Google Scholar 

  2. Cetin, B. C., Barhen, J. and Burdick, J. W. (1993), Terminal repeller unconstrained subenergy tunneling (TRUST) for fast global optimization, Journal of Optimization and Applications 77, 97–126.

    Google Scholar 

  3. Cvijović, D. and Klinowski, J. (1995), Taboo search: an approach to the multiple minima problem, Science 267, 664–666.

    Google Scholar 

  4. Dixon, L. C. W., Gomulka, J. and Herson, S. E. (1976), Reflection on global optimization problems, in Dixon, L. C. W. (ed.), Optimization in Action, Academic Press, New York, 398–435.

    Google Scholar 

  5. Ge, R. P. (1990), A filled function method for finding a global minimizer of a function of several variables, Mathematical Programming 46, 191–204.

    Google Scholar 

  6. Ge, R. P. and Qin, Y. F. (August 1987), A class of filled functions for finding global minimizers of a function of several variables, Journal of Optimization Theory and Applications 54(2), 241–252.

    Google Scholar 

  7. Horst, R., Pardalos, P. M. and Thoai, N. V. (1995), Introduction to Global Optimization, Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  8. Horst, R. and Tuy, H. (1993), Global Optimization: Deterministic Approaches, Second Edition, Springer, Heidelberg.

    Google Scholar 

  9. Levy, A. V. and Montalvo, A. (1985), The tunneling algorithm for the global minimization of functions, SIAM Journal on Scientific and Statistical Computing 6, 15–29.

    Google Scholar 

  10. Li, D., Sun, X. L., Biswal, M. P. and Gao, F. (2001), Convexification, concavification and monotonization in global minimization, to appear in Annals of Operations Research, Vol. 105.

  11. Liu, Xian (2001), Finding global minima with a computable filled function, Journal of Global Optimization 19, 151–161.

    Google Scholar 

  12. Litinetski, V. V. and Abramzon, B. M. (1998), MARS — a multi-start adaptive random search method for global constrained optimization in engineering applications, Engineering Optimization 30, 125–154.

    Google Scholar 

  13. Pardalos, P. M., Romeijn, H. E. and Tuy, H. (2000), Recent development and trends in global optimization, Journal of Computational and Applied Mathematics 124, 209–228.

    Google Scholar 

  14. Pardalos, P. M. and Rosen, J. B. (1987), Constrained Global Optimization: Algorithms and Applications, Springer, Berlin.

    Google Scholar 

  15. Rinnoy Kan, A. H. G. and Timmer, G. T. (1989), Global Optimization, in Nemhauser, G. L., Rinnooy Kan, A. H. G. and Todd, M. J. (eds.), Handbooks of Operations Research and Management Science 1, Optimization, North-Holland, Amsterdam, 631–662.

    Google Scholar 

  16. Sun, X. L., McKinnon, K. I. M. and Li, D. (2001), Convexification method for a class of global optimization problems with applications to reliability optimization, Journal of Global Optimization 21, 185–199.

    Google Scholar 

  17. Xu, Zheng, Huang, Hong-Xuan, Pardalos, Panos M. and Xu, Cheng-Xian (2001), Filled functions for unconstrained global optimization, Journal of Global Optimization 20, 49–65.

    Google Scholar 

  18. Yao, Y. (1989), Dynamic tunneling algorithm for global optimization, IEEE Transactions on Systems, Man and Cybernetics 19, 1222–1230.

    Google Scholar 

  19. Zheng, Q. and Zhuang, D. (1995), Integral global minimization: algorithms, implementations and numerical tests, Journal of Global Optimization 7(4), 421–454.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, China

    Lian-Sheng Zhang

  2. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, China, E-mail

    Chi-Kong Ng

  3. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, China, E-mail

    Duan Li

  4. Department of Mathematics, Shanghai University, Jiading, Shanghai, China, E-mail

    Wei-Wen Tian

Authors
  1. Lian-Sheng Zhang
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  2. Chi-Kong Ng
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  3. Duan Li
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  4. Wei-Wen Tian
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Zhang, LS., Ng, CK., Li, D. et al. A New Filled Function Method for Global Optimization. Journal of Global Optimization 28, 17–43 (2004). https://doi.org/10.1023/B:JOGO.0000006653.60256.f6

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  • DOI: https://doi.org/10.1023/B:JOGO.0000006653.60256.f6

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