The normal score transformation applied to a multi-univariate method of global optimization | Journal of Global Optimization Skip to main content
Springer Nature Link
Log in

The normal score transformation applied to a multi-univariate method of global optimization

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

Nonparametric global optimization methods have been developed that determine the location of their next guess based on the rank-transformed objective function evaluations rather than the actual function values themselves. Another commonly-used transformation in nonparametric statistics is the normal score transformation. This paper applies the normal score transformation to the multi-univariate method of global optimization. The benefits of the new method are shown by its performance on a standard set of global optimization test problems. The normal score transformation yields a method that gives equivalent searches for any monotonic transformation of the objective function.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kushner, H. J. (1963), A New Method of Locating the Maximum of an Arbitrary Multipeak Curve in the Presence of Noise, Proceedings of the Joint Automatic Control Conference, pp. 69–79.

  2. Stuckman, B. E. (1988), A Global Search Method for Optimizing Nonlinear Systems, IEEE Trans. Systems Man & Cybernetics 18 (6), 965–977.

    Google Scholar 

  3. Perttunen, C. D. (1989), A Nonparametric Global Optimization Method Using the Rank Transformation, Proceedings of the 28th IEEE Conference on Decision and Control, Tampa, FL, pp. 888–893.

  4. Perttunen, C. D. and B. E. Stuckman (1989) The Rank Transformation Applied to a Multi-Univariate Method of Global Optimization, Proceedings of the IEEE International Conference on Systems Engineering, Dayton, OH, pp. 217–220.

  5. Dixon, L. C. W. and G. P. Szegö (1978), The Optimisation Problem: An Introduction, in L. C. W. Dixon and G. P. Szegö (eds.), Towards Global Optimisation 2, North-Holland.

  6. van der, Waerden, B. L. (1953), Order Tests for the Two-Sample Problem and Their Power, Indagationes Mathematicae 15, 303–316.

    Google Scholar 

  7. Conover, W. J. (1980), Practical Nonparametric Statistics, Wiley, New York.

    Google Scholar 

  8. MINITAB Reference Manual, Release 6, Minitab Inc., State College, PA, 1988.

  9. Hartman, J. K. (1972), Rep. NP55HH72051A, Naval Postgraduate School, Monterey.

    Google Scholar 

  10. Branin, F. K. (1972), A Widely Convergent Method for Finding Multiple Solutions of Simultaneous Non-Linear Equations, IBM Journal of Research & Development, pp. 504–522.

  11. Goldstein, A. A. and I. F. Price (1971), On Descent from Local Minima, Mathematics of Computation 25, No. 115.

Download references

Author information

Authors and Affiliations

  1. Dept. of Electrical Engineering, University of Louisville, 40292, Louisville, KY, U.S.A.

    Cary D. Perttunen & Bruce E. Stuckman

Authors
  1. Cary D. Perttunen
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Bruce E. Stuckman
    View author publications

    You can also search for this author inPubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Perttunen, C.D., Stuckman, B.E. The normal score transformation applied to a multi-univariate method of global optimization. J Glob Optim 2, 167–176 (1992). https://doi.org/10.1007/BF00122053

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00122053

Key words