Abstract
This paper presents a taxonomy of existing approaches for using response surfaces for global optimization. Each method is illustrated with a simple numerical example that brings out its advantages and disadvantages. The central theme is that methods that seem quite reasonable often have non-obvious failure modes. Understanding these failure modes is essential for the development of practical algorithms that fulfill the intuitive promise of the response surface approach.
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Alexandrov, N.M., Lewis, R.M., Gumbert, C. R., Green, L.L., and Newman, P.A. Optimization with variable-fidelity models applied to wing design. In Proceedings of the 38 th Aerospace Sciences Meeting & Exhibit, January 2000. AIAA Paper 2000–0841.
American Institute of Aeronautics and Astronautics. Proceedings of the 8 th AIAA / USAF / NASA / ISMMO Symposium of Multidisciplinary Analysis & Optimization, September 2000. Available on CD-ROM from the AIAA at http://www.aiaa.org.
Booker, A. J. Examples of surrogate modeling of computer simulations. Presented at the ISSMO/NASA First Internet Conference on Approximations and Fast Reanalysis in Engineering Optimization, June 14-27, 1998. Conference abstract available at http://www.blarg.net/~mandoid/webcon/. Full text in pdf format available by sending email to andrew.j.booker@boeing.com.
Booker, A. J., Dennis, J.E. Jr., Frank, P.D., Serafini, D.B., Torczon, V. and Trosset M.W. (1999). A rigorous framework for optimization of expensive functions by surrogates. Structural Optimization, 17, 1–13.
Cox, D. D and John S. (1997). SDO: A statistical method for global optimization. In N. Alexandrov, and M.Y. Hussaini, editors, Multidisciplinary Design Optimization: State of the Art, 315–329. SIAM, Philadelphia.
Dennis, J.E. Jr. and Torczon, V. (1991). Direct search methods on parallel machines. SIAM Journal of Optimization, 1, 448–474.
L.C.W. Dixon and G.P. Szego (1978). The global optimisation problem: an introduction. In L.C.W. Dixon and G.P. Szego, editors, Towards Global Optimisation 2, 1–15. North Holland, New York.
J.F. Elder IV (1992). Global R d optimization when probes are expensive: the GROPE algorithm. Proceedings of the 1992 IEEE International Conference on Systems, Man, and Cybernetics, Vol. 1, 577–582, Chicago.
Gutmann, H.M. (2001). A radial basis function method for global optimization. Journal of Global Optimization, 19(3) pp. 201–227.
Jones, D.R., Schonlau, M. and Welch W.J. (1998). Efficient global optimization of expensive black-box functions. Journal of Global Optimization, 13, 455–492.
J. Koehler and A. Owen. (1996). Computer experiments. In S. Ghosh and C.R. Rao, editors, Handbook of Statistics, 13: Design and Analysis of Experiments, 261–308. North Holland, New York.
H.J. Kushner (1964). A new method of locating the maximum point of an arbitrary multipeak curve in the presence of noise. Journal of Basic Engineering, 86, 97–106.
M. Locatelli (1997). Bayesian algorithms for one-dimensional global optimization. Journal of Global Optimization 10, 57–76.
J. Mockus. Application of Bayesian approach to numerical methods of global and stochastic optimization. Journal of Global Optimization, 4, 347–365, 1994.
C. Perttunen (1991). A computational geometric approach to feasible region division in constrained global optimization. Proceedings of the 1991 IEEE Conference on Systems, Man, and Cybernetics.
J. Sacks, W. J. Welch, T.J. Mitchell, and H. P. Wynn (1989). Design and analysis of computer experiments (with discussion). Statistical Science 4, 409–435.
Sasena, M.J., Papalambros, P.Y. and Goovaerts, P. Metamodeling sampling criteria in a global optimzation framework. In Proceedings of the 8 th AIAA / USAF / NASA / ISMMO Symposium of Multidisciplinary Analysis & Optimization, September 2000. AIAA Paper 2000–4921.
Schonlau, M., Welch, W.J. and Jones, D.R. Global versus local search in constrained optimization of computer models. In N. Flournoy, W.F. Rosenberger, and W.K. Wong, editors, New Developments and Applications in Experimental Design, Institute of Mathematical Statistics. Also available as Technical Report RR-97-11, Institute for Improvement in Quality and Productivity, University of Waterloo, Waterloo, Ontario, CANADA, December 1997.
B.E. Stuckman (1988). A global search method for optimizing nonlinear systems. IEEE Transactions on Systems, Man, and Cybernetics 18, 965–977.
Theil, H. (1971). Principles of Econometrics. John Wiley, New York.
Torn, A. and Zilinskas, A. (1987). Global Optimization, Springer, Berlin.
A. Zilinskas (1992). A review of statistical models for global optimization. Journal of Global Optimization 2, 145–153.
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Jones, D.R. A Taxonomy of Global Optimization Methods Based on Response Surfaces. Journal of Global Optimization 21, 345–383 (2001). https://doi.org/10.1023/A:1012771025575
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DOI: https://doi.org/10.1023/A:1012771025575