Abstract
Global and mid-range approximation concepts are used in engineering optimisation in those cases were the commonly used local approximations are not available or applicable. In this paper the response surface method is discussed as a method to build both global and mid-range approximations of the objective and constraint functions. In this method analysis results in multiple design points are fitted on a chosen approximation model function by means of regression techniques. Especially global approximations rely heavily on appropriate choices of the model functions. This builds a serious bottleneck in applying the method. In mid-range approximations the model selection is much less critical. The response surface method is illustrated at two relatively simple design problems. For building global approximations a new method was developed by Sacks and co-workers, especially regarding the nature of computer experiments. Here, the analysis results in the design sites are exactly predicted, and model selection is more flexible compared to the response surface method. The method will be applied to an analytical test function and a simple design problem. Finally the methods are discussed and compared.
Similar content being viewed by others
References
Barthelemy JFM, Haftka RT (1993) Recent advances in approximation concepts for optimum structural design. Structural Optimization 5(3):129–144
Bernardo MC, Buck R, Liu L, Nazaret WA, Sacks J, Welch WJ (1992) Integrated circuit design optimization using a sequential strategy. IEEE Transactions on computer-aided design 11(3):361–372
Box GEP, Draper NR (1987) Empirical model building and response surfaces. John Wiley, New York
Currin C, Mitchell T, Morris M, Ylvisaker D (1991) Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments. Journal of the American Statistical Association 86(416):953–963
Etman LFP (1994) Design and analysis of computer experiments: The method of sacks et al. Technical Report WFW 94.098, Eindhoven University of Technology
Fleury C (1978) Automatic dimensioning of elastic structures. PhD thesis, University of Liege
Lancaster P, Salkauskas K (1981) Surfaces generated by moving least squares methods. Math. Comput. 37:141–158
Sacks J, Schiller SB, Welch J (1989) Designs for computer experiments. Technometrics 31(1):41–47
Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer exeriments. Statistical Science 4(4):409–435
Svanberg K (1987) The method of moving asymptotes — a new method for structural optimization. International Journal of Numerical Methods in Engineering 24:359–373
Toropov VV, Filatov AA, Polynkin AA (1993) Multiparameter structural optimization using fem and multipoint explicit approximations. Structural Optimization 6:7–14
Welch WJ, Buck RJ, Sacks J, Wynn HP, Mitchell TJ, Morris MD (1992) Screening, predicting, and computer exeriments. Technometrics 34(1):15–25
Welch WJ, Sacks J (1991) A system for quality improvement via computer experiments. Commun. statist.-theory meth. 20(2):477–495
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schoofs, A.J.G., van Houten, M.H., Etman, L.F.P. et al. Global and mid-range function approximation for engineering optimization. Mathematical Methods of Operations Research 46, 335–359 (1997). https://doi.org/10.1007/BF01194860
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01194860