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A Study on the Construction of Response Surfaces for Design Optimization

최적설계를 위한 반응표면의 생성에 관한 연구

  • Published : 2000.06.01

Abstract

Gradient-based optimization methods are inefficient in applications which require expensive function evaluations, and useless in applications where objective and/or constraint functions are 'noisy' due to modeling and cumulative numerical inaccuracy since gradient evaluation results cannot be reliable. Moreover, it is difficult to be integrated with commercial analysis software, and they cannot be employed when only experimental analysis results are available. In this research an optimization program based on a response surface method has been developed to overcome the aforementioned difficulties. Various methods for design of experiments and new proposed approximation models are implemented in the program. The effectiveness of the optimization program is tested on several test problems and results are discussed.

Keywords

Optimization;Response Surface Method;Design of Experiments;Approximation Model

References

  1. Rikard, R., 1993, 'Elaboration of Optimal Design Model for Objects from Data of Experiments,' In Pederson, P. (ed) Optimal Design with Advanced Materials, Amsterdam, Elsevier, pp. 148-162
  2. Guinta, A. A., Dudley, J. M., Narducci, R., Grossman, B., Haftka, R. T. and Mason, W. H., 1994, 'Noisy Aerodynamic Response and Smooth Approximations in HSCT Design,' HPCCP related papers, Virginia Polytechnic Institute and State University
  3. Miller, A. J. and Nam-ky Nguyen, 1994, 'A Fedorov Exchange Algorithm for D-optimal Designs,' Applied Statistics, 43, No.4, pp. 669-678 https://doi.org/10.2307/2986264
  4. Michalewicz, Z., 1996, Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag Berlin Heidelberg, New York
  5. Vanderplaats, G. N., 1985, 'ADS-A FORTRAN Program for Automated Design Synthesis,' NASA CR 172460
  6. Schittkowski, K., 1987, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag Berlin Heidelberg, New York
  7. ADAMS Seminar Series-DOE and Optimization using ADAMS/View 8.0, Mechanical Dynamics Inc., Ann Arbor, MI
  8. Vanderplaats, G. N., 1995, DOT-Design Optimization Tools Users Manual, Vanderplaats Research & Development, Inc.
  9. Myers, R. H. and Montgomery, D. C, 1995, Response Surface Methodology-Process and Product Optimization Using Designed Experiments, John Wiley & Sons, New York
  10. Box, G. E. P. and Wilson, K. B., 1951, 'On the Experimental Attainment of Optimum Conditions,' Journal of the Royal Statistical Society, Series B., 13, pp. 1-14
  11. Box, M. J. and Draper, N. R., 1971, 'Factorial Designs, the |X'X| Criterion and Some Related Matters,' Technometrics, 13, pp. 731-742 https://doi.org/10.2307/1266950
  12. Mitchell, T. J., 1974, 'An Algorithm for the Construction of D-optimal Designs,' Technometrics, 20, pp. 203-210 https://doi.org/10.2307/1267940
  13. Nguyen, N. K. and Miller, F. L., 1992, 'A Review of Some Exchange Algorithms for Construction Discrete D-optimal Designs,' Computational Statistics & Data Analysis, North-Holland. 14, pp. 489-498 https://doi.org/10.1016/0167-9473(92)90064-M
  14. Roux, W. J., Stander Nielen and Haftka, R. T., 1996, 'Response Surface Approximations for Structural Optimization,' AIAA Paper 96-4042, AIAA/NASA/ISSMO, Symposium on Multidisciplinary Analysis and Optimization, 6th, Bellevue, WA, Sept. 4-6