Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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Sequential Approximate Optimization Using Kriging Metamodels

크리깅 모델을 이용한 순차적 근사최적화

  • 신용식 (한양대학교 대학원 기계설계학과) ;
  • 이용빈 (한양대학교 대학원 기계설계학과) ;
  • 류제선 (한양대학교 최적설계신기술연구센터) ;
  • 최동훈 (한양대학교 최적설계신기술연구센터)
  • Published : 2005.09.01
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Abstract

Nowadays, it is performed actively to optimize by using an approximate model. This is called the approximate optimization. In addition, the sequential approximate optimization (SAO) is the repetitive method to find an optimum by considering the convergence of an approximate optimum. In some recent studies, it is proposed to increase the fidelity of approximate models by applying the sequential sampling. However, because the accuracy and efficiency of an approximate model is directly connected with the design area and the termination criteria are not clear, sequential sampling method has the disadvantages that could support an unreasonable approximate optimum. In this study, the SAO is executed by using trust region, Kriging model and Optimal Latin Hypercube design (OLHD). Trust region is used to guarantee the convergence and Kriging model and OLHD are suitable for computer experiment. finally, this SAO method is applied to various optimization problems of highly nonlinear mathematical functions. As a result, each approximate optimum is acquired and the accuracy and efficiency of this method is verified by comparing with the result by established method.

Keywords

References

  1. Schmit, L. A. and Farshi, B., 1974 'Some Approximation Concepts for Stuctural Synthesis,'AIAA Journal, Vol. 12, No.5, pp.692-699 https://doi.org/10.2514/3.49321
  2. Healy, M. J., Kowalik, J. S. and Ransay, J. W., 1974, 'Airplane Engine Selection By Optimization on Surface Fit Approximation,'Journal of Aircraft, Vol.12. No.7,pp.593-599
  3. Roux, W. J., Stander Nielen and Haftkam, R. T., 1998, 'Response Surface Approximations for Structural Optimization,' International Journal for Numerical Methods in Engineering, Vol. 42, pp.517-534 https://doi.org/10.1002/(SICI)1097-0207(19980615)42:3<517::AID-NME370>3.0.CO;2-L
  4. Simpson, T.W., Peplinkski, J., Koch, P. N. and Allen, J. K., 2001, 'Metamodels for Computer Based Engineering Design: Survey and Recommendations,' Engineering with Computers, Vol. 17, No. 2, pp.129-150 https://doi.org/10.1007/PL00007198
  5. Wang, G. G., 2003, 'Adaptive Response Surface Method Using Inherited Latin Hypercube Design Points,' Transactions of The ASME, Vol. 125, pp.210-220 https://doi.org/10.1115/1.1561044
  6. Giunta, A. A., Wojtkiewicz Jr., S. F. and Eldred, M. S., 2003, 'Overview of Modern Design of Experiments Methods for Computational Simulations,' 41th AIAA Aerosqace Sciences Meeting And Exhibit, Reno, NV, AIAA, Jan 6-9, 2003, AIAA-2003-0649
  7. Myers, R. H. and , Montgomery, D. C., 1995, Response Surface Methodology - Process and Product Optimization Using Designed Experiments, John Wiley & Sons. NY
  8. Koehler, J. R. and Owen, A. B., 1996, 'Computer Experiments,' In: Ghosh, S., Rao, C. R. (Des.), Handhbook of Statistics, 13: Design and Analysis of experiments, North-Holland, Amsterdam, pp.261-308
  9. Jin, R., Chen, W. and Simpson, T. W., 2001, 'Comparative Studies of Metamodeling Techniques under Multiple Modeling Criteria,' Journal of Structural and Multidisciplinary Optimization, Vol. 23, No. 1, pp.1-13 https://doi.org/10.1007/s00158-001-0160-4
  10. Fletcher, R., 1987, Practical Method of Optimization,, Johm Wiley & Somns, Chichester
  11. Rodriguez, J. F., Renaud, J. E. and Watson, T., 1998, 'Trust Region Augmented Lagrangian Methods for Sequential Response Surface Approximation and Optimization,'ASME Journal of Mechanical Design, Vol. 120, pp.58-66 https://doi.org/10.1115/1.2826677
  12. Hong, K. J., Kim, M. S. and Choi, D. H., 20010,'Efficient Approximation Method for Constructing Quadratic Response Surface Model,' KSME International Journal, Vol. 15, No. 7. pp.876-888
  13. Jin, R., Chen, W. and Sudjianto A., 2002, 'On Sequential Sampling for Global Metamodeling in Engineering Design,' Proceeding of DETC'02 ASME 2002 Design Engineering Technical Conferences and Computers and Informationn in Engineering Conferences, DETV2002/DAC-32092
  14. Sacks, J., Welch, W. J., Mitchell, T. J. and Wynn, H. P., 1989, 'Design and Analysisof Computer Experiments,' Statistical Science, Vol.4, No.4, pp.409-435 https://doi.org/10.1214/ss/1177012413
  15. McKay, M.H.,Beckman, R.J. and Conover, W.J., 1979, 'A Compaison of Three Methods for Selecting, Values of Input variables in the Analusis of Optput from a Computer Code,' Technometrics, Vol. 21, No. 2, pp.239-245 https://doi.org/10.2307/1268522
  16. Tang, N., 1993, 'Orthogonal Array-Based Latin Hypercubes,' Journal of the American Statistical Association, Vol. 39, pp.95-111
  17. Park, J. S., 1994, 'Optimal Latin-Hupercube Designs for Computer Experiments,' Journal of Statistical Planning and Inference, Vol. 39, pp.95-111 https://doi.org/10.1016/0378-3758(94)90115-5
  18. Morrism, m. D. and Mitchell, T. J., 1995, 'Exploratory designs for Computational Experiments, 'Journal of Statistical Planning and Inferince, Vol. 43, pp. 281-402 https://doi.org/10.1016/0378-3758(94)00035-T
  19. Kim, J. H. Lee, J. S., Lee, H. J. and Koo, B. H., 2003, 'Applications of Micro Genetic Algorithms to Engineering Design Optimization, 'Transactions of the KSME A, Vol.27, No.1, pp.158-166 https://doi.org/10.3795/KSME-A.2003.27.1.158
  20. Vanderplaats, G. N., 1995, DOT-Design Optimization Tools User Manual, Vanderplaats Research & Development, Inc