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Hybrid Meta-Model Based Design Space Differentiation Method for Expensive Problems

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Abstract

In this work, a hybrid meta-model based design space differentiation (HMDSD) method is proposed for practical problems. In the proposed method, an iteratively reduced promising region is constructed using the expensive points, with two different search strategies respectively applied inside and outside the promising region. Besides, the hybrid meta-model strategy applied in the search process makes it possible to solve the complex practical problems. Tested upon a serial of benchmark math functions, the HMDSD method shows great efficiency and search accuracy. On top of that, a practical lightweight design demonstrates its superior performance.

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References

  1. Venkataraman, S. and Haftka, R.T., Structural optimization complexity:what has Moore’s law done for us?. Structural and Multidisciplinary Optimization, 2004, 28: 375–387.

    Article  Google Scholar 

  2. Myers, R.H. and Montgomery, D.C., Response Surface Methodology: Process and Product Optimization using Designed Experiments. Toronto.: John Wiley & Sons, INC, 2002.

    MATH  Google Scholar 

  3. Krige, D.G., A Statistical Approach to Some Mine Valuation and Allied Problems on the Witwatersrand. Master’s thesis, University of the Witwatersrand, South Africa, 1951.

  4. Cressie, N., Geostatistics. The American Statistician, 1989, 43(4): 197–202.

    Google Scholar 

  5. Sacks, J., Welch, W.J., Mitchell, T.J. and Wynn, H.P., Design and analysis of computer experiments. Statistical Science, 1989a, 4(4): 409–423.

    Article  MathSciNet  Google Scholar 

  6. Hardy, R.L., Multiquadratic equations of topography and other irregular surfaces. Journal of Geophysical Research Atimospheres, 1971, 76: 1905–1915.

    Article  Google Scholar 

  7. Friedman, J.H., Multivariate Adaptive Regression Splines. The Annals of Statistics, 1991, 19(1): 1–67.

    Article  MathSciNet  Google Scholar 

  8. Clarke, S.M., Griebsch, J.H. and Simpson, T.W., Analysis of support vector regression for approximation of complex engineering analyses. Transactions of ASME, Journal of Mechanical Design, 2005, 127(6): 1077–1087.

    Article  Google Scholar 

  9. Barton, R.R., Metamodeling: a state of the art review. In: Proceedings of the 1994 Winter Simulation Conference, edited by Tew, J.D., Manivannan, S., Sadowski, D.A. and Seila, A.F., 1994: 237–244.

  10. Simpson, T. W., Mauery, T.M., Korte, J. J. and Mistree, F., Comparison of response surface and kriging models for multidisciplinary design optimization. In: in AIAA paper 98-4758. 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, 1998: 359–379.

  11. Simpson, T.W., Peplinski, J.D., Koch, P.N. and Allen, J.K., Metamodels for computer-based engineering design: survey and recommendations. Engineering with Computers, 2001, 17: 129–150.

    Article  Google Scholar 

  12. Hussain, M.F., Barton, R.R. and Joshi, S.B., Metamodeling: radial basis functions, versus polynomials. European Journal of Operational Research, 2002, 138: 142–154.

    Article  Google Scholar 

  13. Chen, V.C.P., Tsui, K.L., Barton, R.R. and Meckesheimer, M., A review on design, modeling and applications of computer experiments. IIE Transactions, 2006, 38: 273–291.

    Article  Google Scholar 

  14. Wang, G.G, and Shan, S., Review of metamodeling techniques in support of engineering design optimization. ASME Journal of Mechanical Design, 2007, 129: 370–80. doi: 10.1115/1.2429697.

    Article  Google Scholar 

  15. Jones, D.R., Schonlau, M. and Welch, W., Efficient global optimization of expensive black-box functions. Journal of Global Optimization, 1998, 13: 455–492.

    Article  MathSciNet  Google Scholar 

  16. Wang, L.Q., Shan, S, and Wang, G.G., Mode-pursuing sampling method for global optimization on expensive black-box functions. Engineering Optimization, 2004, 36(4): 419–438.

    Article  Google Scholar 

  17. Wang, G.G., Dong, Z. and Aitchisonc, P., Adaptive response surface method - a global optimization scheme for approximation-based design problems. Engineering Optimization, 2001, 33: 707–733.

    Article  Google Scholar 

  18. Balabanov, V.O., Giunta, A.A., Golovidov, O., Grossman, B., Mason, W.H., Watson, L.T. and Haftka, R.T., Reasonable design space approach to response surface approximation. Journal of Aircraft, 1999, 36(1): 308–315. doi: 10.2514/2.2438.

    Article  Google Scholar 

  19. Wang, G.G. and Simpson, T.W., Fuzzy clustering based hierarchical metamodeling for design space reduction and optimization. Engineering Optimization, 2004, 36(3): 313–335.

    Article  Google Scholar 

  20. Gu, J., Li, G.Y. and Dong, Z., Hybrid and adaptive meta-model-based global optimization. Engineering Optimization, 2012, 44(1): 87–104.

    Article  Google Scholar 

  21. Alexandrov, N.M., Dennis, J.E., Lewis, R.M. and Torczont, V., A trust region framework for managing the use of approximation models in optimization. Structural Optimization, 1998, 15(1): 16–23.

    Article  Google Scholar 

  22. Byrd, R.H., Robert, B.S. and Gerald, A.S., A trust region algorithm for nonlinearly constrained optimization. SIAM Journal on Numerical Analysis, 1987, 24(5): 1152–1170.

    Article  MathSciNet  Google Scholar 

  23. Fadel, G.M., Riley, M.F. and Barthelemy, J.M., Two point exponential approximation method for structural optimization. Structural Optimization, 1990, 2: 117–124.

    Article  Google Scholar 

  24. Fadel, G.M., and Cimtalay, S., Automatic evaluation of move-limits in structural optimization. Structural Optimization, 1993, 6: 233–237.

    Article  Google Scholar 

  25. Grignon, P. and Georges, M.F., Fuzzy move limit evaluation in structural optimization. In: The 5th AIAA/NASA/USAF/ISSMO Fifth Symposium on Multidisciplinary Analysis and Optimization. Panama City, FL, 1994, 7–9 September, AIAA-94-4281.

  26. Younis, A., Xu, R. and Dong, Z., Approximated unimodal region elimination based global optimization method for engineering design. In: Proceedings of the ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDET/CIE, Las Vegas, Nevada, USA, 2007.

  27. Fang, K.T., Li, R. and Sudjianto, A., Design and Modeling for Computer Experiments(9 vols). London, New York: Taylor & Francis Group, LLC., 2006.

    MATH  Google Scholar 

  28. Sttinberg, H.A., Generalized Quota Sampling. Nuclear Science and Engineering, 1963, 15: 142–145.

    Article  Google Scholar 

  29. Mckay, M.D., Beckman, R.J. and Conover, W.J., A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 1979, 42(1): 55–61.

    Article  MathSciNet  Google Scholar 

  30. Xu, S. and Grandhi, R.V., Multipoint global approximation for reducing the response surface model development cost in optimization. In: 1-st ASMO UK/ISMMO Conf. on Engineering Design Optimization, Illkey, UK, 1999.

  31. Shin, Y.S. and Grankhi, R.V., A global structural optimization technique using an interval method. Structural and Multidisciplinary Optimization, 2001, 22: 351–363.

    Article  Google Scholar 

  32. Adorio, E.P., MVF - Multivariate Test Functions Library in C for Unconstrained Global Optimization. 2005, www.geocities.ws/eadorio/mvf.pdf.

  33. Hedar, A.R., Test functions for unconstrained global optimization. In: http://www-optima.amp.i.kyotou.ac.jp/member/student/hedar/Hedar_files/TestGO_files/Page2904.htm.

  34. Sacks, J., Welch, W.J., Mitchell, T.J. and Wynn, H.P., Design and analysis of computer experiments. Statistical Science, 1989b, 4(4): 409–423.

    Article  MathSciNet  Google Scholar 

  35. Sacks, J., Schiller, S.B. and Welch, W., Designs for computer experiments. Technometrics, 1989, 31(1): 41–47.

    Article  MathSciNet  Google Scholar 

  36. Box, G.E.P. and Wilson, K.B., On the experimental attainment of optimum conditions. Journal of the Royal Statistical Society, 1951b, 13(1) (Series B): 1–45.

    MathSciNet  MATH  Google Scholar 

  37. Box, G.E.P. and Wilson, K.B., On the experimental attainment of optimum conditions. Journal of the Roal Statistical Society. Series B(Methodological), 1951a, 13(1): 1–45.

    MathSciNet  MATH  Google Scholar 

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Correspondence to Jichao Gu.

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Project supported by the Plan for the growth of young teachers, the National Natural Science Foundation of China (No. 51505138), the National 973 Program of China (No. 2010CB328005), Outstanding Youth Foundation of NSFC (No. 50625519) and Program for Changjiang Scholars.

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Gan, N., Li, G. & Gu, J. Hybrid Meta-Model Based Design Space Differentiation Method for Expensive Problems. Acta Mech. Solida Sin. 29, 120–132 (2016). https://doi.org/10.1016/S0894-9166(16)30101-X

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  • DOI: https://doi.org/10.1016/S0894-9166(16)30101-X

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