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Kriging surrogate model with coordinate transformation based on likelihood and gradient

Author

Listed:
  • Nobuo Namura

    (Tohoku University)

  • Koji Shimoyama

    (Tohoku University)

  • Shigeru Obayashi

    (Tohoku University)

Abstract

The Kriging surrogate model, which is frequently employed to apply evolutionary computation to real-world problems, with a coordinate transformation of the design space is proposed to improve the approximation accuracy of objective functions with correlated design variables. The coordinate transformation is conducted to extract significant trends in the objective function and identify the suitable coordinate system based on either one of two criteria: likelihood function or estimated gradients of the objective function to each design variable. Compared with the ordinary Kriging model, the proposed methods show higher accuracy in the approximation of various test functions. The proposed method based on likelihood shows higher accuracy than that based on gradients when the number of design variables is less than six. The latter method achieves higher accuracy than the ordinary Kriging model even for high-dimensional functions and is applied to an airfoil design problem with spline curves as an example with correlated design variables. This method achieves better performances not only in the approximation accuracy but also in the capability to explore the optimal solution.

Suggested Citation

  • Nobuo Namura & Koji Shimoyama & Shigeru Obayashi, 2017. "Kriging surrogate model with coordinate transformation based on likelihood and gradient," Journal of Global Optimization, Springer, vol. 68(4), pages 827-849, August.
    • Handle: RePEc:spr:jglopt:v:68:y:2017:i:4:d:10.1007_s10898-017-0516-y
    DOI: 10.1007/s10898-017-0516-y
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    References listed on IDEAS

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    1. Haitao Liu & Shengli Xu & Ying Ma & Xiaofang Wang, 2015. "Global optimization of expensive black box functions using potential Lipschitz constants and response surfaces," Journal of Global Optimization, Springer, vol. 63(2), pages 229-251, October.
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    Cited by:

    1. Krishnan, K V Vishal & Ganguli, Ranjan, 2021. "Multi-fidelity analysis and uncertainty quantification of beam vibration using co-kriging interpolation method," Applied Mathematics and Computation, Elsevier, vol. 398(C).
    2. Yaohui Li & Junjun Shi & Zhifeng Yin & Jingfang Shen & Yizhong Wu & Shuting Wang, 2021. "An Improved High-Dimensional Kriging Surrogate Modeling Method through Principal Component Dimension Reduction," Mathematics, MDPI, vol. 9(16), pages 1-18, August.
    3. Junjun Shi & Jingfang Shen & Yaohui Li, 2021. "High-Precision Kriging Modeling Method Based on Hybrid Sampling Criteria," Mathematics, MDPI, vol. 9(5), pages 1-25, March.

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