Abstract
To effectively tackling high dimensional, expensive, black-box (HEB) problems, this paper proposes a modified radial basis function based high dimensional model representation method using proportional sampling strategy (denoted as RBF-HDMR-PS). Different from the standard RBF-HDMR, the proposed RBF-HDMR-PS sequentially adds first order sample points with a predetermined proportion coefficient to effectively construct each component RBF, which avoids the stochastic influence of random sampling process in RBF-HDMR. The proposed RBF-HDMR-PS using different proportion coefficients is tested through two benchmark numerical problems with highly nonlinear first order components for comparing with RBF-HDMR. A best proportion coefficient is chosen and integrated into RBF-HDMR-PS. The comparison results show that RBF-HDMR-PS outperforms RBF-HDMR in terms of approximation accuracy.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant No. 51105040, 51675047, 11372036), Aeronautic Science Foundation of China (Grant No. 2015ZA72004), and Fundamental Research Fund of Beijing Institute of Technology (Grant No. 20130142008).
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Li, X., Long, T., Gary Wang, G., Hajikolaei, K.H., Shi, R. (2018). RBF-Based High Dimensional Model Representation Method Using Proportional Sampling Strategy. In: Schumacher, A., Vietor, T., Fiebig, S., Bletzinger, KU., Maute, K. (eds) Advances in Structural and Multidisciplinary Optimization. WCSMO 2017. Springer, Cham. https://doi.org/10.1007/978-3-319-67988-4_18
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DOI: https://doi.org/10.1007/978-3-319-67988-4_18
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