Finding optimal points for expensive functions using adaptive RBF-based surrogate model via uncertainty quantification

Ray-Bing Chen, Yuan Wang and C. F. Jeff Wu ()
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Ray-Bing Chen: National Cheng Kung University
Yuan Wang: Wells Fargo
C. F. Jeff Wu: Georgia Institute of Technology

Journal of Global Optimization, 2020, vol. 77, issue 4, No 9, 919-948

Abstract: Abstract Global optimization of expensive functions has important applications in physical and computer experiments. It is a challenging problem to develop efficient optimization scheme, because each function evaluation can be costly and the derivative information of the function is often not available. We propose a novel global optimization framework using adaptive radial basis functions (RBF) based surrogate model via uncertainty quantification. The framework consists of two iteration steps. It first employs an RBF-based Bayesian surrogate model to approximate the true function, where the parameters of the RBFs can be adaptively estimated and updated each time a new point is explored. Then it utilizes a model-guided selection criterion to identify a new point from a candidate set for function evaluation. The selection criterion adopted here is a sample version of the expected improvement criterion. We conduct simulation studies with standard test functions, which show that the proposed method has some advantages, especially when the true function has many local optima. In addition, we also propose modified approaches to improve the search performance for identifying optimal points.

Keywords: Expected improvement; Markov chain Monte Carlo; Radial basis functions; Sequential design (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-020-00916-w

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