Kriging surrogate model with coordinate transformation based on likelihood and gradient

Nobuo Namura (), Koji Shimoyama () and Shigeru Obayashi ()
Additional contact information
Nobuo Namura: Tohoku University
Koji Shimoyama: Tohoku University
Shigeru Obayashi: Tohoku University

Journal of Global Optimization, 2017, vol. 68, issue 4, No 8, 827-849

Abstract: 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.

Keywords: Kriging model; Efficient global optimization; Coordinate transformation; Likelihood; Eigenvalue decomposition; Airfoil design (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s10898-017-0516-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:68:y:2017:i:4:d:10.1007_s10898-017-0516-y

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-017-0516-y

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().