Abstract
The Kriging surrogate model, which is frequently employed to apply evolutionary computation to real-world problems, with coordinate transformation of design space is proposed to improve the approximation accuracy of objective functions with correlated design variables. Eigenvalue decomposition is used to extract significant trends in the objective function from its gradients and identify suitable coordinates. Comparing with the ordinary Kriging model, the proposed method shows higher accuracy in the approximation of two-dimensional test functions and reduces the computational cost to achieve the global optimization. In the application to an airfoil design problem with spline curves as correlated design variables, the proposed method achieves better performances not only in the approximation accuracy but also the ability to explore the optimal solution.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Queipo, N.V., Haftka, R.T., Shyy, W., Goel, T., Vaidyanathan, R., Tucker, P.K.: Surrogate-Based Analysis and Optimization. Progress in Aerospace Sciences 41, 1–28 (2005)
Namura, N., Obayashi, S., Jeong, S.: Efficient global optimization of vortex generators on a super critical infinite-wing using kriging-based surrogate models. In: 52nd AIAA Aerospace Sciences Meeting, AIAA-2014-0904. National Harbor (2014)
Forrester, A.I.J., Keane, A.J.: Recent Advances in Surrogate-Based Optimization. Progress in Aerospace Sciences 45, 50–79 (2009)
Regis, R.G., Shoemaker, A.S.: Local Function Approximation in Evolutionary Algorithms for the Optimization of Costly Functions. IEEE Trans. on Evolutionary Computation 8, 490–505 (2004)
Broomhead, D.S., Lowe, D.: Multivariate Functional Interpolation and Adaptive Networks. Complex Systems 2, 321–355 (1988)
Jones, D.R., Schonlau, M., Welch, W.J.: Efficient Global Optimization of Expensive Black-Box Function. J. of Global Optimization 13, 455–492 (1998)
Joseph, V.R., Hung, Y., Sudjianto, A.: Blind Kriging: a New Method for Developing Metamodels. ASME J. of Mechanical Design 130, 031102-1-8 (2008)
Namura, N., Shimoyama, K., Jeong, S., Obayashi, S.: Kriging/RBF-Hybrid Response Surface Methodology for Highly Nonlinear Functions. J. of Computational Science and Technology 6, 81–96 (2012)
Mullur, A.A., Messac, A.: Extended radial basis functions: more flexible and effective metamodeling. In: 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization. Conference, AIAA-2004–4573. Albany (2004)
Xiong, Y., Chen, W., Apley, D., Ding, X.: A Non-Stationary Covariance-Based Kriging Method for Metamodeling in Engineering Design. International J. for Numerical Methods in Engineering 71, 733–756 (2007)
Samareh, J.A.: Aerodynamic shape optimization based on free-form deformation. In: 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA-2004-4630. Albany (2004)
McKay, M.D., Beckman, R.J., Conover, W.J.: A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code. Technometrics 21, 239–245 (1979)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Trans. on Evolutionary Computation 6, 182–197 (2002)
Jeong, S., Yamamoto, K., Obayashi, S.: Kriging-based probabilistic method for constrained multi-objective optimization problem. In: AIAA 1st Intelligent Systems Technical Conference, AIAA-2004-6437. Chicago (2004)
Constantine, P.G., Dow, E., Wang, Q.: Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces. SIAM J. on Scientific Computing 36, A1500–A1524 (2014)
Rosenbrock, H.H.: An Automatic Method for Finding the Greatest or Least Value of a Function. The Computer J. 3, 175–184 (1960)
Drela, M.: XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils. In: Mueller, T.J. (ed.) Low Reynolds Number Aerodynamics. Lecture Notes in Engineering, pp. 1–12. Springer-Verlag, New York (1989)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Namura, N., Shimoyama, K., Obayashi, S. (2015). Kriging Surrogate Model Enhanced by Coordinate Transformation of Design Space Based on Eigenvalue Decomposition. In: Gaspar-Cunha, A., Henggeler Antunes, C., Coello, C. (eds) Evolutionary Multi-Criterion Optimization. EMO 2015. Lecture Notes in Computer Science(), vol 9018. Springer, Cham. https://doi.org/10.1007/978-3-319-15934-8_22
Download citation
DOI: https://doi.org/10.1007/978-3-319-15934-8_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15933-1
Online ISBN: 978-3-319-15934-8
eBook Packages: Computer ScienceComputer Science (R0)