Selection of a covariance function for a Gaussian random field aimed for modeling global optimization problems

Anatoly Zhigljavsky1, Antanas Žilinskas2
1School of Mathematics, Cardiff University, Cardiff, UK
2Institute of Data Science and Digital Technologies, Vilnius University, Vilnius, Lithuania

Tóm tắt

Từ khóa


Tài liệu tham khảo

Knowles, J., Corne, D., Reynolds, A.: Noisy multiobjective optimization on a budget of 250 evaluations. In: Ehrgott, M., et al. (eds.) Lecture Notes in Computer Science, vol. 5467, pp. 36–50. Springer, New York (2009)

Loh, W.-L., Lam, T.-K.: Estimating structured correlation matrices in smooth Gaussian random field models. Ann. Stat. 28, 880–904 (2000)

Mockus, J.: Bayesian Approach to Global Optimization. Kluwer Academic Publishers, Dordrecht (1988)

Pepelyshev, A.: Fixed-domain asymtotics of the maximum likelihood estiomator and the gaussian process approach for deterministic models. Stat. Methodol. 8(4), 356–362 (2011)

Sacks, J., Schiller, S.B., Welch, W.J.: Designs for computer experiments. Technometrics 31(1), 41–47 (1989)

Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P.: Design and analysis of computer experiments. Stat. Sci. 4, 409–423 (1989)

Wanting, X., Stein, M.L.: Maximum likelihood estimation for smooth Gaussian random field model. SIAM/ASA Uncertain. Quantif. 5, 138–175 (2017)

Zhigljavsky, A., Žilinskas, A.: Stochastic Global Optimization. Springer, New York (2008)

Žilinskas, A.: Optimization of one-dimensional multimodal functions, Algorithm AS133. J. R. Stat. Soc. Ser. C 23, 367–385 (1978)

Žilinskas, A.: A statistical model-based algorithm for black-box multi-objective optimisation. Int. J. Syst. Sci. 45(1), 82–92 (2014)

Žilinskas, A., Zhigljavsky, A.: Stochastic global optimization: a review on the occasion of 25 years of Informatica. Informatica 27(2), 229–256 (2016)

Žilinskas, A., Žilinskas, J.: Parallel hybrid algorithm for global optimization of problems occurring in MDS-based visualization. Comput. Math. Appl. 52, 211–224 (2006)