An adaptive framework for costly black-box global optimization based on radial basis function interpolation
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In this paper, we present a framework for the global optimization of costly black-box functions using response surface (RS) models. The main iteration steps of the framework which is referred to as the Adaptive Framework using Response Surface (ADFRS) consist of two phases. In the first phase, we implement a mixture of local searches and global searches to get a rough solution before the number of consecutive unsuccessful iterations exceeds a user-defined threshold. A procedure is embedded into this phase to check whether a small neighborhood of a global minimizer of the current RS model is fully explored or not, and then determine the search type (global search or local search) to be implemented next. Before performing a local search or a global search, the distance between the two global minimizers of the last and the current response surface models is checked, and the current global minimizer will be taken as the new evaluation point if this distance is very small. This strategy can quickly return a good evaluation point. In the second phase, we perform pure local search in the vicinity of the current best point to search for a better solution. Local searches are only implemented in the vicinities of the global minima of the RBF models in our scheme. Numerical experiments on some test problems are conducted to show the effectiveness of the present algorithm.
KeywordsGlobal optimization Costly black-box functions Response surface model Radial basis function interpolation Local search Global search
We would like to thank the two anonymous referees for their very helpful comments and insightful suggestions that have helped improve the presentation of this paper greatly.
- 7.Dixon, L.C.W., Szegö, G.: The global optimization problem: an introduction. In: Dixon, L.C.W., Szegö, G. (eds.) Towards Global Optimization 2, pp. 1–15. North-Holland, Amsterdam (1978)Google Scholar
- 8.Emmerich, M., Giotis, A., Özdemir, M., Bäck, T., Giannakoglou, K.: Metamodel-assisted evolution strategies. In: Parallel Problem Solving from Nature VII. Springer, pp. 361–370 (2002)Google Scholar
- 13.Jones, D.R.: Global optimization with response surfaces. In: Presented at the Fifth SIAM Conference on Optimization, Victoria, Canada (1996)Google Scholar
- 18.Powell, M.J.D.: The theory of radial basis function approximation in 1990. In: Light, W. (ed.) Advances in Numerical Analysis, Volume 2: Wavelets, Subdivision Algorithms and Radial Basis Functions, pp. 105–210. Oxford University Press, Oxford (1992)Google Scholar
- 22.Powell, M.J.D.: On trust region methods for unconstrained minimization without derivatives, Technical Report. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK (2002)Google Scholar
- 31.Törn, A., Zilinskas, A.: Glob. Optim. Springer, Berlin (1989)Google Scholar