Journal of Global Optimization

, Volume 41, Issue 3, pp 447–464

An adaptive radial basis algorithm (ARBF) for expensive black-box global optimization


DOI: 10.1007/s10898-007-9256-8

Cite this article as:
Holmström, K. J Glob Optim (2008) 41: 447. doi:10.1007/s10898-007-9256-8


Powerful response surface methods based on kriging and radial basis function (RBF) interpolation have been developed for expensive, i.e. computationally costly, global nonconvex optimization. We have implemented some of these methods in the solvers rbfSolve and EGO in the TOMLAB Optimization Environment ( In this paper we study algorithms based on RBF interpolation. The practical performance of the RBF algorithm is sensitive to the initial experimental design, and to the static choice of target values. A new adaptive radial basis interpolation (ARBF) algorithm, suitable for parallel implementation, is presented. The algorithm is described in detail and its efficiency is analyzed on the standard test problem set of Dixon–Szegö. Results show that it outperforms the published results of rbfSolve and several other solvers.


Global optimization Expensive function CPU-intensive Costly function Mixed-integer Nonconvex Software Black-box Derivative-free Response surface Radial basis functions Surrogate model Response surface Splines 

Copyright information

© Springer Science+Business Media, LLC. 2007

Authors and Affiliations

  1. 1.Department of Mathematics and PhysicsMälardalen UniversityVästeråsSweden

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