An adaptive framework for costly black-box global optimization based on radial basis function interpolation

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.