A New Framework for Combining Global and Local Methods in Black Box Optimization

We propose a new framework for the optimization of computationally expensive black box problems, where neither closed-form expressions nor derivatives of the objective functions are available. The proposed framework consists of two procedures. The first constructs a global metamodel to approximate the underlying black box function and explores an unvisited area to search for a global solution; the other identifies a promising local region and conducts a local search to ensure local optimality. To improve the global metamodel, we propose a new method of generating sampling points for a wide class of metamodels, such as kriging and Radial Basis Function models. We also develop a criterion for switching between the global and local search procedures, a key factor affecting practical performance. Under a set of mild regularity conditions, the algorithm converges to the global optimum. Numerical experiments are conducted on a wide variety of test problems from the literature, demonstrating that our method is competitive against existing approaches.