Combining radial basis function surrogates and dynamic coordinate search in high-dimensional expensive black-box optimization

This article presents the DYCORS (DYnamic COordinate search using Response Surface models) framework for surrogate-based optimization of HEB (High-dimensional, Expensive, and Black-box) functions that incorporates an idea from the DDS (Dynamically Dimensioned Search) algorithm. The iterate is selected from random trial solutions obtained by perturbing only a subset of the coordinates of the current best solution. Moreover, the probability of perturbing a coordinate decreases as the algorithm reaches the computational budget. Two DYCORS algorithms that use RBF (Radial Basis Function) surrogates are developed: DYCORS-LMSRBF is a modification of the LMSRBF algorithm while DYCORS-DDSRBF is an RBF-assisted DDS. Numerical results on a 14-D watershed calibration problem and on eleven 30-D and 200-D test problems show that DYCORS algorithms are generally better than EGO, DDS, LMSRBF, MADS with kriging, SQP, an RBF-assisted evolution strategy, and a genetic algorithm. Hence, DYCORS is a promising approach for watershed calibration and for HEB optimization.