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

摘要

Abstract 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. Keywords: expensive black-box optimizationhigh-dimensional optimizationradial basis functionscoordinate searchwatershed calibration Acknowledgements The authors would like to thank Saint Joseph's University for providing a Summer Research Grant to Rommel Regis and NSF for grant CCSF1116298 to Prof. Shoemaker. They would also like to thank Dr Bryan Tolson for providing the simulation code for the Townbrook watershed calibration model as well as for some discussions during the initial stages of this project.