Construction and Optimization of Black-Box Models Based on Halving Rectangles Sampling High Dimensional Model Representation Algorithm

This paper proposes an efficient modeling and optimization method for expensive black-box multi-objective optimization problems using Support Vector Regression combined with High-Dimensional Model Representation (SVRHDMR). By leveraging the hierarchical structure of HDMR and the small-sample learning ability of SVR, one method approximates the original black-box model through minimal computational cost. A DIRECT sampling strategy ensures both model accuracy and efficiency. Subsequently, a multi-objective genetic algorithm, specifically NSGA-III, is employed to find optimal parameters based on the constructed SVR-HDMR model. The results demonstrate that the proposed SVR-HDMR model effectively approximates complex, nonlinear problems with high accuracy, and NSGA-III successfully identifies Pareto optimal solutions, outperforming NSGA-II in terms of diversity.