An adaptive metamodel-based global approximation method for black-box type problems

Abstract

An adaptive metamodel-based global approximation (AMGA) method for solving the global approximation problem of black-box models in large design domain is proposed in this study. The method employs the RBF model to compute the Hessian matrix and a heuristic direct search algorithm DIRECT to find the maximum curvature point of the metamodel surface, through which the design domain is split to obtain additional sampling points and to achieve fast update and fast valuation of the metamodel. The initial design domain is split into a series of sub-design domains by continuous iterations, and the metamodels built within the various sub-design domains achieve the global approximate model of the entire design domain. To demonstrate the final effect of the global approximation model and design domain splitting, six common two-dimensional test functions are chosen. The AMGA method is further tested using seven typical test functions and compared to other sampling and metamodel updating methods, with the findings demonstrating the usefulness of the proposed method in the low-dimensional scenario (less than four variables). Finally, the AMGA method is applied to a sophisticated electric car model, yielding good results.