Surrogate-based design optimization with adaptive sequential sampling

In spite of the recent developments in surrogate modeling techniques, the low fidelity of these models often limits their use in practical engineering design optimization. When surrogate models are used to represent the behavior of a complex system, it is challenging to simultaneously obtain high accuracy over the entire design space. When such surrogates are used for optimization, it becomes challening to find the optimum/optima with certainty. Sequential sampling methods offer a powerful solution to this challenge by providing the surrogate with reasonable accuracy where and when needed. When surrogate-based design optimization (SBDO) is performed using sequential sampling, the typical SBDO process is repeated multiple times, where each time the surrogate is improved by addition of new sample points. This paper presents a new adaptive approach to add infill points during SBDO, called Adaptive Sequential Sampling (ASS). In this approach, both local exploitation and global exploration aspects are considered for updating the surrogate during optimization, where multiple iterations of the SBDO process is performed to increase the quality of the optimal solution. This approach adaptively improves the accuracy of the surrogate in the region of the current global optimum as well as in the regions of higher relative errors. Based on the initial sample points and the fitted surrogate, the ASS method adds infill points at each iteration in the locations of: (i) the current optimum found based on the fitted surrogate; and (ii) the points generated using cross-over between sample points that have relatively higher cross-validation errors. The Nelder and Mead Simplex method is adopted as the optimization algorithm. The effectiveness of the proposed method is illustrated using a series of standard numerical test problems.