Enhanced variable-fidelity surrogate-based optimization framework by Gaussian process regression and fuzzy clustering

In order to improve the global optimizing ability of surrogate-based optimizations, an enhanced variable-fidelity surrogate model (VFSM) optimization framework is developed based on the Gaussian process regression algorithm and the fuzzy clustering algorithm, which makes full use of the information fusion of high-fidelity model (HFM) and low-fidelity model (LFM). Firstly, a screening criterion is proposed for determining competitive sampling points based on low-fidelity surrogate model (LFSM). Then, the competitive sampling strategy is combined with the fuzzy clustering algorithm, which can adaptively obtain the reduced design space with more possibility to find the optimal result. In the reduced design space, the VFSM is constructed by means of the Gaussian process regression algorithm. Based on the VFSM, a gradient-based optimization can start from the competitive sampling point to search out the optimal solution quickly. In order to verify the effectiveness of the proposed optimization method, three test functions and an engineering example of hierarchical stiffened shells are carried out. Optimization results indicate that, under the similar computational cost, the proposed optimization method achieves significantly higher global optimizing ability than the high-fidelity surrogate model (HFSM) optimization method, the LFSM optimization method and the traditional VFSM optimization method by direct sampling.