An Optimization Framework Based on Kriging Method with Additive Bridge Function for Variable-Fidelity Problem

Abstract

Variable-fidelity optimization (VFO), which utilizes the precise value of high-fidelity (HF) model and underlying trend of low-fidelity (LF) model, has solved many computationally expensive problems by simulation-based design. Though it has been developed rapidly in recent years, the simpler and cheaper ones are still needed. In this paper, a new optimization framework based on Kriging method with additive bridge function for variable-fidelity problem is proposed. The simple additive bridge function is taken to construct the primal HF model with Kriging method. With the local and global search strategies, the sample sets can be updated and the HF model be refreshed. It is worth mentioning that the fusion of them not only makes the method easy to implement, but also helps to find the optimal result much faster. In order to illustrate the ideas and features of the proposed optimization framework clearly, a mathematic example is presented in detail. Furthermore, another two problems are analyzed, including an engineering problem. The results show that the proposed optimization framework is feasible and effective, indicating it is suitable to solve complicated variable-fidelity problems.