Variable-fidelity probability of improvement method for efficient global optimization of expensive black-box problems
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RESEARCH PAPER
Variable-fidelity probability of improvement method for efficient global optimization of expensive black-box problems Xiongfeng Ruan 1,2 & Ping Jiang 2 & Qi Zhou 1 & Jiexiang Hu 2 & Leshi Shu 2 Received: 19 December 2019 / Revised: 16 May 2020 / Accepted: 4 June 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Variable-fidelity (VF) surrogate models have attracted significant attention recently in simulation-based design because they can achieve a desirable accuracy at a reasonable cost by making use of the data from both low-fidelity (LF) and high-fidelity (HF) simulations. To facilitate the usage of VF surrogate models assisted efficient global optimization, there are still challenging issues on (1) how to construct the VF surrogate model for simulations with variable-fidelity levels under the non-nested sampling data, (2) how to determine the location and fidelity level of the samples simultaneously, and (3) how to handle constraints when VF surrogate models are also used for constraints. In this work, a variable-fidelity probability of improvement (VF-PI) method is proposed for computationally expensive black-box problems. First, a multi-level generalized Co-Kriging (GCK) model, which is extended from the two-level GCK model, is developed for VF surrogate modeling of simulations with three or more levels of fidelities under non-nested sampling data. Second, to determine the location and fidelity level of the sequential samples, an extended probability of improvement (EPI) function is developed. In EPI function, the model correlation and cost ratio between the LF and HF models, together with the sample density, are considered. Third, the probability of satisfying the constraints is introduced and combined with the EPI function, enabling the proposed approach to handle VF optimization problems with constraints. The comparison results illustrate that the proposed VF-PI method is more efficient and robust than the four compared methods on the illustrated cases. Keywords Variable-fidelity surrogate model . Sequential optimization . Probability of improvement . Co-Kriging
1 Introduction Surrogate models have been widely used in engineering optimization problems to replace the computationally expensive simulations (Booker et al. 1999; Jiang et al. 2019a; Zhou et al. 2017). They are constructed based on available input parameter values and the corresponding quantity of interests (QoIs). Generally, the computational burden to construct an accurate surrogate in the whole design domain is unaffordable in the Responsible Editor: Michael Kokkolaras * Qi Zhou [email protected] 1
School of Aerospace Engineering, Huazhong University of Science & Technology, Wuhan 430074, Hubei, People’s Republic of China
2
The State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science & Technology, Wuhan 430074, People’s Republic of China
surrogate model–based design and optimization (SBDO) (Jiang et al. 20
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