Abstract
Bayesian optimization (BO) finds the optimum by iteratively updating a surrogate model to approximate the complex objective function and constructing an acquisition function to guide sequential sampling. As a widely recognized acquisition function, expected improvement (EI) has played an essential role in BO. However, it may fall into “over-exploitation” or “over-exploration” for complex multi-modal problems. To overcome the shortcomings, this paper proposes a novel acquisition function named adaptively varied expected improvement (AVEI), which is essentially the expected value of a newly defined target improvement function. The core idea of AVEI is: (i) a weight coefficient and a target parameter (difference between the present optimal value and a desired improvement) are innovatively introduced to intelligently control the precise balance of local exploitation and global exploration; (ii) a real-time performance monitoring parameter (ratio of the actual improvement to the desired improvement) and a convenient control law are proposed to update the weight coefficient and target parameter adaptively. An efficient Bayesian optimization called AVEI-BO is thus developed using the Gaussian process (GP) and AVEI. The traditional EI-BO is also constructed using GP and EI for comparison. The performance of AVEI-BO and EI-BO is first evaluated by using eight benchmark problems. Extended discussions are then conducted by comparing AVEI-BO with five classical acquisition functions. The results show that AVEI-BO possesses advantages in optimization capability, convergence speed, and numerical robustness. Moreover, a typical design optimization task of a turbine disk is employed to investigate the engineering applicability of AVEI-BO. The results prove that AVEI-BO is superior.
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Acknowledgements
The authors would like to thank the anonymous reviewers for their valuable comments.
Funding
This study was co-supported by the National Natural Science Foundation of China (No. 52005421), the Natural Science Foundation of Fujian Province of China (No. 2020J05020), the National Science and Technology Major Project (No. J2019-I-0013-0013), the Fundamental Research Funds for the Central Universities (No. 20720210090), and the Project Funded by the China Postdoctoral Science Foundation (Nos. 2020M682584, 2021T140634).
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Yan, C., Du, H., Kang, E. et al. AVEI-BO: an efficient Bayesian optimization using adaptively varied expected improvement. Struct Multidisc Optim 65, 164 (2022). https://doi.org/10.1007/s00158-022-03256-3
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DOI: https://doi.org/10.1007/s00158-022-03256-3