AVEI-BO: an efficient Bayesian optimization using adaptively varied expected improvement

doi:10.1007/s00158-022-03256-3

2022-05-18

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DOI：10.1007/s00158-022-03256-3

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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.

Keyword:

Bayesian optimization

Acquisition function

Expected improvement

Adaptively varied expected improvement

Surrogate model

Gaussian process