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The confidence bound (CB) is one of the most popular acquisition functions for Bayesian optimization (BO). It realizes the balance between local exploitation and global exploration through an explicit trade-off coefficient. In practice, researchers tend to employ fixed or random trade-offs for CB, which however is inflexible in tackling challenging optimization scenarios. Therefore, this article presents an adaptive CB acquisition function, called ACB, to address the issue. Specifically, this article uses Lipschitz conditions to identify a set of potentially optimal trade-off coefficients dynamically by the estimated prediction mean and the leave-one-out cross-validation variance. Thereby, the proposed ACB achieves adaptive trade-off between exploitation and exploration by cycling through the set of dynamically updated coefficients. This article verifies the superiority of the proposed ACB by comparing it against current CB-based BOs using different trade-off strategies on nine numerical examples and the design optimization of a supercritical carbon dioxide centrifugal compressor. [ABSTRACT FROM AUTHOR]