The use of collections of independent local Gaussian processes (GP-ind) combined with trust regions is a widely adopted approach for large-scale and high-dimensional Bayesian optimisation (BO). However, this approach suffers from several limitations, including discontinuities at the boundaries of disjoint regions, an inability to capture long-range spatial correlations, potential information loss, and abrupt increases in computational overhead. To address these limitations, this paper introduces a novel BO algorithm, termed BO-pro-c-tr. The proposed method employs a product-of-experts Gaussian process model with uncertainty calibration (GP-pro-c) as its surrogate model and incorporates a one-to-many association strategy for integrating GP-pro-c with trust regions. Empirical results suggest that, when combined with the GP-LCB acquisition function, BO-pro-c-tr achieves an average reduction of 2.6% in simple regret and 34.9% in computational overhead relative to BO algorithms based on independent local GP models coupled with trust regions.

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