Global optimization of expensive functions has important applications in physical and computer experiments. It is a challenging problem to develop efficient optimization scheme, because each function evaluation can be costly and the derivative information of the function is often not available. We propose a novel global optimization framework using adaptive Radial Basis Functions (RBF) based surrogate model via uncertainty quantification. The framework consists of two iteration steps. It first employs an RBF-based Bayesian surrogate model to approximate the true function, where the parameters of the RBFs can be adaptively estimated and updated each time a new point is explored. Then it utilizes a model-guided selection criterion to identify a new point from a candidate set for function evaluation. The selection criterion adopted here is a sample version of the expected improvement (EI) criterion. We conduct simulation studies with standard test functions, which show that the proposed method has some advantages, especially when the true surface is not very smooth. In addition, we also propose modified approaches to improve the search performance for identifying global optimal points and to deal with the higher dimension scenarios.

中文翻译：

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使用基于 RBF 的自适应代理模型通过不确定性量化寻找昂贵函数的最佳点

昂贵函数的全局优化在物理和计算机实验中具有重要的应用。开发有效的优化方案是一个具有挑战性的问题，因为每个函数评估都可能代价高昂，而且函数的导数信息通常不可用。我们通过不确定性量化使用基于自适应径向基函数 (RBF) 的代理模型提出了一种新颖的全局优化框架。该框架由两个迭代步骤组成。它首先采用基于 RBF 的贝叶斯代理模型来逼近真实函数，每次探索新点时，可以自适应地估计和更新 RBF 的参数。然后它利用模型引导的选择标准从候选集中识别新点以进行功能评估。此处采用的选择标准是预期改进 (EI) 标准的示例版本。我们使用标准测试函数进行模拟研究，这表明所提出的方法具有一些优势，特别是当真实表面不是很光滑时。此外，我们还提出了改进的方法来提高搜索性能，以识别全局最优点并处理更高维度的场景。