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 criterion. We conduct simulation studies with standard test functions, which show that the proposed method has some advantages, especially when the true function has many local optima. In addition, we also propose modified approaches to improve the search performance for identifying optimal points.

昂贵功能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，因为每个功能的评估都可能成本很高，并且功能的派生信息通常不可用。我们提出了一种新的全局优化框架，该框架通过不确定性量化使用基于自适应径向基函数（RBF）的替代模型。该框架包括两个迭代步骤。它首先采用基于RBF的贝叶斯代理模型来逼近真实函数，其中RBF的参数可以在每次探索新点时进行自适应估计和更新。然后，它利用模型指导的选择标准从候选集中识别新点，以进行功能评估。这里采用的选择标准是预期改进标准的样本版本。我们使用标准测试函数进行了仿真研究，结果表明该方法具有一定的优势，特别是当真实函数具有许多局部最优值时。此外，我们还提出了改进的方法来提高搜索性能，以识别最佳点。