Bayesian Optimization (BO) is an effective method for finding the global
optimum of expensive black-box functions. However, it is well known that
applying BO to high-dimensional optimization problems is challenging. To
address this issue, a promising solution is to use a local search strategy that
partitions the search domain into local regions with high likelihood of
containing the global optimum, and then use BO to optimize the objective
function within these regions. In this paper, we propose a novel technique for
defining the local regions using the Covariance Matrix Adaptation (CMA)
strategy. Specifically, we use CMA to learn a search distribution that can
estimate the probabilities of data points being the global optimum of the
objective function. Based on this search distribution, we then define the local
regions consisting of data points with high probabilities of being the global
optimum. Our approach serves as a meta-algorithm as it can incorporate existing
black-box BO optimizers, such as BO, TuRBO, and BAxUS, to find the global
optimum of the objective function within our derived local regions. We evaluate
our proposed method on various benchmark synthetic and real-world problems. The
results demonstrate that our method outperforms existing state-of-the-art
techniques.

通过使用协方差矩阵适应 (CMA) 策略，本文提出了一种新的技术，用于定义具有高概率包含全局最优解的局部区域，从而在局部区域内使用贝叶斯优化 (BO) 来优化目标函数。我们的方法作为元算法，能够结合黑盒子优化器，如 BO、TuRBO 和 BAxUS，在我们得到的局部区域内找到目标函数的全局最优解，并在各种基准合成和真实问题上进行了评估，结果表明我们的方法优于现有的尖端技术。

高维贝叶斯优化通过协方差矩阵适应策略

High-dimensional Bayesian Optimization via Covariance Matrix Adaptation  Strategy

Surrogate-assisted evolutionary algorithms have been widely developed to
solve complex and computationally expensive multi-objective optimization
problems in recent years. However, when dealing with high-dimensional
optimization problems, the performance of these surrogate-assisted
multi-objective evolutionary algorithms deteriorate drastically. In this work,
a novel Classifier-assisted rank-based learning and Local Model based
multi-objective Evolutionary Algorithm (CLMEA) is proposed for high-dimensional
expensive multi-objective optimization problems. The proposed algorithm
consists of three parts: classifier-assisted rank-based learning,
hypervolume-based non-dominated search, and local search in the relatively
sparse objective space. Specifically, a probabilistic neural network is built
as classifier to divide the offspring into a number of ranks. The offspring in
different ranks uses rank-based learning strategy to generate more promising
and informative candidates for real function evaluations. Then, radial basis
function networks are built as surrogates to approximate the objective
functions. After searching non-dominated solutions assisted by the surrogate
model, the candidates with higher hypervolume improvement are selected for real
evaluations. Subsequently, in order to maintain the diversity of solutions, the
most uncertain sample point from the non-dominated solutions measured by the
crowding distance is selected as the guided parent to further infill in the
uncertain region of the front. The experimental results of benchmark problems
and a real-world application on geothermal reservoir heat extraction
optimization demonstrate that the proposed algorithm shows superior performance
compared with the state-of-the-art surrogate-assisted multi-objective
evolutionary algorithms. The source code for this work is available at
this https URL

提出了一种基于分类器辅助排名学习和局部模型的多目标进化算法 (CLMEA)，它用于高维昂贵的多目标优化问题，实验结果表明该算法在基准问题和地热储层热采优化实施方面显示出优秀的性能，相对于现有的基于替代模型的多目标进化算法具有更好的性能。