## 1 Introduction  
With the improvement of design levels and application requirements [1; 2; 3], the optimal performance of products has attracted much attention. Although the computing power of computers continues to increase, both the computer simulation and analysis of complex problems are still very time consuming. The traditional modeling method requires more expensive simulation evaluation, so it is not suitable for solving black-box problems. Therefore, using Kriging surrogate models with higher approximation accuracy instead of complex simulation sequential modeling methods has become a research hotspot in the field of product design and optimization [4; 5; 6; 7; 8; 9]. Approximate construction and space exploration are mainly completed through experimental design in Kriging models, given their potential to estimate information. The Kriging model, which could also help to shorten the design cycle, reduce research and development costs, and improve design accuracy, is suitable for solving complex black-box problems. Although Kriging has demonstrated its great advantages in many fields [10; 11; 12; 13; 14], there are still bottlenecks that need to be overcome when using Kriging to solve high-dimensional modeling problems. There are two main solutions. One is the use of parallel computing [15; 16; 17]; the other is to use dimensionality reduction methods to reduce the dimensionality of Kriging modeling, thereby improving the efficiency of Kriging modeling. In this work, we prefer the latter. Depending on the different commonly used benchmark functions, it takes about 2000 s to 3500 s to complete the modeling of the 80-dimensional problem by sampling 200 training design points through sequential Kriging optimization according to our test. Therefore, the construction of a Kriging surrogate under high-dimensional problems is time consuming. Most of the time is spent on the inversion of the covariance correlation matrix and the solving of the Kriging correlation parameter (also known as the hyper-parameter). Kriging modeling [18; 19; 20] not only considers the relationship between the location of the estimated point and the known data location, but also considers the spatial correlation of the variables. The relationship between positions is mainly coordinated and improved by the distance between data points. Moreover, the spatial correlation of variables [21; 22], which is the key to constructing the covariance correlation matrix, is manifested in the Kriging correlation parameters obtained by maximizing the likelihood function through the pattern search algorithm. For Kriging sequential modeling with an increasing number of data points, the dimensions of the correlation parameter vectors are consistent with the dimensions of the design variables without considering dimensionality reduction, while the optimal correlation parameters are obtained by maximizing the complex multimodal likelihood functions. The estimation of the likelihood function in each loop demands the inversion of the covariance matrix. In addition, the dimensionality of the covariance matrix increases with the increase in the amount of sample data, which will cause the complexity of the inversion operation of the covariance matrix to also increase, so that the time spent obtaining the optimal correlation parameters will also increase. The above observations may explain why the Kriging modeling of high-dimensional problems is time consuming. If the dimensionality of the design variables is high, the optimization of the correlation parameters becomes a complex and multimodal high-dimensional optimization problem, which will exceed our preset calculation amount. Many of the latest works have been focused on solving the \"curse of dimensionality\" problems that affect Kriging modeling.