But there is an important problem in the application of meta-heuristic optimization approaches in some engineering fields (e.g., CFD-based optimal design [4; 26; 27; 31; 32] and large ANN hyperparameter optimization [35]): as global optimization approaches, they will produce a large number of sequences, unlike gradient-based methods that produce only one sequence, which makes them need to perform a large number of function evaluations to obtain approximate optimal solutions. For example, the studies based on the meta-heuristic optimization approaches in Table 1 use a sample size of a few hundred to a few thousand. The number of repeated evaluations increases exponentially with the number of parameters, and the computational cost required to perform a single optimization is very high, so to overcome this problem, surrogate-based optimization is promising [36]. Some of the more widely used surrogate models are ANN [37] (optimize a fan-shaped hole), the Kriging model [14] (optimize the shape of a hole), the least squares support vector machine [38] (optimize a fan-shaped hole), the radial basis function [39] (random forest hyperparameter optimization), and the response surface methodology [40] (optimization of laser shock hole clinching), etc. Currently, these studies mainly focus on the field of geometric optimization, and although they have all achieved good optimization results, their performance in the field of air supply is unclear. And ANN in Table 1 is mentioned again. In fact, not only ANN but also the other surrogate models mentioned above are widely used because creating an accurate surrogate model can effectively cope with the problem of long and costly CFD computation, which is of great importance in the field of real-time control. The methods using surrogate models have similar characteristics, while most of the recent studies use ANN, so the authors do not show other surrogate models separately in Table 1. But the major difference between surrogate-based methods and them is that it is not necessary to build an accurate enough surrogate model at the beginning of optimization, which will greatly reduce the number of samples. For example, [PERSON] [17] used 3,356,496 samples to build the initial database. The approach when using surrogate-based optimization is to generate a number of parameter combinations, then calculate the target values (response values) and assemble them into an initial set (\(D\)) of samples. A surrogate model is built based on the set, a new combination of parameters (subgeneration) is generated by combining an infill criteria, the target values are calculated again and the set (\(D\)) is updated, and the process is repeated until global approximate optimal solutions are obtained [41]. [PERSON], [PERSON] et al. [41] concluded that the initial parameter combinations were selected based on the space filling maximin [42] and the Latin hypercube sampling technique [43], which has excellent performance. In terms of infill criteria, there are minimizing surrogate model prediction (MSP) [44], mean squared error (MSE) [41], expected improvement [45], probability of improvement [46], etc. Table 1 also shows that in the optimal design of air supply, there has been an increasing amount of study on multi-objective optimization in recent years compared to the previous single-objective optimization [2; 4; 47], because multi-objective optimization can provide designers with more options in some restricted scenarios. For example, by increasing the number of target areas, the Pareto set is obtained with multi-objective optimization to help us choose a more comprehensive air supply scheme. Noteworthy is the POD method in the current study of air supply optimization, which, together with the surrogate-based methods, is based on an interpolation process and has a simplifying effect (at the expense of some accuracy) when dealing with super-many objectives (reconfiguration fields).