## 1 Introduction  
Evolutionary algorithms (EAs), such as genetic algorithms (GAs) [1], differential evolution (DE) [2], and particle swarm optimization (PSO) [3], have been successfully utilized in various practical engineering problems, such as the design of aircraft wings [4], robotics [5], wireless networks [6], and the optimization of vehicle technology trajectory [7, 8]. However, the utilization of EAs to address optimization problems requires hundreds of expensive exact fitness evaluations (FEs) to achieve an acceptable solution, which severely hinders their application in practical engineering problems. To solve this problem, SAEAs have been proposed. SAEAs are a class of techniques that combine EAs with surrogate models, which build inexpensive surrogate models for predicting the fitness values of candidate solutionsas a replacement for FEs in the EAs. In recent years, the use of SAEAs for optimization problems has received increasing attention because the computational cost of constructing surrogates and predicting fitness values is less than FEs. Model management strategy is crucial for SAEAs, which select some new samples for exact FEs and use them in the reconstruction of the surrogate model [9]. Currently developed model management strategies are mainly categorized as generation-based and individual-based, where the former selects all samples by generation for accurate FEs and the latter selects promising individuals for real evaluation. Both strategies have been shown to be effective, but in general, individual-based criteria are more flexible than generation-based criteria [10; 11]. There are usually two criteria for selecting promising individuals. The first is the performance-based criterion that chooses the individual with the best fitness value for accurate evaluation to effectively enhance the performance of the surrogate and facilitate the exploitation of the currently promising area [12]. The second category is the uncertainty-based criterion, which can enhance exploration by selecting the most uncertain individual for accurate evaluation [13]. It has been shown [14] that using only one infill criterion may lead to early convergence or falling into a local optimum. Therefore, this paper selects the optimal or average individual for real function evaluation. The current SAEAs can be classified into two principal categories. The first category is the single-layer SAEAs, which do not have hierarchically organized components and usually use only one model, i.e., a local or global surrogate, to assist one evolutionary algorithm. [PERSON] et al. [15] presented a fast algorithm using the global radial basis function (RBF) to assist PSO, in which they combined the performance-based criterion with a new criterion that considered the distance and fitness value concurrently, boosting the efficiency of the algorithm. [PERSON] et al. [16] also developed a surrogate-assisted multi-swarm optimization technique that alternately carries out teaching-learning-based optimization (TLBO) to enhance exploration and PSO to accelerate convergence. Global surrogates can summarize the overall fitness landscape. [PERSON] et al. [17] combined graphical neural networks (GNNs) and PSO for optimal design of truss structures. However, generally speaking, a large number of exactly evaluated samples are required to build highly accurate global surrogates when solving large-scale expensive optimization problems, which can make it difficult for algorithms to balance between high accuracy and low time consumption. Therefore, local surrogates are commonly used to increase the accuracy by capturing the regional characteristics of the fitness landscape. [PERSON] et al. [18] presented a search technique based on trust region, which is to establish a local RBF model in the trust region surrounding the optimal population, thereby boosting the optimization efficiency. [PERSON] et al. [19] used neighbor samples to train a local RBF model with higher accuracy to assist the TLBO and DE alternately and proposed a new prescreening criterion.