## 1 Introduction
The second type is known as the hierarchical SAEAs, where multiple models are used to assist different EAs. The fine local surrogate is utilized to depict the specifics of the fitness landscape, while the rough global surrogate is utilized to mitigate the impact of local optima. [PERSON] et al. [20] developed a hierarchical surrogate that uses both local and global models to assist PSO in directing the swarm towards the global optima. [PERSON] et al. [21] developed the use of global RBF and local Kriging to assist DE for high-dimensional expensive problems. [PERSON] et al. [22] integrated global RBF and a new Lipschitz-based-surrogate-assisted global optimization procedure with local optimization based on a local RBF model. Hierarchical SAEAs may increase the computational overhead compared to single-layer SAEAs, which can provide a solution in a shorter amount of time. However, for high-dimensional multimodal problems, hierarchical SAEAs are preferred. Hierarchical SAEAs can first identify promising regions in the global search phase and then explore more deeply in local regions, which is very beneficial for a comprehensive search of the decision space. The reliability of SAEAs is mainly influenced by the surrogate and the evolutionary algorithm. With an increase in problem dimensions, the single surrogate easily causes the algorithm to be trapped in local optima. Meanwhile, the fixed surrogate makes it quite difficult to accurately describe different optimization problems. Therefore, to address this issue, the ensemble of surrogates is widely used in SAEAs [23; 24]. [PERSON] et al. [25] developed a hybrid algorithm that first carries out a series of global searches, then takes turns with global and local searches and employs social learning particle swarm optimization (SL-PSO) and DE for global searches assisted by a surrogate ensemble and local searches assisted by RBF, respectively. [PERSON] et al. [13] replaced the time-consuming Gaussian processes with a heterogeneous integration composed of models with different input characteristics, which improves the diversity and reliability of the surrogate. Moreover, research on adaptive surrogate model selection techniques has also received more and more attention. [PERSON] et al. [26] adaptively selected one from an RBF or an ensemble model to facilitate PSO according to standard deviation. [PERSON] et al. [27] introduced a decision space partition-based SAEA when addressing expensive optimization problems, which divides the space into several disjoint regions by the k-means clustering technique and establishes an RBF model on each region to assist PSO in global search, and an adaptive surrogate is utilized to assist local exploitation. [PERSON] et al. [28] designed a hierarchical surrogate framework that adopts RBF-assisted TLBO to locate promising regions and the dynamic surrogate-assisted DE to precisely determine the global optimal solution. The evolutionary algorithm is also a key component of SAEAs. When faced with a complex problem, a single EA may induce the optimization process to follow a similar trajectory and become trapped into local optima [29]. As a result, several SAEAs use different EAs at the same time. In addition, some SAEAs using the multi-task evolutionary algorithm have been developed. Multi-task optimization (MTO) is a method that can process several optimization tasks simultaneously, and it can promote the overall task solving progress through the data transfer between different tasks. [PERSON] et al. [30] introduced a multi-tasking algorithm design framework that uses the generalized multi-factorial evolutionary algorithm (G-MFEA) to assist global and local surrogates simultaneously in addressing expensive optimization problems. [PERSON] et al. [31] took a global Kriging or a local RBF model as the assistant task at different stages and then used the MFEA to optimize the assistant task and the target task simultaneously.