## 2 Related Works  
Traditional clustering usually refers to hard clustering in which each node is classified into a unique category, clusters are independent of each other, and nodes belong exclusively to one cluster. Node grouping can be based on different parameters, mainly residual energy and physical proximity [12]. For instance, K-means clustering is an iterative distance-based clustering algorithm that updates CHs based on the distance of nodes to the cluster center [30]. In view of the problems existing in classical clustering and routing protocols, such as CH selection, difficulty in handling large-scale data, and incomplete parameter selection, scholars have been trying to improve traditional algorithms and propose new algorithms to solve the above shortcomings and improve the performance of the protocol. The exceptional multi-objective optimization capabilities of meta-heuristic algorithms have enabled them to be extensively employed by scholars in WSNs. In [18], CSO is used to optimize the selection of CHs by simulating the tracking mode of a cat. The received signal strength, residual energy, and intra-cluster distance are considered factors in this scenario, and only CHs are allowed to communicate with the BS. The authors completed indoor experiments with sensor nodes, a microcontroller, and a LabVIEW interface. The results showed that the algorithm has a significant improvement in extending the network lifetime and reducing the computation time. However, the performance of the network is affected when the cluster has numerous nodes. In [22], the BOA (butterfly optimization) algorithm is proposed to optimize the selection of CHs, constructing an objective function based on factors such as residual energy, distance to neighbors, distance to the BS, node degree, and node centrality. Then the ACO (ant colony optimization) algorithm is adopted to plan the optimal transmission path from the source node to the BS via CH. The distance to the BS, residual energy, and node degree are taken into consideration. Compared with traditional algorithms and some existing methods, the network lifetime is significantly improved. In [24], a two-tier protocol for clustering and routing (THSI-RP) was proposed. In the first tier, THSI-RP designed the objective function incorporating energy, the intra-cluster distance, the distance between CH and BS, and node centrality as parameters to select the optimal CHs. Additionally, GWO (grey wolf optimization) and MPA (marine predator algorithm) were combined for clustering to enhance search efficiency. In the second tier, THSI-RP established a communication routing tree between CHs and BS to achieve the shortest data transmission path. Experimental results showed that THSI-RP can effectually improve the network lifetime, but a two-tier protocol design results in a higher network complexity. The two-level genetic algorithm [31] introduced a novel approach to solve two problems simultaneously: selection of CHs and optimal multi-hop routing. In this proposed method, the energy consumption of the multi-hop routing, designed by the second-level algorithm, is considered as a parameter when evaluating the chromosomes in the first-level algorithm. The experimental results showed that network lifetime has been increased when compared to three approaches. The selection of CHs and the routing among them are performed separately. Furthermore, the GA algorithm was substituted with another meta-heuristic algorithm for a two-level framework, and the results of the two methods are quite close. It can be concluded that the results obtained from the proposed framework are not heavily influenced by the algorithms used for optimization. In [32], [PERSON] et al. proposed a novel protocol for clustering and routing. OAFS-IMFO used the OAFS (oppositional artificial fish swarm) algorithm to optimize the selection of CHs, which constructed an objective function based on residual energy, distance between CHs, and distance between CHs and CMs (cluster members).