## 1 Introduction  
The wireless sensor network (WSN), which has exerted a great influence in the 21 st century, combines several advanced technologies, such as wireless communication and sensor technology, to effectively achieve an interaction between human society and the physical world, resulting in a profound impact on promoting social progress. WSNs currently have a wide range of applications in military defense, environmental monitoring, and smart homes. As the basic component of a WSN, the sensor node is generally powered by a dry battery. Once the battery is exhausted, the node is dead and cannot participate in subsequent data operations. If these nodes are placed in harsh environments, it becomes impractical to replace the batteries. Therefore, how to effectively reduce the energy consumption of sensor nodes for long-term operation has become a research hotspot [1]. It was under this context that the WSN clustering routing protocol came into being. The WSN protocol combines a large number of sensor nodes into clusters to form a hierarchical management system from cluster members (CMs) to cluster heads (CHs) to base stations (BS), which can effectively reduce the energy consumption of the network, thus extending the lifetime of the network and achieving more rounds of data iteration. In recent years, researchers in various countries have proposed a variety of WSN clustering routing protocols. The most classic protocol is LEACH (Low-Energy Adaptive Cluster Hierarchical) [2], which achieves the goal of energy balance by periodically changing the CHs in the area. However, because it adopts a random number mechanism, the suitability of the CH is full of uncertainties. [PERSON] and [PERSON] [3] proposed an energy center-based WSN routing mechanism that mainly grades all nodes in the area according to the residual energy of the node and the average distance from the member nodes then selects higher-level nodes to become the CHs. A hierarchical routing protocol based on a k-d tree algorithm was proposed in [4], which uses a spatial partitioned data structure to organize the nodes into clusters. A multi-aware query-driven (MAQD) routing protocol based on a neuro-fuzzy inference system was introduced in [5]. An energy-aware cluster-based CRSN routing protocol (EACRP) was introduced in [6], which considers several factors such as the energy and the dynamic spectrum. A multi-access WSN routing protocol based on the transmission power control applied to underground coal mines was introduced in [7], which uses the transmission power control algorithm to find the optimal transmission radius and transmission power, and the non-uniform clustering idea is used to optimize the CH selection mechanism. An energy chain-based WSN routing protocol (E-CBCCP) for underwater environments was introduced in [8]. [PERSON] et al. [9] combined static clustering and dynamic clustering, then took the nodes' residual energy, the energy required to receive the information, and the number of neighbor nodes into consideration to select the CHs. The simulation results showed that, compared with other methods, this method could improve the stability and efficiency of the network. The CH selection mechanism introduced in [10] was divided into three stages: only the advanced node was selected as the CH in Stage 1; all the nodes performed CH selection with the same probability in Stage 2; and the planar topology replaced the clustering topology in Stage 3. The cluster structure optimization problem was divided into multiple sub-optimization problems and solved by multi-objective evolutionary algorithms (MOEAs) in [11].