## 1 Introduction  
As a symbol of the 4 th generation of sensor networks, wireless sensor network (WSN) is a distributed self-organizing network that integrates data acquisition, processing and communication functions. It has a wide range of applications in many important fields, such as agriculture, transportation, and military. Usually, the nodes are powered by limited batteries, so the purpose of extending the lifetime of WSN can be achieved by reducing the energy consumption. As an effective scheme to save energy consumption of WSN, a reasonable clustering routing protocol is generally divided into three phases: cluster setup phase, cluster heads (CHs) election phase, and data transmission phase. In the cluster setup phase, the sensor node groups in the detection area form clusters of different sizes. Based on a certain electoral mechanism, some nodes are selected as the CHs and the remaining nodes act as the member nodes in the CHs election phase. Finally, in the data transmission phase, the member nodes are responsible for collecting environmental information and then transmitting it to the CHs. After the aggregation and data fusion, the CHs send it to the base station (BS). The latter transmits it to the control center (CC) via satellite, Internet, or a mobile communication network, eventually the center personnel make decisions based on current environmental information. Figure 1 shows a typical WSN logical hierarchy diagram. In recent years, researchers in various countries have proposed various kinds of clustering protocols for WSNs. There are several classical protocols, such as LEACH (Low-Energy Adaptive Cluster Hierarchical) [1; 2], SEP (Stable Election Protocol) [3], DEEC (Distributed Energy-Efficient Clustering) [4], and HEED (Hybrid Energy Efficient Distribution) [5]. A new group-based cluster-based hierarchical partitioning scheme that minimizes the number of hops in a cluster is proposed in [6] and a hybrid clustering method combining static and dynamic clustering is proposed in [7]. [PERSON], [PERSON], [PERSON] and [PERSON] [8] propose multi-objective evolutionary algorithms (MOEAs) to obtain the optimal network configuration. A Chain Based Cluster Cooperative Protocol (CBCCP) is proposed in [9] and Markov model is considered in [10]. [PERSON], [PERSON] et al. [11] propose a new network structure model, then according to the original energy consumption model [12], the formula for determining the optimal cluster number of WSN in the region is proposed. In addition, the proposed protocol introduces some common algorithms, such as ant colony optimization (ACO) [13; 14], particle swarm optimization (PSO) [15; 16], principal component analysis (PCA) [17], harmony search algorithm (HSA) [18; 19], spectral partitioning [11] and so on. It is not difficult to find that the protocols have been improved in the following aspects: (1) intra-cluster data transmission path [20], (2) inter-cluster data transmission path, (3) data transmission amount compression [21], (4) implementation of mobile BS or relay node [22], (5) data security consideration [23], (6) increase in the number of sink nodes [24], (7) CHs selection mechanism optimization [21; 25; 26]. As the WSN works continuously, the nodes will eventually die due to the continuous loss of energy. The problems faced by energy consumption in WSN mainly include two aspects: (1) The large total energy consumption; (2) The unbalanced energy consumption. (1) will cause the average energy consumption of the nodes in the network to be too large, resulting in a decline in the overall performance of WSN. (2) will cause a large difference in the death time of the node groups in WSN, which will adversely affect the stability of the network and the efficiency of information transmission. From the perspective of efficient energy and balanced energy consumption, this paper proposes an energy-efficient clustering routing protocol in WSNs.