# A Hybrid Routing Protocol Based on Naive Bayes and Improved Particle Swarm Optimization Algorithms
## 2 Related Works  
### Clustering Routing Algorithms  
A cluster routing protocol divides the monitored area into a set of nodes called clusters. In each cluster, one or more nodes are selected to be cluster heads in a certain way, and the nodes in the cluster perform data communication with the \(BS\) through the cluster head. After the network adopts a cluster structure, the network is divided into multiple relatively independent clusters, which reduces the impact of the change in the network topology on the system and improves the stability and maintainability of the network. The cluster head can fuse the data in the cluster before forwarding them, which reduces the amount of data transmitted and the network's energy consumption [9; 10]. Clustering routing algorithms have the advantages of a simple structure, efficient topology management, and no requirement for complex routing information. The classical clustering routing protocol LEACH [11] uses ordinary nodes as cluster heads in a probabilistic way, which balances the additional energy consumption of cluster heads to a certain extent and prolongs the network's lifetime. The advantage of the LEACH algorithm lies in the simplicity of the cluster head selection algorithm because the random selection of a cluster head cannot ensure the dispersion of the cluster head's position and sufficient residual energy, which can easily cause an imbalance in the network node energy consumption and affect the network's lifetime. In order to solve the problem of imbalances in energy consumption caused by randomly selected cluster heads in the LEACH algorithm, researchers proposed a series of improved algorithms, such as LEACH-C, LEACH-F, DEEC, CHCS, and other centralized cluster head selection methods [12]. The weight is calculated according to the residual energy of nodes and the distance from the BS, and the node weight is used as the basis for cluster head selection. The cluster head cycle switching schemes (CHCS) algorithm votes for the neighbor node with the highest residual energy, and the node with the highest number of votes in the region is declared to be the cluster head node [13]. [PERSON] et al. [14] proposed a method for calculating the cluster head score according to the ratio of the distance from the cluster head to the \(BS\) to the total energy consumption. The node with the highest score becomes the cluster head. [PERSON] et al. [15] proposed a k-center approximation algorithm to select the cluster head that optimizes the distance from the nodes in the cluster to the cluster head and, hence, reduces and balances the energy consumption. This kind of algorithm optimizes the selection of cluster heads, but the general sensing node adopts the minimum distance principle when accessing the cluster, which may lead to the overload of cluster heads at some key locations. Aiming to solve the problem of unbalanced communication loads between clusters, a series of improved algorithms, such as HEED and EECS, were designed. In the energy efficient clustering scheme (EECS), a new communication cost is used to determine which cluster nodes join [16] as shown in Equation (1). \[\cos t(j,i)=w\times f(d(P_{j},CH_{i}))+(1-w)\times g(d(CH_{i},BS)) \tag{1}\]  
\[f(\cdot)=\frac{d(P_{j},CH_{i})}{EX(\max\{d(P_{j},CH_{i})\})},\ g(\cdot)=\frac{d( CH_{i},BS)-\min\{d(CH_{i},BS)\}}{\max\{d(CH_{i},BS)\}-\min\{d(CH_{i},BS)\}} \tag{2}\]  
where cost(\(j\),\(i\)) is the cost of node \(P_{j}\) joining cluster head \(CH_{i}\); \(d(P_{j},CH_{i})\) is the distance from the node to the cluster head; \(d(CH_{i},BS)\) is the distance from the cluster head \(CH_{i}\) to the base station; the weight \(w\) determines the ratio of member node energy consumption to cluster head energy consumption, which varies according to the application scenario; the function is the minimum communication cost between the node and the cluster head; and the function is the minimum communication cost from cluster head \(CH_{i}\) to the base station.