# A Hybrid Routing Protocol Based on Naive Bayes and Improved Particle Swarm Optimization Algorithms
## 3 Network Model and Assumptions
### Cluster Head Selection Based on a Naive Bayes Classifier
There are some differences between the transmission data curve (Figure 9) and the alive node curve (Figure 2). The transmission data curves of the HAR-NP and FC-RBAT algorithms shown in Figure 9 seem to be lower than those shown in Figure 2 compared with the DUCF and ECRRS algorithms. This is mainly because of the different average numbers of hops in the four algorithms as shown in \[\mathbf{Y}^{(i)}=\left\{re^{(i)},ds^{(i)},de^{(i)},dc^{(i)},Lqc^{(i)},Df^{(i)}\right\} \tag{8}\]7 Thus, HAR-NP and FC-RBAT would have fewer transmission bits than the other two algorithms. Moreover, the clustering's organization may also have an impact on the data transmission performance because of the data fusion in the cluster head. ## 6 Conclusions

Aiming at the requirement of high-energy-efficiency WSN monitoring in a noisy environment, a hybrid routing algorithm based on Naive Bayes and improved particle

\[\mathbf{Y}^{(i)}=\left\{re^{(i)},ds^{(i)},de^{(i)},dc^{(i)},Lqc^{(i)},Df^{(i)}\right\} \tag{8}\]8 Comparison of the average number of network hops. \[\mathbf{Y}^{(i)}=\left\{re^{(i)},ds^{(i)},de^{(i)},dc^{(i)},Lqc^{(i)},Df^{(i)}\right\} \tag{8}\]9 Comparison of network transmission data. swarm optimization algorithms is proposed. In HRA-NP, the sensor nodes are grouped together to form balanced clusters using the Naive Bayes algorithm. After the clusters are formed, a CH from each cluster is selected according to the CH conditional probability of the sensor nodes. The score of the sensor node is defined using four factors (residual energy, distance from the BS, distance from the cluster's center, and intra-cluster distance). Therefore, energy balancing can be implemented in the WSN. Furthermore, the best multi-hop path between cluster heads is determined according to an improved PSO approach. A novel fitness function was designed to evaluate the solutions generated by the PSO approach. The fittest solution provides information about the best routing path towards the BS. Simulations were carried out on various evaluation factors, and HRA-NP was found to outperform DUCF, ECRRS, and FC-RBAT in terms of the evaluation factors. Possible future research direction include consideration of end-to-end delay and other features that affect the algorithm's performance. A mobile sink is also a prospective way to improve the network performance. Conceptualization, X.W. and H.Z. ; data curation, X.W. and H.W. ; formal analysis, X.W. and H.W. ; funding acquisition, H.Z. ; investigation, X.W., H.W. and Y.M. ; methodology, H.W. and H.Z. ; project administration, H.Z. ; resources, X.W. and Y.M. ; software, X.W. and H.W. ; supervision, H.Z. ; validation, X.W., Y.M. and H.Z. ; visualization, X.W. and Y.M. ; writing--original draft, X.W. and Y.M. ; writing--review and editing, H.W. and H.Z. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China, grant number 61871041 and the Youth Found of Beijing Academy of Agriculture and Forestry Sciences, grant number QNJJ202030. Not applicable. The authors declare no conflict of interest.