## 4 EBCRP: Energy-Balanced Cluster-Routing Protocol
### Clustering Sensor Nodes Based on Particle Swarm Optimization with Five Mutation Operators
#### 4.1.4 Five Mutation Operators
Thus, the network lifetime of SEP is higher than that of LEACH, but it is still lower than the proposed EBCRP method. Although the IICMH also considers the balance of the number of sensor nodes between clusters, the CH of each cluster is reselected after the energy of the previous CH is lower than a threshold. This makes the energy of sensor nodes selected as CHs for the first time to quickly depleted. In addition, sensor nodes close to the sink in each cluster are preferentially selected as CHs in IICMH, which increases the energy consumption of some sensor nodes (i.e., cluster members far away from their CHs) when they send data to their CHs. Thus, the network lifetime of IICMH is lower compared to the other methods. Overall, the proposed EBCRP method performs better in prolonging the network lifetime by performing balanced clustering and employing the rotation CH selection scheme based on the highest residual energy. Figure 10: Network lifetime of different methods for different numbers of sensor nodes. ## 6 Conclusions

This study proposes an energy balanced cluster-routing protocol based on particle swarm optimization with five mutation operators for wireless sensor networks to balance energy consumption of sensor nodes and prolong the network lifetime. An adaptive sensor node clustering scheme based on the PSO is proposed to determine the number of clusters and group sensor nodes into clusters evenly, which is helpful to balance the energy consumption between sensor nodes. To increase the search diversity, five mutation operators are specially proposed in EBCRP to improve the performance of PSO in optimizing sensor node clustering. In addition, a rotation CH selection scheme based on the highest residual energy is used in EBCRP to dynamically select a CH for each cluster. In each round, the sensor node with the highest residual energy in each cluster is selected as a CH responsible for aggregating data from the remaining sensor nodes within each cluster and sending these data to the sink. This can balance the energy consumption of sensor nodes within each cluster. Comprehensive simulations are performed to investigate the effectiveness of the proposed EBCRP method and compare it to some other methods. The simulation results demonstrate that the proposed EBCRP method can effectively balance the number of sensor nodes between clusters and energy consumption of sensor nodes, thereby prolonging the network lifetime. Some limitations still exist in the EBCRP method and become important research work in the future. The PSO-based sensor node clustering scheme is greatly affected by the performance of the PSO. For the multimodal, high-dimensional, complex, and nonlinear optimization problems in WSNs, the PSO is easy to prematurely converges to local optima. To find an optimal or near-optimal solutions, PSO and other optimization algorithms could be studied in the future to further improve the performance of EBCRP. In addition, the EBCRP selects CH for each cluster in each round, which reduces the stability of the network system. A more efficient CH selection mechanism could be further studied, e.g, each cluster selects multiple CHs to cooperate with each other to aggregate the data from other sensor nodes within their cluster. When the energy of the current CHs is lower than a threshold, the new CHs are reselected. Another important future work is about the application of the EBCRP to complex WSNs problems with large sensing region, some relay nodes can be selected to assist the communication between CHs. Conceptualization, Y.H. and H.B. ; methodology, Y.H., H.B. and L.Z. ; software, Y.H. and L.Z. ; validation, Y.H., H.B. and L.Z. ; writing, Y.H., H.B. and L.Z. ; funding acquisition, H.B. All authors have read and agreed to the published version of the manuscript. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2020R1A2C1004390). The authors declare no conflict of interest.