## 3 System Models
### Sensing Coverage Model
(2) This paper does not consider other factors affecting network QSC, such as node mobility or MC carrying capacity. Future work should address these limitations by designing an online optimization algorithm based on the network dynamic characteristics and considering the impact of other factors on network performance. Compared with other studies, the uniqueness of this study is that the impact of the mobile charging sequence on network QSC is considered. The results found that the IQPSO algorithm is superior to other common algorithms regarding its global search ability and convergence speed. The results of this study have practical implications for the design of MC mobile charging in WRSNs. Optimizing the mobile charging sequence can ensure that all nodes

Figure 6: Effect of different MC moving speeds. (**a**) Performance index. (**b**) Coverage rate. (**c**) Number of off-working nodes. are charged efficiently and that the network maintains a high level of network QSC in practical applications. ## 8 Conclusions

Considering the impact of mobile charging sequences on network QSC, this paper studies the novel MSSQ problem and proposes an IQPSO algorithm. In addition, we propose a new performance index for the network QSC that considers both sensing coverage and the survival rate of nodes. The proposed IQPSO algorithm adaptively adjusts the contraction expansion coefficient to obtain better global search capability and improve the convergence speed of the algorithm effectively. Through extensive simulation experiments, the IQPSO algorithm can achieve excellent performance improvements in network sensing coverage, especially in large-scale WRSNs. The state in real WRSN applications changes dynamically according to the real-time demand; therefore, designing online mobile charging scheduling algorithms for the optimal network QSC is an important research trend. Conceptualization, J.L., T.X. and W.X. ; methodology, J.L. ; software, J.L. and C.J. ; validation, J.L. and C.J. ; formal analysis, J.L. ; investigation, J.L. and J.W. ; data curation, J.L. and C.J. ; writing--original draft preparation, J.L. ; writing--review and editing, T.X. and W.X. ; supervision, T.X. and W.X. ; project administration, W.X. All authors have read and agreed to the published version of the manuscript. This work was supported in part by the National Natural Science Foundations of China (NSFC) under grant 62173032, the Foshan Science and Technology Innovation Special Project under grant BK22 BF005, and the Regional Joint Fund of the Guangdong Basic and Applied Basic Research Fund under grant 2022A1515140109. Not applicable. The authors declare no conflict of interest. The following abbreviations are used in this manuscript: \begin{tabular}{l l} WSRNs & Wireless rechargeable sensor networks \\ WSNs & Wireless sensor networks \\ MC & Mobile charger \\ QSC & Quality of sensing coverage \\ QoI & Quality of information \\ MSSQ & Mobile charging sequence scheduling for network QSC \\ ETSP & Extended TSP \\ QPSO & Quantum-behaved particle swarm optimization \\ IQPSO & Improved quantum-behaved particle swarm optimization \\ SN & Sink node \\ CS & Charging station \\ CTS & Charging time step \\ AoCS & Area of cooperation sensing \\ AoIS & Area of independent sensing \\ TSR & Total sensing range \\ SCNS & Sensing coverage and node survival rate \\ TSCNS & Total SCNS \\ MSSQ-P & Particular case of MSSQ \\ \end{tabular} 

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