## 3 System Models
### Sensing Coverage Model
Therefore, the mobile charging sequence optimization performance in IQPSO is superior to the other heuristic algorithms in different scale networks. The more extensive the network, the more obvious the advantages. ### Comparison of Charging Powers

The charging efficiency of MC is mainly affected by its charging power. If a single MC is used to ensure the sustainable work of all nodes, it has very high requirements. In this part, we will analyze the changes in the network QSC, the average coverage rate, and the number of off-working nodes for \(v_{c}=\{10,20,40,60,80,100\}\). It can be intuitively seen from Figure 5a that the network QSC enhances with the increase in \(v_{c}\). As shown in Figure 5b, when \(v_{c}\geq 100\), in the IQPSO and QPSO algorithms, the MC can realize 'full-charge instantly', and the network will consistently achieve perfect sensing coverage. When \(v_{c}\leq 40\), the charging power is severely limited, and the nodes with insufficient remaining energy or off-working nodes cannot be charged in time. Compared with the other three algorithms shown in Figure 5c, with the decrease in \(v_{c}\), the number of off-working nodes increases linearly. The minimum number is 20 and the maximum is 64. At this time, the IQPSO algorithm can find the approximate optimal mobile charging sequence with obvious advantages. When the \(v_{c}\) increases to a certain extent, its charging strategy gradually approaches Greedy-A. Figure 4: Effect of different network scales. (**a**) Performance index. (**b**) Coverage rate. (**c**) Number of off-working nodes. Figure 5: Effect of different MC charging powers. (**a**) Performance index. (**b**) Coverage rate. (**c**) Number of off-working nodes. ### Comparison of MC Moving Speeds

The moving speed also has an important influence on the charging efficiency. The faster the \(v_{m}\), the shorter the waiting time of nodes. In this part, we will analyze the changes in network QSC, the average coverage rate, and the number of off-working nodes for \(v_{m}=\{1,3,5,7,9,11\}\). It can be seen from Figure 6a that compared with the other three algorithms, the IQPSO algorithm can still learn the suboptimal mobile charging sequence to ensure the optimal network QSC. With the increase in \(v_{m}\), although the fluctuation in network QSC obtained by the four algorithms is relatively stable, the average network coverage rate and the number of off-working nodes both increase and decrease slowly. As shown in Figure 6b,c, in the IQPSO algorithm, the average network coverage and the number of off-working nodes are superior to the other three algorithms. In this paper, the network energy consumed during MC moving accounts for less than \(e_{m}\). As \(v_{m}\) increases from one to eleven, \(t_{l}\) shortens and the energy consumed by the nodes decreases. The average network coverage rate and the number of off-working nodes increase and decrease gradually, eventually becoming stable. If \(v_{m}\) continuously increases, \(t_{l}\to 0\), and the energy consumed by the nodes can be ignored. Therefore, in the MSSQ problem, \(v_{m}\) has little impact on network QSC. ## 7 Discussion

The results of this study demonstrate the effectiveness of the proposed IQPSO algorithm in improving QSC in WRSNs, especially for large-scale networks. This is an important study, as previous research on mobile charging sequence optimization in WRSNs has primarily focused on the charging efficiency as a performance index, ignoring the importance of network QSC. Moreover, previous research on the network QSC optimization has been studied in energy-harvesting WSNs and has yet to be considered in WRSNs with mobile charging. The limitations of this study include the following: (1) IQPSO is an off-line optimization algorithm that can only be implemented in WRSNs where the state is known and highly predictable. It cannot effectively find the suboptimal mobile charging sequence for WRSNs with dynamic changes in the actual state.