## 3 MVO Algorithm and Its Application to Solve the RNP-WMN Problem
### MVO Algorithm

Table 5: Network instance use for simulationthe CCRs when using algorithms MVO, WOA, GA and PSO are 89.1%, 74.4%, 77.5% and 83.9%, respectively. Thus, the CCR of algorithm MVO is greater than that of algorithms WOA, GA and PSO by 14.7%, 11.6% and 5.2%, respectively. For the INS-2 (Figure 5a), the CCR is smaller than INS-1 due to the larger number of clients (350 clients). However, algorithm MVO always yields higher CCR than other algorithms. The details of the CCR values when executing INS-1 and INS-2 are shown in Table 6.

Next, we analyze the PL in WMN. As described in the previous section, PL is the signal power loss between the mesh client and the nearest mesh router, calculated according to (15). This is an important performance measure that greatly affects the quality of transmission (QoT) in WMN. The smaller the PL, the better the QoT. The results obtained in Figure 6 show the average PL in the entire network when executing INS-1 and INS-2 simulations. We can observe that the higher the number of mesh routers, the smaller the average PL for all algorithms, where the average PL is the best for the case of the MVO algorithm. This is because the larger the number of mesh routers, the higher the CCR (as analyzed in Figure 5), leading to a decrease in the average distance from the mesh client to the nearest mesh router. As a result, the average PL decreases. Comparing INS-1 (Figure 6a) and INS-2 (Figure 6a), we can observe that INS-1 performs better than INS-2 in terms of average PL \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multirow{2}{*}{\(n\)} & \multicolumn{6}{c}{**Number of Connected Clients**} & \multicolumn{6}{c}{**Connected Client Ratio (\%)**} \\ \cline{3-10}  & & **MVO** & **WOA** & **GA** & **PSO** & **MVO** & **WOA** & **GA** & **PSO** \\ \hline \multirow{8}{*}{INS-1} & 10 & 67.4 & 55.4 & 57.0 & 63.7 & 44.9 & 36.9 & 38.0 & 42.4 \\  & 15 & 91.7 & 74.0 & 75.2 & 87.7 & 61.1 & 49.3 & 50.2 & 58.5 \\  & 20 & 108.4 & 88.7 & 93.0 & 105.0 & 72.3 & 59.2 & 62.0 & 70.0 \\  & 25 & 124.0 & 103.3 & 108.4 & 116.3 & 82.7 & 68.9 & 72.3 & 77.5 \\  & 30 & 133.7 & 111.6 & 116.3 & 125.9 & 89.1 & 74.4 & 77.5 & 83.9 \\  & 35 & 140.1 & 120.2 & 129.5 & 131.8 & 93.4 & 80.1 & 86.3 & 87.9 \\  & 40 & 145.1 & 129.2 & 135.4 & 137.7 & 96.8 & 86.1 & 90.2 & 91.8 \\  & 45 & 147.5 & 134.0 & 139.4 & 139.2 & 98.4 & 89.3 & 93.0 & 92.8 \\ \hline \multirow{8}{*}{INS-2} & 10 & 146.9 & 119.3 & 121.5 & 136.4 & 42.0 & 34.1 & 34.7 & 39.0 \\  & 15 & 200.9 & 157.9 & 163.5 & 185.9 & 57.4 & 45.1 & 46.7 & 53.1 \\  & 20 & 245.6 & 197.9 & 207.9 & 231.4 & 70.2 & 56.6 & 59.4 & 66.1 \\ \cline{1-1}  & 25 & 285.9 & 229.8 & 240.4 & 261.0 & 81.7 & 65.6 & 68.7 & 74.6 \\ \cline{1-1}  & 30 & 314.3 & 261.3 & 270.9 & 292.0 & 89.8 & 74.7 & 77.4 & 83.4 \\ \cline{1-1}  & 35 & 330.5 & 279.4 & 290.3 & 310.2 & 94.4 & 79.8 & 83.0 & 88.6 \\ \cline{1-1}  & 40 & 341.0 & 299.5 & 312.7 & 326.2 & 97.4 & 85.6 & 89.4 & 93.2 \\ \cline{1-1}  & 45 & 344.9 & 314.9 & 325.5 & 329.9 & 98.5 & 90.0 & 93.0 & 94.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance comparison of the number of connected clients and CCR when executing INS-1 and INS-2. Figure 5: Performance comparison of the CCR versus the number of routers. (**a**) INS-1. (**b**) INS-2. In other words, when the number of mesh clients is moderate (150 for this case), the QoT in the whole network is better than that of the case where the number of mesh clients is heavy (350 for this case). Comparing between four algorithms, MVO algorithm always gives the best QoT, and the difference in average PLs compared to algorithms WOA, GA and PSO are about 1.3, 0.9 and 0.6 dB, respectively. The box plots in Figure 7 show the distribution of PL values for all clients. These results are obtained through INS-1 and INS-2 simulations with 40 mesh routers. We can observe that the MVO algorithm gives better PL than other algorithms for both INS-1 and INS-2. Considering the results of INS-1 (Figure 7a), the PL of the MVO algorithm ranges from 70.4 to 86.1 dB.