## 6 Results and Discussions
Considering the trend of convergence for each method, the WCA is capable of determining faster optimum solutions with a higher level of precision in comparison with the ICA, as can be seen in Figure 6. It can be observed that the convergence rate for the WCA is faster than the ICA at earlier \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{2}{c}{**Best Solution**} & \multicolumn{2}{c}{**Average Solution**} & \multicolumn{2}{c}{**Worst Solution**} & \multicolumn{2}{c}{**SD \({}^{1}\)**} \\ \cline{2-9}  & **WCA** & **ICA** & **WCA** & **ICA** & **WCA** & **ICA** & **WCA** & **ICA** \\ \hline \(C_{T}\) & 23,494.8 & 23,683.5 & 24,024.0 & 24,145.1 & 24,354.1 & 24,889.9 & 220.5 & 242.6 \\ \(C_{u}\) & 16,692.6 & 16,761.2 & 16,917.3 & 17,027.9 & 17,174.5 & 17,503.2 & 123.9 & 160.7 \\ \(C_{o}\) & 6703.6 & 6814.9 & 6993.4 & 7002.5 & 7208.6 & 7259.4 & 110.3 & 91.7 \\ \(C_{w}\) & 4922.1 & 5042.1 & 5217.8 & 5232.2 & 5385.5 & 5506.6 & 104.0 & 95.2 \\ \(C_{ui}\) & 2168.3 & 2293.2 & 2313.9 & 2409.8 & 2494.5 & 2694.7 & 79.8 & 103.6 \\ \(C_{fF}\) & 634.2 & 680.1 & 727.7 & 737.1 & 792.4 & 817.3 & 34.0 & 28.7 \\ \(C_{mF}\) & 1059.1 & 1135.8 & 1215.6 & 1231.3 & 1323.4 & 1365.4 & 56.7 & 48.0 \\ \(C_{pF}\) & 1412.6 & 1406.3 & 1463.0 & 1439.2 & 1557.5 & 1481.9 & 37.5 & 17.9 \\ \(C_{s}\) & 98.7 & 106.1 & 113.4 & 114.8 & 123.6 & 127.4 & 5.3 & 4.6 \\ \(A_{F}\) & 5.1 & 4.9 & 5.6 & 5.4 & 6.3 & 5.9 & 0.3 & 0.2 \\ \(T_{VK}\) & 403.49 & 432.7 & 463.07 & 469.1 & 504.15 & 520.1 & 21.65 & 18.22 \\ \(T_{PK}\) & 3062.38 & 3140.62 & 3350.81 & 3386.80 & 3623.83 & 3867.35 & 137.96 & 186.42 \\ \hline \hline \end{tabular} \({}^{1}\) “SD” stands for standard deviation, and the values are in RM.  
\end{table} 
Table 10: Statistical optimization results for each cost term. All cost values are in RM. Figure 5: The deviation percentage associated with the corresponding optimization algorithms. Figure 6: Comparison of the convergence rate and cost history (in RM) with respect to the number of iterations for the considered optimizers. iterations. Figure 7 illustrates the location and variation of the total cost (\(C_{T}\)) and its main components, namely \(C_{u}\), \(C_{o}\) and \(C_{s}\), or 50 independent runs of each optimization algorithm. It can be observed that the lowest levels for the average cost terms are 24,023.97, 16,917.10, 6993.46 and 113.45, respectively, for \(C_{T}\), \(C_{u}\), \(C_{o}\) and \(C_{s}\) with the WCA. The differences between the cost terms of both algorithms for the average cost values are 121, 110.6, 8.9 and 1.5, respectively, for \(C_{T}\), \(C_{u}\), \(C_{o}\) and \(C_{s}\). It can be highlighted that the lowest level of the average cost in terms of both algorithms becomes nearly the same. However, the ICA shows minimal variation in levels between the first and third quartiles compared to the WCA. In terms of \(C_{T}\) for the ICA, the second and third quartile boxes are approximately the same size. The box plot for that dataset would look like one for a normal distribution, however, with a number of outliers beyond one whisker. Table 11 provides the best solution obtained by the WCA among all of the runs, which is illustrated in Figures 8-10. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & **Route** & **Route Length** & **Route** \\
**Route No. ** & **Route Structure** & **Demand** & **(km)** & **Frequency** \\  & & **(Passenger/h)** & **(Km)** & **(Trip/h)** \\ \hline  
emand** & **(Km)As shown in Table 11, the transit network consists of 17 feeder bus routes with an average service frequency of 6.24 trips per hour (the average headway is 9.61 min). The case solution includes 3062.4 passenger-km of travel. The provided total cost consists of 71.05% user, 28.53% operator and 0.42% social costs, which is illustrated graphically in Figure 8. It can be observed that the main costs are ranked as user, operator and social costs, respectively, from the maximum to minimum.