## 6 Results and Discussions
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Unit** & **Value** \\ \hline \(\mu_{a}\) & RM/passenger-h & 28 \\ \(\mu_{av}\) & RM/passenger-h & 28 \\ \(\mu_{I}\) & RM/passenger-h & 14 \\ \(\lambda_{J}\) & RM/veh-h & 50.30 \\ \(\lambda_{I}\) & RM/veh-km & 1.30 \\ \(\lambda_{I}\) & RM/veh-h & 40 \\ \(\lambda_{m}\) & RM/veh-km & 2.62 \\ \(\lambda_{p}\) & RM/veh-h & 35.70 \\ \(\lambda_{s}\) & RM/veh-km & 0.25 \\ \(V\) & km/h & 32 \\ \(S_{ij}\) & min & 15 \\ \(t_{aF}\) & min & 7.5 \\ \(t_{aTj}\) & min & 4 \\ \(t_{dT}\) & min/passenger & 0.03 \\ \(t_{df}\) & min/passenger & 0.096 \\ \(V_{T}\) & km/h & 40 \\ \(F_{T}\) & veh/h & 20 \\ \(f_{min}\) & veh/h & 2 \\ \(f_{max}\) & veh/h & 20 \\ \(N\) & veh & 100 \\ \(LF\) & pass/seat & 1 \\ \(C\) & pass/veh & 36 \\ \(l_{min}\) & km & No constraint \\ \(l_{max}\) & km & 5 \\ \(\lambda_{lt}\) & RM /veh-h & 630 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Selected values for the parameters used in the Petaling Jaya study area. The best solution obtained in the PJ area is provided by the WCA, as shown in Table 8. Additionally, the main costs are illustrated graphically in Figure 4. A total cost of RM 23,494.8 per hour is achieved, with an average service frequency of 6.2 trips per hour (buses on average arriving at intervals of 9.67 min). Accordingly, Table 9 demonstrates the comparison of the statistical optimization results obtained for the two reported optimizers for the FNDSP. Table 9 shows that the WCA obtained the best cost (minimum cost) for the FNDSP. The WCA performed better compared to the ICA, having better solution stability. The detailed statistical optimization results associated with each term in the modified cost function using the applied algorithms are presented in Table 10.  
As shown in Table 10, it can be concluded that the WCA is superior over the ICA optimizer for finding all cost terms (except the \(C_{P}\)) with minimum statistical optimization results. Figure 5 shows the deviation percentage associated with the corresponding optimization algorithms for 50 independent runs. Acceptable stability can be seen in the results among different runs. In fact, Figure 5 confirms the reliability of the presented optimization methods. The stochastic nature of the method applied to produce the initial values for each iteration makes it natural not to obtain the same results through different independent runs. However, the final results (\(C_{T}\)) are similar for various runs, with about 0.92% and 1% for the WCA and ICA, respectively. The ICA is only about 0.08% worse than the WCA. Both methods are comparable. The convergence rate and cost history (_i.e._, cost reduction) of the applied optimization algorithms have been compared and are illustrated in Figure 6. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Method** & \(C_{W}\) & \(C_{ui}\) & \(C_{F\!F}\) & \(C_{mF}\) & \(C_{pF}\) & \(C_{u}\) & \(C_{o}\) & \(C_{s}\) & \(C_{T}\) & \(A_{F}\) & \(T_{PK}\) \\ \hline ICA & 5042.0 & 2333.6 & 688.6 & 1150.1 & 1420.3 & 16,761.3 & 6815 & 107.3 & 23,683.5 & 5.8 & 3179.6 \\ WCA & 4922.2 & 2384.7 & 634.2 & 1059.2 & 1497.6 & 16,692.6 & 6704 & 98.8 & 23,494.8 & 6.2 & 3062.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of the best solutions obtained for the transit service model using the reported methods. All cost values are based on Malaysian Ringgit (RM). Figure 4: Comparison of obtained best results and main cost terms (RM). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Optimizers** & **Best Solution** & **Average Solution** & **Worst Solution** & **SD** \\ \hline
**ICA** & 23,683.45 & 24,145.10 & 24,889.90 & 242.55 \\
**WCA** & 23,494.80 & 24,024.00 & 24,354.05 & 220.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of statistical results gained by the optimizers under consideration.