# Solving the Urban Transit Routing Problem Using a Cat Swarm Optimization-Based Algorithm
## 4 Computational Results
### Applying CSO to Mandl's Network Instance
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Solution with Seven Routes**} \\ \cline{2-6}  & \(d_{0}\)**(\%)** & \(d_{1}\)**(\%)** & \(d_{2}\)**(\%)** & \(d_{unsatt}\)**(\%)** & \(att\)**(mpu)** \\ \hline
**[PERSON]**[36] & 93.91 & 6.09 & 0.00 & 0.00 & 10.70 \\
**[PERSON] and [PERSON]**[31] & 89.15 & 10.85 & 0.00 & 0.00 & 10.15 \\
**[PERSON] and [PERSON]**[37] & 93.32 & 6.36 & 0.32 & 0.00 & 10.42 \\
**[PERSON], [PERSON] and [PERSON]**[15] & 92.55 & 6.68 & 0.77 & 0.00 & 10.44 \\
**[PERSON], [PERSON] and [PERSON]**[16] & 92.89 & 7.11 & 0.00 & 0.00 & 10.46 \\
**[PERSON] and [PERSON]**[17] & 95.57 & 4.43 & 0.00 & 0.00 & 10.27 \\
**[PERSON] and [PERSON]**[39] & 97.04 & 2.83 & 0.83 & 0.00 & 10.23 \\
**[PERSON] and [PERSON]**[41] & 98.52 & 1.48 & 0.00 & 0.00 & 10.15 \\
**[PERSON] and [PERSON]**[43] & 97.17 & 2.83 & 0.00 & 0.00 & 10.16 \\
**[PERSON] and [PERSON]**[26] & 80.99 & 19.01 & 0.00 & 0.00 & 12.50 \\ \hline
**ESO** & 97.94 & 2.06 & 0.00 & 0.00 & **10.12** \\
**ESO** & 97.11 & 2.89 & 0.00 & 0.00 & 10.23 \\
**Average** & 97.422 & 2.579 & 0.00 & 0.00 & 10.1895 \\
**Std** & 0.705 & 0.705 & 0.00 & 0.00 & 0.0350 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparative results for the best seven-route solutions for Mandl’s network. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Solution with Eight Routes**} \\ \cline{2-6}  & \(d_{0}\)**(\%)** & \(d_{1}\)**(\%)** & \(d_{2}\)**(\%)** & \(d_{unsatt}\)**(\%)** & \(att\)**(mpu)** \\ \hline
**[PERSON]**[36] & 84.73 & 15.27 & 0.00 & 0.00 & 11.22 \\
**[PERSON] and [PERSON]**[31] & 90.38 & 9.58 & 0.00 & 0.00 & 10.46 \\
**[PERSON] and [PERSON]**[37] & 94.54 & 5.46 & 0.00 & 0.00 & 10.36 \\ [PERSON], [PERSON] and [PERSON]**[15] & 91.33 & 8.67 & 0.00 & 0.00 & 10.45 \\
**[PERSON], [PERSON] and [PERSON]**[16] & 93.14 & 6.86 & 0.00 & 0.00 & 10.42 \\
**[PERSON] and [PERSON]**[39] & 97.37 & 2.63 & 0.00 & 0.00 & 10.20 \\
**[PERSON] and [PERSON]**[41] & **98.97** & **1.03** & **0.00** & **0.00** & 10.09 \\
**[PERSON] and [PERSON]**[17] & 97.82 & 2.18 & 0.00 & 0.00 & 10.19 \\
**[PERSON] and [PERSON]**[43] & 97.75 & 2.25 & 0.00 & 0.00 & 10.13 \\
**[PERSON] and [PERSON]**[26] & 79.96 & 20.04 & 0.00 & 0.00 & 11.86 \\ \hline
**ESO** & **98.97** & **1.03** & **0.00** & **0.00** & **10.08** \\
**CSO** & **99.04 & 0.96 & 0.00 & 0.00 & 10.17 \\
**Average** & 98.478 & 1.523 & 0.00 & 0.00 & 10.125 \\
**Std** & 0.397 & 0.397 & 0.00 & 0.00 & 0.0309 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparative results for the best eight-route solutions for Mandl’s network. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Solution with Four Routes**} \\ \hline  & \(d_{0}\)**(\%)** & \(d_{1}\)**(\%)** & \(d_{2}\)**(\%)** & \(d_{unsatt}\)**(\%)** & \(att\)**(mpu)** & \(tt\)**(mpu)** \\ \hline
**[PERSON] and [PERSON]**[40] & **95.05** & 4.95 & 0.00 & 0.00 & 186,368 \\
**(11 nodes)** & 93.77 & 5.72 & 0.51 & 0.00 & **146,320** \\ \hline
**[PERSON] et al.**[38] & 95.83 & 3.60 & 0.57 & 0.00 & 10.35 \\
**(13 nodes)** & **96.27** & 3.73 & 0.00 & 0.00 & **10.31** \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparative results for the best four-route solutions for [PERSON]’s network. The best solution (route set) with four routes found by the proposed CSO algorithm, which is presented in Figure 8, is the following:  
1 st Route: {9 6 14 5 2 1 3 11}  
Route: {5 3 11 10 9 6 14 8}  
Route: {0 1 2 5 7 9 10 12}  
Route: {12 13 9 7 5 3 4 1}  
As Table 5 shows, the route set that the CSO approach produced for a four-route route set is the second best achieved solution among other approaches. Even the worst achieved solution by the CSO algorithm is better than many of the best solutions achieved by other approaches. The route set that CSO produces has an average travelling time per user that differs by only 5.34% from the ideal one (see Table 4).