# Solving the Urban Transit Routing Problem Using a Cat Swarm Optimization-Based Algorithm
## 4 Computational Results
### Applying CSO to Mandl's Network Instance
The best solution (route set) with six routes found by the proposed CSO algorithm is the following:  
1 st Route: {0 1 2 5 14 6 9 13}  
Route: {0 1 4 3 5 7 9 10}  
Route: {0 1 2 5 7 9 10 12}  
Route: {0 1 3 11 10 12 13 9} \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Solution with Six Routes**} \\ \hline  & \(d_{\mathbf{0}}\) **(\%)** & \(d_{\mathbf{1}}\) **(\%)** & \(d_{\mathbf{2}}\) **(\%)** & \(d_{unsatt}\) **(\%)** & \(att\) **(mpu )** & \(ttc\) **(mpu)** \\ \hline
**[PERSON] and [PERSON]**[40] & 94.34 & 5.65 & 0.00 & 0.00 & & 185,224 \\
**(11 nodes)** & **97.43** & 2.57 & 0.00 & 0.00 & & **153,510** \\ \hline
**[PERSON] et al.**[38] & **98.91** & 1.09 & 0.00 & 0.00 & **10.10** \\ \hline
**CSO (13 nodes)** & 98.84 & 1.16 & 0.00 & 0.00 & **10.10** \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparative results for the best six-route solutions for Mandl’s network. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Solution with Six Routes**} \\ \hline  & \(d_{\mathbf{0}}\) **(\%)** & \(d_{\mathbf{1}}\) **(\%)** & \(d_{\mathbf{2}}\) **(\%)** & \(d_{unsatt}\) **(\%)** & \(att\) **(mpu )** & \(ttc\) **(mpu)** \\ \hline
**[PERSON] and [PERSON]**[40] & 94.41 & 5.59 & 0.00 & 0.00 & & 185,405 \\
**(11 nodes)** & **98.27** & 1.73 & 0.00 & 0.00 & & **153,120** \\ \hline
**[PERSON] et al.**[38] & 99.55 & 0.45 & 0.00 & 0.00 & 10.07 & \\ \hline
**CSO (13 nodes)** & 99.36 & 0.64 & 0.00 & 0.00 & **10.06** & \\ \hline \hline \end{tabular}
\end{table} 
Table 12: 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{6}{c}{**Solution with Eight Routes**} \\ \hline  & \(d_{\mathbf{0}}\) **(\%)** & \(d_{\mathbf{1}}\) **(\%)** & \(d_{\mathbf{2}}\) **(\%)** & \(d_{unsatt}\) **(\%)** & \(att\) **(mpu )** & \(ttc\) **(mpu)** \\ \hline
**[PERSON] and [PERSON]**[40] & 96.40 & 3.60 & 0.00 & 0.00 & & 185,590 \\
**(11 nodes)** & **98.33** & 1.67 & 0.00 & 0.00 & & **154,100** \\ \hline
**[PERSON] et al.**[38] & 99.86 & 0.14 & 0.00 & 0.00 & **10.03** & \\ \hline
**CSO (13 nodes)** & 99.61 & 0.39 & 0.00 & 0.00 & 10.04 & \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Comparative results for the best six-route solutions for Mandl’s network. As Table 6 shows, the route set that the CSO approach produced for a six-route route set improves the best achieved solution ([38]) to 0.06% (same average travelling time; better zero transfers' satisfied transfer demands). Even the worst achieved solution by the CSO algorithm is better than many of the best solutions achieved by other approaches, and all transfer demands are satisfied with no more than one transfer. The route set that CSO produced gives an average travelling time per user that differs by 2.14% from the ideal one (see Table 4). The best solution (route set) with routes found by the proposed CSO algorithm is the following:  
1 st Route: {0 1 2 5 7 9 10 12}  
Rout: {7 9 6 14 5 2 1 0}  
Rout: {6 14 7 5 3 1 2 -1}  
Rout: {0 1 4 3 5 7 9 10}  
Rout: {5 3 11 10 9 6 14 8}  
Rout: {8 14 5 2 1 4 3 11}  
Rout: {0 1 3 11 10 12 13 9}  
As Table 7 shows, the route set that the CSO approach produced for a seven-route route set improves the best achieved solution ([23]) to 0.3% (10.12 min per user from 10.15 min per user). Even the worst achieved solution by the CSO algorithm is better than many of the best solutions achieved by other approaches. All transfer demands are satisfied with no more than one transfer in both best and worst solutions. The route set that CSO produced gives an average travelling time per user that differs by 1.14% from the ideal one (see Table 4). The best route set with eight routes created using the proposed CSO algorithm:  
1 st Route: {0 1 4 3 5 7 9 10}  
Rout: {0 1 2 5 14 6 9 13}  
Rout: {0 1 2 5 7 9 10 12}  
Figure 8: The best route set with four routes produced by CSO.