# Solving the Urban Transit Routing Problem Using a Cat Swarm Optimization-Based Algorithm
## 4 Computational Results
### Applying CSO to Mandl's Network Instance  
There were executed 100 repeatable Monte Carlo runs per instance per required number of routes. In Tables 5-12, the best and worst results achieved by the proposed CSO algorithm are selected based on the three criteria presented in the former paragraphs using the proposed order of significance. Moreover, the average and standard deviation values presented are the ones calculated over all 100 repeatable Monte Carlo runs. In bold are the values which determine which of the proposed approaches achieve the best results. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Solution with Six Routes**} \\ \cline{2-6}  & \(d_{\theta}\)**(\%)** & \(d_{1}\)**(\%)** & \(d_{2}\)**(\%)** & \(d_{unsatt}\)**(\%)** & \(att\)**(mpu )** \\ \hline
**[PERSON]**[36] & 77.92 & 19.62 & 2.40 & 0.00 & 11.87 \\
**[PERSON] and [PERSON]**[31] & 86.04 & 13.96 & 0.00 & 0.00 & 10.30 \\
**[PERSON] and [PERSON]**[37] & 91.52 & 8.48 & 0.00 & 0.00 & 10.48 \\
**[PERSON], [PERSON] and [PERSON]**[15] & 93.19 & 6.23 & 0.58 & 0.00 & 10.46 \\
**[PERSON], [PERSON] and [PERSON]**[16] & 91.12 & 8.88 & 0.00 & 0.00 & 10.50 \\
**[PERSON] and [PERSON]**[39] & 95.50 & 4.50 & 0.00 & 0.00 & 10.29 \\
**[PERSON] and [PERSON]**[17] & 95.57 & 4.43 & 0.00 & 0.00 & 10.28 \\
**[PERSON] and [PERSON]**[41] & 95.63 & 4.37 & 0.00 & 0.00 & 10.23 \\
**[PERSON] and [PERSON]**[43] & 96.15 & 3.73 & 0.13 & 0.00 & **10.22** \\
**[PERSON] [13]** & 94.54 & 5.14 & 0.32 & 0.00 & 10.33 \\
**[PERSON] and [PERSON]**[26] & 78.61 & 21.39 & 0.00 & 0.00 & 11.86 \\ \hline  & **Best** & **96.21** & 3.66 & 0.13 & 0.00 & **10.22** \\
**CSO** & **Worst** & 95.25 & 4.75 & 0.00 & 0.00 & 10.32 \\
**Average** & 95.95 & 4.012 & 0.038 & 0.00 & 10.2655 \\
**Std** & 0.584 & 0.562 & 0.079 & 0.00 & 0.031 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: 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{5}{c}{**Solution with Four Routes**} \\ \cline{2-6}  & \(d_{\theta}\)**(\%)** & \(d_{1}\)**(\%)** & \(d_{2}\)**(\%)** & \(d_{unsatt}\)**(\%)** & \(att\)**(mpu )** & \(tt\)**(cmpu)** \\ \hline
**[PERSON]**[25] & 69.94 & 29.93 & 0.13 & 0.00 & 12.90 \\
**[PERSON]**[36] & 72.95 & 26.91 & 0.13 & 0.00 & 12.72 \\
**[PERSON] and [PERSON]**[31] & 79.38 & 17.60 & 3.02 & 0.00 & 11.52 \\
**[PERSON] and [PERSON]**(published) & 86.86 & 12.00 & 1.14 & 0.00 & 11.90 \\
**[PERSON] and [PERSON]**[37] & 93.26 & 6.74 & 0.00 & 0.00 & 11.37 \\
**[PERSON], [PERSON] and [PERSON]**[15] & 90.88 & 8.35 & 0.77 & 0.00 & 10.65 \\
**[PERSON] and [PERSON]**[41] & 92.1 & 7.19 & 0.71 & 0.00 & **10.51** \\
**[PERSON] and [PERSON]**[39] & 91.33 & 8.16 & 0.51 & 0.00 & 10.56 \\
**[PERSON], [PERSON] and [PERSON]**[16] & 91.46 & 8.54 & 0.00 & 0.00 & 10.65 \\
**[PERSON] et. al**[42] & 93.77 & 6.23 & 0.00 & 0.00 & 206,770 \\
**[PERSON] and [PERSON]**[17] & 93.71 & 6.29 & 0.00 & 0.00 & 10.82 \\
**[PERSON] and [PERSON]**[43] & 91.84 & 7.64 & 0.51 & 0.00 & 10.64 \\ \hline  & **Best** & 91.52 & 7.77 & 0.71 & 0.00 & 10.54 \\
**CSO** & **Worst** & 91.2 & 8.8 & 0.00 & 0.00 & 10.81 \\
**Average** & 89.605 & 9.985 & 0.414 & 0.00 & 10.6765 \\
**Std** & 1.815 & 1.826 & 0.419 & 0.00 & 0.0749 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparative results for the best four-route solutions for Mandl’s network.