# Solving the Urban Transit Routing Problem Using a Cat Swarm Optimization-Based Algorithm
## 5 Conclusions--Future Work  
In this work, a robust CSO-based algorithm has been constructed and applied to the urban transit routing problem (UTRP). Efficient and feasible near-optimal route networks for public transit networks were designed using this novel approach. To our knowledge, this is the first time that a CSO-based algorithm is applied to solve the UTRP. Five input instances were used as benchmark \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multicolumn{13}{c}{**Kechagiopoulos and Beligiannis [43]**} & \multicolumn{8}{c}{**CSO**} \\ \hline \(x_{4m}\) & \(d_{0}\) & \(d_{1}\) & \(d_{2}\) & \(d_{amsatt}\) & \(Att\) & \(L_{tot}\) & \(d_{0}\) & \(d_{1}\) & \(d_{2}\) & \(d_{unsatt}\) & \(att\) & \(L_{tot}\) \\ \hline
**80** & 74.07 & 23.5 & 2.38 & 0.05 & 13.4 & 82.45 & 71.79 & 24.80 & 3.38 & 0.03 & 13.42 & 74.00 \\
**100** & 82.3 & 16.34 & 1.36 & 0.00 & 13.06 & 95.20 & 69.67 & 26.58 & 3.71 & 0.04 & 13.54 & 72.85 \\
**120** & 87.63 & 11.53 & 0.84 & 0.00 & 11.48 & 114.05 & 72.67 & 24.00 & 3.32 & 0.00 & 13.32 & 74.40 \\
**140** & 90.56 & 8.80 & 0.65 & 0.00 & 10.90 & 131.60 & 73.84 & 23.85 & 2.32 & 0.02 & 13.12 & 74.10 \\
**160** & 90.78 & 8.60 & 0.62 & 0.00 & 10.83 & 142.40 & 72.70 & 24.23 & 3.07 & 0.00 & 13.09 & 75.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 18: Comparative results for providers’ operational cost for a route set with 4 routes and 10 nodes per route (average values). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multicolumn{13}{c}{**Kechagiopoulos and Beligiannis [43]**} & \multicolumn{8}{c}{**CSO**} \\ \hline \(x_{4m}\) & \(d_{0}\) & \(d_{1}\) & \(d_{2}\) & \(d_{amsatt}\) & \(Att\) & \(L_{tot}\) & \(d_{0}\) & \(d_{1}\) & \(d_{2}\) & \(d_{unsatt}\) & \(att\) & \(L_{tot}\) \\ \hline
**20** & 68.45 & 24.73 & 6.51 & 0.30 & 13.69 & 75.53 & 65.354 & 24.801 & 8.615 & 1.23 & 14.3915 & 72.05 \\
**40** & 68.68 & 25.35 & 5.83 & 0.13 & 13.79 & 76.03 & 63.922 & 27.3 & 8.071 & 0.729 & 14.5495 & 71.6 \\
**60** & 71.71 & 24.06 & 4.12 & 0.11 & 13.18 & 77.00 & 65.7 & 28.498 & 5.502 & 0.302 & 14.0675 & 72.35 \\
**80** & 75.37 & 21.97 & 2.47 & 0.18 & 12.40 & 80.20 & 69.299 & 26.577 & 4.11 & 0.013 & 13.584 & 73.55 \\
**100** & 84.28 & 14.92 & 0.33 & 0.46 & 11.41 & 98.80 & 70.279 & 26.179 & 3.517 & 0.026 & 13.4155 & 73.85 \\
**120** & 89.66 & 9.60 & 0.65 & 0.10 & 10.94 & 116.77 & 70.851 & 25.797 & 3.301 & 0.052 & 13.318 & 74.15 \\
**140** & 90.21 & 9.13 & 0.66 & 0.00 & 10.77 & 133.04 & 71.268 & 26.198 & 2.522 & 0.013 & 13.263 & 74.45 \\
**160** & 89.96 &problems, derived from international literature, which consist of well-known test instances for the UTRP in the respective literature. Experimental results showed that the proposed CSO-based algorithm achieves in all test instances very satisfactory results comparable with the best results found to date by other effective published approaches applied to the same test instances using the same evaluation criteria. This fact demonstrates that applying CSO-based algorithms is a very good choice to effectively solve the UTRP, excluding the fact that the proposed algorithm also considers the optimization of the provider's operational cost. Some experimental results show that by adjusting the algorithm's parameters, the proposed algorithm can both fulfill passengers' demands and, at the same time, succeed in decreasing operational costs. A weak spot of the proposed algorithm is the determination of parameters' values, which plays a significant role in the algorithm's optimization capability. A more systematic method to determine the (near) optimal values of all algorithms' parameters will be one of the main issues of our future work. Moreover, further research toward optimizing the cost of the service provider as well as applying the algorithm to relevant vehicle routing problems, such as the capacitated vehicle routing problem (CVRP) and the open vehicle routing problem, are future goals of the authors. Formal analysis, investigation, resources, software, validation, visualization, writing--original draft, I.V.K.