# Solving the Urban Transit Routing Problem Using a Cat Swarm Optimization-Based Algorithm
## 4 Computational Results  
To evaluate the performance of the algorithm, five input files from the international bibliography containing five road networks data were used: the file of [PERSON]'s road network [25] and four files introduced by [PERSON] [13], namely Mumford0, Mumford1, Mumford2 and Mumford3. Table 4 contains the attributes of these files.  
Evaluation and comparison of route sets is made considering the following criteria (in order of significance):  
1. Unsatisfied travel requirements (\(d_{unsatt}\)), which should be as small as possible and ideally 0%.
2. Average travelling time per user (\(att\)), which should be as small as possible and is equal to \(\frac{\sum_{i,j}d_{ij}\cdot t_{ij}}{\sum_{i,j}d_{ij}}\), where 0\(\leq i\leq\)_number of nodes_, 0\(\leq j\leq\)_number of nodes_, \(d_{ij}\) represents the transferring demands and \(t_{ij}\) symbolizes the travelling time between node \(i\) and node \(j\), respectively, using the route set which is under evaluation (transferring delays are included). Note that this is different from Equation (4), in which we consider only the travelling demands that are satisfied by the route set, i.e., travelling demands that are satisfied with less than three transfers. Alternatively, we use the total user cost (\(ttc\) in minutes [40; 42]) which also should be as small as possible.
3. Percentage of travels with zero transfers (\(d_{0}\)), which should be as large as possible and ideally 100%.  
Code was created in Java, using the Eclipse IDE. All tests were performed in a Windows Vista Home Premium (SP2) 32-bit OS machine, with an Intel Core 2 CPU, T7200 @2.00 GHz and 2.00 GB RAM.  
All five instances have been evaluated using the same method. If there are any discrepancies between the published results and our evaluation, both results are published (this is the case for Mumford [13] solutions). Details about how to run the proposed CSO algorithm, the input files used, the output files containing the best results achieved, as well as, the executable program of the proposed CSO algorithm are available online at [53], so as to be easy for the interested reader to reproduce the below-mentioned results.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Network Name** & **Mandl** & **Mumford0** & **Mumford1** & **Mumford2** & **Mumford3** \\ \hline
**Number of Nodes** & 15 & 30 & 70 & 110 & 127 \\ \hline
**Number of Edges** & 21 & 90 & 210 & 385 & 425 \\ \hline
**Total Transfer Demands** & 15,570 & 342,160 & 1,926,170 & 4,847,900 & 6,934,950 \\ \hline
**Lower Bound for Average** & & & & & \\
**Travelling Time per** & 10.0058 & 13.0121 & 19.2695 & 22.1689 & 24.7453 \\
**User (mins)**[13] & & & & & \\ \hline
**Required Number of** & 4-6-7-8 & 12 & 15 & 56 & 60 \\
**Routes per Route Set** & 8 & 15 & 30 & 22 & 25 \\ \hline
**Maximum Number of** & & & & & \\
**Nodes per Route** & 3 & 2 & 10 & 10 & 12 \\ \hline
**Maximum Length per** & & & & & \\
**Route (mins)** & 50 & - & - & - & - \\ \hline
**Artificial (A) or Real (R)** & R & A & R & R & R \\ \hline \hline \end{tabular}
\end{table}
Table 4: Attributes of input instances’ road networks.