## 4 Computational Experiments
### Results and Analysis  
With the given operation information and the passenger OD demand, we expect to obtain a more efficient timetable using the proposed method. In this experiment, we set weights \(\theta_{1}\) and \(\theta_{2}\) as 10 and 1, respectively. A result was obtained with the gap 14.9% after 30,000 s. The \(RPD\) and \(TTT\) included in the objective are 1 and 1606, respectively. Figure 5 shows the optimized train stop plans, where the solid dot \"\(\bullet\)\" indicates the stations that the train services. It can be seen that Train 6 and Train 9 have the largest number of stops; they both have 8 stops on the railway line. Train 11 has the least number of stops. The relationship between the stop frequency and passenger demand is shown in Figure 6, which indicates that the frequency of train stops and the size of passenger demand at stations are closely related. Except for the terminal stations, Stations \(D\), \(E\) and \(G\) have a relatively high stop frequency, which is in line with the given larger passenger travel demand of these three stations. The lower passenger demand also results in fewer stops at Stations \(C\), \(F\) and \(H\). Experimental results show that the scale of passenger demand determines the stopping pattern of trains to a certain extent. Figure 7 shows the obtained train timetable in the experiment. The horizontal axis indicates the time, the vertical axis indicates the station, and the lines of different colors indicate different train services in this figure. It can be seen that Trains 4-11 in the dashed box are in denser departure compared with other trains. The peak hour for the given passenger demand is 8:30-9:30. The timetable structure obtained is relatively consistent with the passenger demand distribution. The expected departure times of passengers also affect the structure of the timetable. Besides the number of stops, overtaking will also increase the train travel time. In this test result, four instances of overtaking occurred. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(t_{ac}\) & 2 min & \(h_{ap}\) & 5 min \\ \(t_{de}\) & 2 min & \(h_{pd}\) & 2 min \\ C & 600 & \(h_{pp}\) & 3 min \\ \(\mu\) & 100\% & \(h_{dd}\) & 5 min \\ \(t_{s}^{ab}\) & 2 min & \(h_{ap}\) & 3 min \\ \(t_{s}^{lb}\) & 10 min & \(h_{pa}\) & 3 min \\ \(num\) & 3 & \(h_{aa}\) & 4 min \\ \(\overline{num}\) & 8 & \(\Delta T\) & 15 min \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Parameters involved in the model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Section** & **Distance (km)** & **Pure Running Time (min)** \\ \hline \(A\)–\(B\) & 64 & 17 \\ \(B\)–\(C\) & 27 & 7 \\ \(C\)–\(D\) & 45 & 10 \\ \(D\)–\(E\) & 39 & 9 \\ \(E\)–\(F\) & 13 & 3 \\ \(F\)–\(G\) & 29 & 7 \\ \(G\)–\(H\) & 10 & 2 \\ \(H\)–\(I\) & 24 & 5 \\ \(I\)–\(J\) & 50 & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Distance and pure running time in each section. To further track the passenger distribution per train, we give the seat occupancy during each serviced section for each train, as shown in Figure 8. The seat occupancy can be calculated by Equation (19):  
\[\omega_{i}^{s}=\frac{\sum\limits_{m=1}^{s}\sum\limits_{n=s+1}^{|S|}\sum\limits_{ l=1}^{|T|}q_{i,l}^{m,n}}{C} \tag{19}\]  
where \(\omega_{i}^{s}\) represents the seat occupancy of train \(i\) between station \(s\) and \(s+1\). Passenger distribution in each train is closely related to the passenger flow scale of different OD and the distribution in the time dimension. It can be seen that passengers on Trains 1-8 are mainly concentrated in the second half of the train journey. Trains 9 and 10 are more  
Figure 5: Optimized train stop plan in the experiment. crowded in the middle of their journey. The passenger distribution of the remaining trains is relatively balanced, among which Train 11 has the largest seat occupancy rate. The average occupancy rate of all trains is more than 70%, which means that train resources are well utilized.