## 6 Case Study
### Parameters  
The safety operation parameters we set in the example are shown in Table 6. These parameters are used to calculate the timetable. The dwell time is usually two minutes. It should be noted that Beijing Nan Station and Shanghai Hongqiao Station have no dwell time. Because the dwell time is for passengers to get on and off trains, they are generally set up at stations along railway lines. These two stations are stations at both ends of the line and will only be used as starting or terminal stations. Figure 15: The Beijing–Shanghai HSR line. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Start addition time & 2/min \\ Stop addition time & 3/min \\ Headway & 3/min \\ Departure interval & 4.5/min \\ Arrival interval & 4/min \\ Dwell time & 2/min \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The safety operation parameters. \begin{table}
\begin{tabular}{c c} \hline \hline
**Station** & **Train Service Quantity** \\ \hline Beijing Nan & 157 \\ Langfang & 22 \\ Tianjin Nan & 51 \\ Cangzhou Xi & 32 \\ Dezhou Dong & 35 \\ Jinan Xi & 128 \\ Taian & 32 \\ Qufu Dong & 26 \\ Tengzhou Dong & 31 \\ Zaozhuang & 26 \\ Xuzhou Dong & 101 \\ Suzhou Dong & 29 \\ Bengbu Nan & 34 \\ Dingyuan & 21 \\ Chuzhou & 38 \\ Nanjing Nan & 159 \\ Zhenjiang Nan & 24 \\ Danyang Bei & 24 \\ Changzhou Bei & 27 \\ Wuxi Dong & 26 \\ Suzhou Bei & 32 \\ Kunshan Nan & 17 \\ Shanghai Hongqiao & 135 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The service plan. \begin{table}
\begin{tabular}{c c} \hline \hline
**Boundary Station** & **Old State** & **New State** \\ \hline Beijing Nan & 28 & 35 \\ Tianjin Nan & 17 & 12 \\ Jinan Xi & 15 & 18 \\ Xuzhou Dong & 12 & 9 \\ Nanjing Nan & 25 & 17 \\ Shanghai-Hongqiao & 29 & 35 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The train-set position. In Figure 17, the best solution among 80 initial feasible solutions is better, because if there are more initial solutions, it is more likely to generate better solutions. We evaluate the quality of the timetable in two ways, one is the satisfaction of the number of stops in each period, the other is the number of adjustments required to make the timetable meet the safety operation constraints. The first way has an impact on the quality of the timetable and the second way has an impact on the train-set circulation. The solving speed is the fastest if we only initial 30 feasible solutions. However, from the perspective of passenger satisfaction, there are 1207 stops in the original service plan. In case III the sum of the number of stops in each period is 1142, which is 31.42% higher than case I. Moreover, the number of adjustments in case III is 50% lower than case I. It means that the timetable and the train-set circulation plan in case III is better than case I. From the perspective of practical application, the HSR operation department can select the number of initial feasible solutions generated according to their demands. If they want to obtain higher quality solutions and do not require to obtain solutions in a short time, they can set more initial feasible solutions. Moreover, we tested the case of not dividing the time, the result shows that although the number of stops is similar to the approach proposed in this paper, the passenger travel demands satisfaction of each period is very poor. To verify the performance of the GA, we compared the approach proposed in this paper with the normal approach, in which the timetable is solved by CPLEX at first and then adjust the timetable to meet the train-set position constraints. The time consumption of the normal approach is 38 minutes because the CPLEX needs to solve the stop plan and the timetable at the same time. Moreover, the satisfaction of passenger travel demands is 33.8% lower than the case of 80 solutions. This result is caused by the CPLEX solver arranging all the trains with fewer stops at the front of the timetable. This will lead to unbalanced station stops, too few stops of trains in the early period and too many stops of