## 1 Introduction
The advantage of the first method is that the train does not need to run empty after the end of the operation, so, it will not result in an increase in operating costs and the waste of resources. The disadvantage is that it will occupy the standby train, which will affect the robustness of the timetable in the implementation process. If there is an emergency, the number of standby train-set may be insufficient, which will expand the negative impact. The advantage of the second method is that it will not affect the robustness in the timetable implementation process, but the disadvantage is as mentioned above, which will cause the waste of resources. In the past, the train timetable was adjusted infrequently, perhaps only a few times a year. Under this adjustment frequency, there is little difference between the two methods. However, as the number of passengers who chose to travel by HSR increased significantly, the fluctuation range of the number of passengers has increased too. In this case, the previous operation mode of only changing the timetable a few times a year has a large lag relative to passenger travel demands. In order to meet the travel demands of passengers better  
Figure 3: The schematic diagram of the timetable switching method. Figure 2: The schematic diagram of the old state and the new state. and save the cost of the operation department, it is necessary to increase the adjustment frequency of the train timetable. The increase in the frequency of train timetable adjustment will amplify the disadvantages of the above two modes, resulting in increased waste of resources or greatly affecting the robustness in the process of timetable implementation. How to avoid the disadvantages of the above two methods and meanwhile scheduling the train-sets, is a problem that is worth studying, because saving resources while meeting the travel demands of passengers is of great significance for practical applications. Thus, we proposed an approach to extend the transition time. In this approach, we extend the transition time from a few hours to a day and realize the train-set rescheduling from the old state to new state through a one-day operation. We call the operation plan during the transition time the transition timetable. The transition timetable proposed in this paper is an approach for the HSR operation department to transition from the old timetable to the new timetable through the operation. The new timetable and the old timetable have been determined by the operation department. The transition timetable scheduling is a train timetabling problem (TTP), and the relevant train-set circulation plan scheduling is a train-set rescheduling problem (TRP). In the scenario proposed in this paper, the TRP has a higher priority, to avoid the disadvantages of the above two methods. Both train timetabling problem (TTP) and train-set rescheduling problem (TRP) are complex for long distance HSR lines:  
Firstly, train timetables are designed to meet the travel demands of passengers. For the long distance HSR line, the passenger travel demands are more complex. The demand that passengers travel from the origin station to the destination station is called O-D. For example, the number of types of O-D for an HSR line with six stations is:  
\[C_{6}^{2}=15 \tag{1}\]  
Let \(n\) be the quantity of stations of the HSR line, the number of O-D types is:  
\[C_{n}^{2}=\frac{n\times(n-1)}{2} \tag{2}\]  
Obviously, with the increase in the quantity of stations along the HSR line, the types of O-D increase too. For the long distance HSR line, there are more than twenty stations and there will be more than 300 types of O-D.  
Secondly, there are more passengers on the long distance HSR line. The operation department needs to prepare more train-sets to meet the travel demands of passengers. Thus, the complexity of scheduling a train-set circulation plan is higher than a normal railway line. Thirdly, due to the increasing adjustment frequency of timetables, the requirement of solving efficiency is higher than that of the past.