## 7 Conclusions  
In this paper, an approach is proposed to solve the problem of scheduling the timetable and train-set circulation plan under the frequency switching scenario of the timetable. This approach considers the travel demands of passengers and the operational requirements of HSR. It can save the cost of railway operation department while realizing the state changing of train-set during the transition time.  
Firstly, we design an inter programming model including section sequence for train-set, so that the operating distance can be decided based on each section's operating profits. We use CPLEX to solve the model in a very short time. By this model, we obtained a maximum benefit oriented primary train-set circulation plan, which will be matched with the stop plan.  
Secondly, we design a method for solving the stop plan based on passenger travel demands. For the passenger travel demands, we adopted the travel demands decomposition method to covert the complex passenger travel demands into the service plan. Then we use CPLEX to calculate the stop plan according to the service plan efficiently.  
Thirdly, we design the matching and adjusting method of the stop plan and the primary train-set circulation plan. In the method, we split the primary train-set circulation plan into different schemes at first. Then we match the schemes in the stop plan and the schemes in the train-set circulation plan by a customized GA we designed. After one-to-one correspondence is determined between the schemes in the stop plan and schemes in the primary train-set circulation plan, the timetable can be calculated. Finally, the final train-set circulation plan and timetable are obtained.  
Fourthly, we test the approach we proposed by the Beijing-Shanghai HSR. The results show that for the aspect of passenger travel demands, the approach proposed in this paper can meet 94.61% of passenger travel demands, and the solving efficiency is higher than the normal approach. What is more, it can save the costs of the operation department.  
In the future, we will continue to take the practical application as the guidance to study the collaborative scheduling of timetable and train-set circulation plan:  
Firstly, some other algorithms can be used to improve the solving efficiency. We will try to use gradient methods and compare the solving efficiency and the quality of solutions between different algorithms.  
Secondly, as there are always some stochastic effects that affect railway traffic, we will optimize the reserve deposit between train intervals to balance the railway traffic efficiency and robustness. Moreover, also, we need to study how to recover normal operation order as soon as possible after disturbance.  
Thirdly, we will consider adding the maintenance mileage of the train into the model, which is urgently needed in practical applications. The maintenance of the train may affect the scheduling of the circulation plan of the train-set because, under the existing train-set utilization system, the train-set needs to be checked and repaired at specific locations, which may affect the stop position of the train.  
Conceptualization, Z.W. and L.Z.; Data curation, W.Z.; Formal analysis, Z.W. and Z.B.; Funding acquisition, Z.B. and L.Z.; Methodology, Z.W.; Project administration, L.Z.; Resources, H.Z.; Software, Z.W. and C.H.; Supervision, Z.B.; Validation, Z.W., Z.B. and B.G.; Visualization, Z.W. and W.Z.; Writing--original draft, Z.W.; Writing--review & editing, Z.W., B.G. and H.Z.. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the High-speed Rail Joint Fund of National Natural Science Foundation of China, grant number U1934216.  
Not applicable.  
The authors declare no conflict of interest.