# An Integrated Optimization Method of High-Speed Railway Rescheduling Problem at the Network Level
## 4 NSGA-III Algorithm
### Initial Populations and Infeasible Solution Adjustment
Rather than simply weighting and summing the three objectives, the algorithm optimizes the objectives together and provides a Pareto front with a group of non-dominated solutions for operators to choose from. We tested the adaptability of the proposed model and algorithm on a real-world railway network in China. After 1000 iterations, we obtained a Pareto front containing a group of feasible solutions for the operators to choose from in different situations. We compared the average value of the three objectives in these solutions before and after optimization and obtained the optimization rate, which is 12.12%, 14.12, and 10.57%, respectively, indicating that our method can improve the quality of the solutions effectively. We also run the algorithm 10 times and calculate the mean value, the standard deviation, and the coefficient of variation of the objectives. The coefficients of variation are 2.82%, 0.35%, and 0.95%, respectively, which indicates that our algorithm has considerable reliability and reproducibility. Figure 14: The number of times for each depot being a key depot. We also proposed an integrated optimization method to reschedule the train timetable and the train set circulation plan at the network level. The proposed method combines different dispatching methods in the model and reschedules the above two plans integratedly rather than rescheduling them in stages. Moreover, we designed a group of experiments with one-direction interruptions that occur in different sections and at different times. Then, we analyzed the total delay and discovered the bottleneck section (section 15) and the bottleneck time (11:00). Finally, we set up a series of cases to analyze the importance of the depots. By counting the number of times that the depot is a key depot, we give the operator some advice to set more standby train sets in depot II when formulating the train set layout scheme and conclude that depot II is more important than other depots in the network. We assume the probability of interruption occurring in each section is equal when we analyze the importance of the depots. However, the occurrence of emergencies has certain regularities. If future research conducts an in-depth study of the regularities, the analysis and suggestions for the deployment of the standby train sets will be more convincing and significant. Conceptualization, W.Z., L.Z. and B.G. ; methodology, W.Z., B.G. and Y.Y. ; software, W.Z. and Z.W. ; validation, W.Z. and B.G. ; formal analysis, W.Z. and Y.M. ; investigation, W.Z., B.G. and C.H. ; resources, W.Z. and Y.M. ; data curation, W.Z. ; writing--original draft preparation, W.Z. ; writing--review and editing, L.Z., B.G. and Y.Y. ; visualization W.Z., C.H. and Y.M. ; supervision, L.Z. and B.G. ; project administration, W.Z., B.G. and Y.Y., funding acquisition, B.G. and Z.W. All authors have read and agreed to the published version of the manuscript. This research was funded by Research Supported by the Fundamental Research Funds for the Central Universities (Science and technology leading talent team project), grant number 2022)BQY005; Research project of China State Railway Group Co., Ltd., grant number K2021X002; and Research project of China Railway Beijing Group Co., Ltd., grant number 2022 BY02. Not applicable. The authors would like to express great appreciation to editors and reviewers for their positive and constructive comments. And thanks are due to [PERSON] for data curation and funding acquisition. The authors declare no conflict of interest. ## References

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