# An Integrated Optimization Method of High-Speed Railway Rescheduling Problem at the Network Level
## 4 NSGA-III Algorithm
### Initial Populations and Infeasible Solution Adjustment
So, if one interruption occurs in section 15, many trains will be influenced, and the delay of these trains will propagate through the railway network, and then, the total delay of the whole network will increase greatly. We also find that in the right part of Figure 13, for each occurrence time, the total delay of section 29 is obviously greater than other sections, as the blue dashed line indicates. We think the reason is that section 29 is located at the junction of the TB Line and TQ Line, and there are more trains (especially cross-line trains) operated in section 29 than in other sections of the two lines. If the cross-line trains are delayed, it will directly influence more lines and sections, and the propagation of delays will be more significant. Therefore, section 29 should also be given more attention by the operator. Above all, we can find that the operators should pay more attention to the sections in which most trains operate or are located at the junction of the network. Because they are likely to become bottleneck sections. #### 5.3.2 Key Time

From the Y-axis (occurrence time) point of view, the total delay of 11:00 is always the highest for any section, as indicated by the green dashed line in Figure 13. So, we can call 11:00 the bottleneck time. It means that if the interruption occurs at this time, the interruption will have a greater influence on the network and the total delay will have a significant increase, which should be given more attention during the operation. We think the reason is similar to the above; from the data of the train timetable, most trains operate on the network around 11:00. In addition, this period is popular for passengers, and the average number of passengers on each train is high. If one interruption occurs at this time, more trains and passengers will be influenced and delayed, and the total delay will be high. Figure 13: The total delay of three lines after optimization. (**a**) The total delay of BS Line after optimization. (**b**) The total delay of TQ Line and TB Line after optimization. ### Analysis of the Importance of the Depots

In order to analyze the importance of the depots, we assume that each depot has unlimited standby train sets for emergencies and design a series of experiments as follows. We set a one-direction interruption in each of the 36 sections, respectively. All 36 interruptions start at 9:00 am. and last for 180 min. For each interruption, we run our algorithm and get a Pareto front with a group of solution points. For each front, the sum of the standby train sets dispatched from each depot is calculated, and the depot dispatching the most standby train sets is called the \"key depot\" of the interruption. For all the interruptions, 36 Pareto fronts are obtained, and the times of each depot being a key depot are calculated and plotted in Figure 14.

We can see that depot II becomes a key depot 18 times, which is the most. So, we can say that, compared with other depots, depot II plays a significantly important role in this railway network. It means that if the number of train sets in all depots is unlimited and the probability of interruption occurring in each section is equal, dispatching standby train sets from depot II is the most efficient. In other words, the operation department should deploy more standby train sets in depot II. We think the reason is that depots I, III, IV, V, and VI are located on the BS Line and mainly serve the BS Line. Depot II is located in the center of the railway network and has a wider service scope, as mentioned in Section 5.1. For most of the sections, depot II can provide rescue with less additional cost because of its location and connection to the network. ## 6 Conclusions

In the event of emergencies occurring in the HSR network, we proposed a multi-objective model with the objectives of additional operation cost, total delay, and the number of transfer passengers. We designed an algorithm based on NSGA-III to solve the model.