# An Integrated Optimization Method of High-Speed Railway Rescheduling Problem at the Network Level
## 2 Literature Review
Aimed at improving the punctuality rate of trains, reducing the fluctuation of train operation time in sections, and improving the speed of freight trains, [PERSON] [36] proposed a multi-objective optimization model to synergistically optimize the deviation of the train timetable under disturbance, the energy consumption, and the number of stranded passengers. And the model was further transformed into a linear model to promote problem-solving. [PERSON] [37] took minimizing the generalized punishment of train operation delay and the stability of train operation as the optimization objective functions and defined the satisfaction of the two objective functions for the two-objective programming problem to obtain a feasible solution. [PERSON] et al. [26] aimed at optimizing both the average deviation of departure intervals and the maximum train loading rate under time-varying passenger transport demand, proposed an optimization model for an irregular train schedule, and designed a heuristic simulated-annealing algorithm to solve the model. [PERSON] et al. [38] developed a mixed-integer linear programming model with three objective functions: The penalty value of canceling the train, the penalty value of the scheduling plan, and the penalty value of the deviation between the actual end station and the planned end station. Then they weighted the three objective functions to convert the multi-objective programming into single-objective programming and tested it on a Dutch railway line. A multi-objective function can solve problems with more than one objective and provide a set of diverse solutions for decision-makers. But the computational complexity can be increased compared to a single-objective function. Above all, we can find that:  
* Firstly, many researchers study the rescheduling problem on one railway line; few researchers solve the rescheduling problem on a railway network. While, considering the strong correlations between the railway lines, minor disturbances in the section likely tend to cause larger delays and propagate across the network. Thus, it is of great significance to solve the rescheduling problem on a railway network rather than on one line. * Secondly, some studies focus on rescheduling train timetables or train set circulation plans, respectively. A small part of the studies uses integrated adjustment methods to deal with the two aspects. However, considering the train set circulation plan supports the feasibility of the train timetable, if emergencies occur, both the train timetable and the train set circulation plan will be deeply influenced. So, it is of great significance to propose an integrated adjustment method for the two aspects when rescheduling. * Thirdly, in the process of modeling, many studies consider only one objective, such as minimizing train delay, minimizing passenger delay, minimizing the number of canceled trains, etc. Some studies formulate the model with multiple objectives, but most of them use the method of weighting and summing these objectives. While the rescheduling problem is a complex one that involves many factors, it is difficult to describe the problem well with one objective, and the method of weighting and summing objectives is also not appropriate because it is difficult to find a scientific and acknowledged method to determine the weight of objectives. The main contributions of the paper are as follows:
* In order to deal with the unforeseen events in the HSR network, reduce the propagation of delays on lines and even the whole network, and reduce the influence on passenger travel, we expand our research scope to the network level, which is more challenging and more significant. * Compared with simply weighing and summing the objectives, we design an algorithm based on NSGA-III to solve the rescheduling problem and obtain a non-dominated Pareto front for three objectives. Each solution in the Pareto Front has a comparative advantage, and the operator can choose a reasonable rescheduling scheme from the front under different circumstances.