# An Integrated Optimization Method of High-Speed Railway Rescheduling Problem at the Network Level
## 2 Literature Review
In order to solve the train rescheduling problem, [PERSON] [28] used the Brownian motion weighted-based salp swarm optimization (BMW-SSO) algorithm and the modified weight-based deep learning neural network (MWDLNN) algorithm and obtained good results. These algorithms can be applied to a wide range of problem types and domains. They are not limited to specific problem structures or constraints, making them flexible and adaptable in various scenarios. But they also have disadvantages. For example, the branch and price algorithm can be computationally expensive for large-scale problems due to the exponential growth of the solution space; the ant colony algorithm may require a large number of iterations to converge to a good solution; the heuristic simulated-annealing algorithm requires careful tuning of the cooling schedule and acceptance criterion; the particle swarm optimization algorithm may be susceptible to premature convergence, etc. In 2002, [PERSON] [29] proposed the NSGA-II algorithm to solve two-objective models; based on NSGA-II, [PERSON] [30] proposed the NSGA-III algorithm to solve multi-objective models. The NSGA-III algorithm has been widely studied and applied in various research fields. The NSGA-III algorithm provides a set of diverse solutions that represent the trade-off between different objectives, handles multi-objective optimization problems efficiently without requiring problem decomposition, and enables decision-makers to explore different Pareto optimal solutions and make suitable decisions. It also has disadvantages, such as that the algorithm's performance heavily depends on the selection of algorithmic parameters, and the computational complexity increases with the number of objectives and the size of the population. From the perspective of the objectives, some studies used a single objective function model to solve the rescheduling problem after an emergency. Most of them formulated the model with the objective function of train delay. [PERSON] et al. [31] took the minimum total delay time of the train as the objective function and used the branch and bound method to obtain the optimal solution or approximate optimal solution. [PERSON] et al. [32] established a mixed-integer linear programming model with the goal of minimizing the total delay of trains and decomposed the model into two sub-problems by using the master-slave solution algorithm. [PERSON] et al. [33] used the SIS infectivity dynamics model to predict the train delay and took the Wuhan-Guangzhou HSR as an example to study the regularities and the trend of delay propagation within the system. [PERSON] [34] also used the SIS infectivity dynamics model to predict the train delay, and different from [PERSON] et al. [33], they took the section of Shanhaiguan station to Fuyu North station as an example to test the efficacy of the model. At the level of the railway network, [PERSON] [27] used the random forest model (RF) to predict the delay of trains on the network of the Netherlands, compared the results with the artificial neural network and XGBoost model, and obtained high-precision prediction results. Different from them, [PERSON] et al. [35] established a mixed-integer linear programming model with the objective of reducing passenger delays and then tested the model on the Dutch railway network. The single objective function is suitable for problems that have just one optimal objective, but for multi-objective problems, it is not applied. In order to better describe the rescheduling problem, some studies established models with more than one objective. [PERSON] et al. [6] took the sum of train-related costs and service-related costs as the optimization objective, proposed a train rescheduling model, and finally tested the effectiveness of the model in the busy part of the Dutch railway network.