Robust Optimization of High-Speed Railway Train Plan Based on Multiple Demand Scenarios

The optimization of train plans is highly dependent on the space-time distribution of passenger demand in high-speed railway systems. A train plan usually needs to be implemented on multiple operation days, and obviously the amount and space-time distribution of demand over these days has noteworthy differences. To ensure the same train plan is able to be implemented on multiple operation days while effectively satisfying the different levels of demand on those days, a novel robust optimization of a high-speed railway train plan based on multiple demand scenarios is performed in this research. Firstly, the passenger demand of each operation day is described as a demand scenario, and a candidate train set is generated that is able to satisfy the multiple demand scenarios. Then, a regret value corresponding to the total cost, including the train operation cost and passenger travel expense, is proposed to measure the deviation in the costs generated between the robust and the optimal train plan under each demand scenario. Then a robust optimization model for a high-speed railway train plan is constructed to minimize the maximum regret value. Moreover, a simulated annealing algorithm for solving the model is designed by constructing some neighborhood solution search strategies for multiple demand scenarios. Finally, the validity and feasibility of the proposed robust optimization method for train planning are verified on the Shijiazhuang-Jinandong high-speed railway line in China.