A line planning approach based on time-varying demand for high-speed rail under the combined operation of periodic and aperiodic services

• Propose a new type of line planning combining regularity with flexibility. • Line planning takes into account the time-varying demand of passengers. • Build an optimization model for line planning combined periodic and aperiodic. • Design a simulated annealing algorithm to improve the efficiency of line planning. • A real-life case-study on a Chinese high-speed rail demonstrates the method. Passenger demand for high-speed rail systems is highly fluctuating in temporal and spatial throughout the day. In order to effectively improve passenger satisfaction and service level for high-speed rail, the formulation of line plan must make the distribution of the trains’ capacities be meet with the time-varying demand of passengers. The aperiodic line plan can well meet this demand since it is more flexible with different stop patterns and various headways. However, the irregular arrival/departure times are not convenient for travel planning. We propose a new type of line plan that would combine both the regularity of the periodic line plan and the flexibility of the aperiodic ones. An optimization method of high-speed railway line plan based on a combination of periodic and aperiodic operation is structured, which can well satisfy the temporal-spatial distributions of passenger demands in different time periods. The main challenge is to coordinate the numbers of periodic and aperiodic trains, and their temporal-spatial distributions on the rail network considering the passengers’ train-choice decisions. Based on generating a set of candidate routes and constructing a passenger travel network, we propose a model to optimize the numbers of both periodic and aperiodic trains, and their paths, stops, approximate arrival and departure times at each visited stations for minimizing the total operation cost of trains and the total generalized travel cost of passengers. Then, a simulated annealing algorithm is designed to efficiently solve our proposed optimization model. Finally, numerical experiments based on the Shanghai-Nanjing intercity railway in China verify the effectiveness and practicability of the optimization method.