Multi-Objective Train Trajectory Optimization Of Urban Rail Transit Based On Dynamic Programming

Along with the quick development of national economy and the continuous expediting of urbanization, the city’s traffic demand is increasing quickly. As a kind of safe, comfortable, punctual and large-capacity means of transportation, urban rail transit has been taking on short-and-medium distance turnover passenger traffic in city mostly, and get rapid development in our country in recent years. Due to the nature of public service, urban rail transit has high requirement of the operation energy, punctuality and riding comfort. But nearly all indicators can be affected by the train speed. So, the multi-objective optimization design of train operation trajectory has become a focus in the research of urban rail transit, and caught scholars’ eyes at home and abroad. Considering the above problems, the optimization of train operation trajectory based on the Dynamic Programming algorithm is discussed as follows:Firstly, the optimization of single train operation trajectory based on Dynamic Programming is studied. The mathematical expressions of energy consumption and operation time are derived based on the single mass-point train model and multistage decision theory of Dynamic Programming. Based on the expressions, the single train operation trajectory is optimized for minimum energy consumption, practical travel time and riding comfort. The theoretical inference is tested under the conditions of single and multiple objects, and then, a comparison is given by using Genetic Algorithm. The simulation results show the performance of Dynamic Programming in optimizing the train operation trajectory. The energy consumption can be minimized while the travel time and riding comfort meet the operation requirements.Secondly, the multi-train tracking trajectory optimization problem is studied. The tracking dynamic process of two trains in a section is analyzed, meanwhile, three tracking scenarios are established and optimal strategies accordingly are proposed. The fix time algorithm based on dichotomy is used to approach the fix travel time and solve the optimal coefficient weight in objective function. Then, the tracking trajectories of different scenarios are optimized by using Dynamic Programming. Simulation results demonstrate the effectiveness of optimal strategies:the energy consumption of tracking train can be minimized while the delay time caused by former trains is sharply reduced.Finally, train trajectory design software module is developed according to the single and multiple train trajectory optimal theory. Three-tier architecture and object-oriented language are used in the development process. Optimal indicators and various functions are defined, and database based on a real urban rail line is developed. Through the experiments, optimal theories are further verified:the fix time algorithm based on dichotomy can be well integrated with Dynamic Programming, and performs well in multi-objective train operation trajectory design.