Integrated optimization of regular train schedule and train circulation plan for urban rail transit lines

This paper presents an integrated model to optimize the train schedule and circulation plan simultaneously based on a given service pattern generated by the demand analysis and line planning. The operation of train services, the turnaround operations, the entering/exiting depot operation, and the number of available trains are involved in the model. The proposed integrated and extended integrated optimization problems are transformed into mixed integer linear programming (MILP) problems, which can be efficiently solved by the CPLEX solver. Numerical examples based on the Beijing Yizhuang line are implemented to demonstrate the performance of the proposed models and solution approach.