Optimizing Passenger Flow Control under Large-scale Metro Network Based on Lagrangian Relaxation Decomposition Algorithm

The overcrowding situation of some metro lines has become a common sight due to the excessive travel demands of commuters during peak hours in the metro systems of some megacities. A network-based passenger flow control method is proposed to improve the transportation efficiency and passengers' travel security. First, considering the dynamic characteristics of travel demands and passenger transfer behaviors among different lines, the mixed integer nonlinear programming model is constructed to minimize the number of passengers restricted to enter stations and stranded on platforms, and the number of conducting passenger flow control strategies. By linearizing the nonlinear constraints in the model, the original model is reformulated into a mixed integer linear programming model. Then, a decomposition algorithm based on Lagrangian relaxation is developed to depart the original problem into subproblems of each line to be solved separately and effectively improve the computational efficiency. The simulation results based on the part of the Beijing metro network operation data show that the designed algorithm can obtain solutions with relatively small gaps in a relatively short time period. Besides, the optimized passenger flow control strategy can effectively alleviate platform congestion, verifying the practicability and validity of the proposed method.