Modeling Capacity of Urban Rail Transit Network Based on Bi-Level Programming

Capacity index of Urban Rail Transit (URT) Network plays an improtant role in rational utilization of system capacity and operation management. A definition and calculating method of the capacity of URT Network was first proposed according to the features of URT network and route choice behavior of rail passengers in this paper. Several aspects of influencing factors of URT capacity were analyzed. A bi-level programming model was presented to optimize the URT capacity besides the system utility. Upper level of the model aims at maximizing the total OD flow through the URT network, and the lower level model is one kind of Fisk Equilibrium model. A new kind of impendence function relevant to the lower level model was put forward in consideration of practical traveler behavior. Genetic algorithm technique was applied to solve the bi-level programming model on the premise that the bi-level programming problem be converted into a single-level programming which was achieved by reformulating the lower-level problem model to its equivalent Karush-Kuhn-Tucker conditions. Effective crossover and mutation operators were proposed to enhance the convergence of the Genetic algorithm. A simplified network of Beijing URT was designed and numerical examples were conducted to prove that the proposed model and algorithm are feasible and valid in calculating the capacity of such network.