Optimization Method for Train Plan of Urban Rail Transit with Elastic Demands

In urban rail transit, the train plan directly influences passenger’s travel cost, thus it affects the passenger travel demand. According to current planning and operation for urban rail transit, the train plan consists of train formation, train operation period, and train numbers in each train routing. On the basis of analyzing passengers’ general travel cost, the passenger elastic demand function is established, then passenger’s travel behaviors come down to the distribution of user equilibrium with elastic demands and capacity constraints. According to the relationship between passengers and the operator and on the basis of analyzing related cost, benefits, and constraints of the train plan, a multi-objective bi-level programming model is put forward, and the optimal algorithm based on the simulated annealing algorithm is designed. The instance of Changsha metro line 2 shows that the method can provide results with high efficiency.