Public welfare fare optimization of urban rail transit considering passenger demand of multiple periods

The spatial-temporal imbalance of demand will affect the formulation of urban rail transit public welfare fare schemes, and then affect the passenger benefits and the traffic structure. A bi-level programming model considering multi-period and different direction demands is established. The upper model takes the maximization of social welfare as the objective function, and considers public welfare constraints; the lower model is a stochastic user equilibrium model. A heuristic hybrid algorithm which combines multi-population genetic algorithm, continuous average method and parallel computation is designed. The results show that: compared with for-profit pricing scheme, when public welfare pricing scheme is adopted, ticket price is reduced by 43%; the generalized travel cost per passenger is decreased by 19% and 4% in peak and off-peak periods respectively in up direction, 16% and 6% in down direction; the consumer surplus is increased by 15.2% and 5.7% in peak and off-peak periods respectively in up direction, 12% and 7% in down direction; the urban rail transit sharing rate is increased by 40% and 71% in peak and off-peak periods respectively in up direction, 36% and 66% in down direction. This model provides some reference for government to formulate the fare and management strategy.