Service operation design in a transit network with congested common lines

This paper focuses on a transit service operation design problem that primarily determines the optimal frequency settings with explicit consideration of congested common lines in a bus service network. Other than passengers’ transit route choices, the transit service line choices among congested common lines are also specified in the model formulation. A tri-level programming approach is applied to formulate this problem, wherein the upper-level program optimizes the transit frequency to minimize the total operating costs and passengers’ transit costs; the middle-level program describes passengers’ transit routing choices, in which passengers will select a sequence of transfer nodes to minimize their transit costs; and the lower-level program formulates the equilibrium strategy in the common line problem on the route sections (i.e., between two successive transfer nodes), whose equilibrium solution may have multiple strategies depending on the congestion level of the common lines. The tri-level model is then reformulated into a mathematical program with equilibrium constraints. Two solution methods are proposed to solve the problem. One is to transform the model into a mixed-integer linear program so that the global optimal solution of the linearized problem can be guaranteed, and the other employs a surrogate optimization approach to ensure high solution efficiency for large size problems without compromising solution quality. Finally, we conduct extensive numerical examples to demonstrate the validity of our model formulation and the performance of the proposed solution algorithms.