Bi-level programming model for optimizing bus frequencies and its algorithm

Aiming at minimizing the total cost of the bus operation system as the optimization objective, considering the route choice behaviors of the travelers, a bi-level programming model for optimizing the bus frequencies was presented. In the model, the upper-level optimizes the bus frequencies from the result of passenger assignment, and the lower-level assigns the bus travelers based on the optimal frequencies. An iterative algorithm integrating a label-marking method and a new heuristic algorithm-shuffled complex evolution method (SCE-UA) was designed to solve the lower and upper models. Taking Dalian city bus system as an example, the model and algorithms were tested against the system data, and the results show that the presented model and algorithms are reasonable and effective.