Bi-objective user equilibrium model and algorithm under tradable credit schemes

The assumption of linear time value in the traditional user equilibrium (UE) model under tradable credit scheme (TCS) underestimates the traffic flow of some effective paths, in order to overcome this problem, this paper constructs a biobjective UE model based on the maximization of time surplus. Firstly, the bi-objective UE is defined to describe the travelers' bi-objective route choice behavior that minimizes both travel time and cost. Secondly, the concept of time surplus is introduced to describe the non-compensatory decision-making of the travelers in weighing the route travel time and cost, and the bi-objective UE condition based on the maximization of time surplus is proposed under TCS, and the equivalent variational inequality (VI) model is constructed. Finally, the heuristic algorithm based on two-layer cycle iterations is designed to solve the model. Sioux Falls network is used to validate the model and algorithms, and the results show that: in the traffic equilibrium state, the time surplus of the used paths between the same OD pairs is equal, and all of them are effective paths under the bi-objective of time and cost minimization.