Congestion pricing is an important component of urban intelligent transport system.The efficiency,equity and the environmental impacts associated with road pricing schemes are key issues that should be considered before such schemes are implemented.This paper focuses on the cordon-based pricing with distance tolls,where the tolls are determined by a nonlinear function of a vehicles' travel distance within a cordon,termed as toll charge function.The optimal tolls can give rise to:1) higher total social benefits,2) better levels of equity,and 3) reduced environmental impacts(e.g.,less emission).Firstly,a deterministic equilibrium(DUE) model with elastic demand is presented to evaluate any given toll charge function.The distance tolls are non-additive,thus a modified path-based gradient projection algorithm is developed to solve the DUE model.Then,to quantitatively measure the equity level of each toll charge function,the Gini coefficient is adopted to measure the equity level of the flows in the entire transport network based on equilibrium flows.The total emission level is used to reflect the impacts of distance tolls on the environment.With these two indexes/measurements for the efficiency,equity and environmental issues as well as the DUE model,a multi-objective bi-level programming model is then developed to determine optimal distance tolls.The multi-objective model is converted to a single level model using the goal programming.A genetic algorithm(GA) is adopted to determine solutions.Finally,a numerical example is presented to verify the methodology.
