Combinatorial Optimization Model and Algorithm of Congestion Pricing for Toll Levels and Toll Locations in Multi-Class Network

A combinatorial optimization model of congestion pricing for toll levels and toll locations in multi-class network is proposed with the number of toll links unknown. This model is a bi-level programming model where the upper level program aims to maximize the net social welfare and the lower level proposes a multi-class network equilibrium model with elastic demand. The hybrid genetic algorithm-simulated annealing (GA-SA) method is presented in order to solve the above-stated model containing mixed discrete and continuous variables. The feasibility and effectiveness of the model and its algorithm are illustrated with a numerical example.