A path-based double projection method for solving the asymmetric traffic network equilibrium problem

In this paper we propose a new iterative method for solving the asymmetric traffic equilibrium problem when formulated as a variational inequality whose variables are the path flows. The path formulation leads to a decomposable structure of the constraints set and allows us to obtain highly accurate solutions. The proposed method is a column generation scheme based on a variant of the Khobotov's extragradient method for solving variational inequalities. Computational experiments have been carried out on several networks of a medium-large scale. The results obtained are promising and show the applicability of the method for solving large-scale equilibrium problems.