Alternative Quasi-Newton Methods for Capacitated UE Assignment

In this study we proposed two Quasi-Newton methods to deal with traffic assignment in the capacitated network. The methods combine Newton formula, column generation and penalty techniques. The first method employ the gradient of the objective function to obtain an improving feasible direction scaled by the second-order derivatives. The second one is to employ Rosen gradient to obtain an improving direction scaled by the corresponding origin-destination demand. Both methods make line search to obtain an optimal step size to guarantee feasibility of either path or link flow. The proposed methods are of fast convergence and high accuracy at the expense of saving path information. Numerical examples verify their efficiency and stability, as well as usefulness of the path flow pattern reserved. The Quasi-Newton method with straight gradient demonstrates more stability than that with Rosen gradient for capacitated traffic assignment.