Acceleration of Double-Projection Method in Asymmetrically Formulated Traffic Assignment

Abstract

In this paper, a methodology for accelerating the double-projection method designed for the asymmetric traffic equilibrium assignment problem is proposed. One of the factors that determine the efficiency of the projection method is a properly selected step size. This study customized the step size for each origin-destination (O-D) pair by formulating the assignment problem on the space of path flows. In addition, even if the transportation network is decomposed into each O-D pair, the step size based on the entire path flows is also available. The study developed a step-size selection strategy with two different available step sizes obtained from different spaces of path flows vectors. During the projections of path flows for each O-D pair, the strategy compares the step size customized for that O-D pair and the one from the entire path flow vectors and selected a bigger step size. Several numerical tests have been conducted on various sized networks and convergence criteria. The methodology considerably improves the convergence speed of the solution algorithm. Further analysis on the numerical tests delivered the relevant information on the synergistic effects of the two strategies during the convergence process: the customized step size and the step-size selection strategy.