A New Look at Projected Gradient Method for Equilibrium Assignment



A New Look at Projected Gradient Method for Equilibrium Assignment

Authors

I Constantin, M Florian, D Florian, INRO Consultants and the University of Montreal, CA

Description

This paper presents a very efficient implementation of a projected gradient variant for the solution of equilibrium traffic assignment. It obtains very fine solutions of traffic assignment problems which exhibit relative gaps of the order of 10^-6.

Abstract

This paper presents a very efficient implementation of a projected gradient variant for the solution of the network equilibrium traffic assignment in the space of path flows.

The new algorithm exploits certain properties of the method in order to reduce the necessary computations for flow changes. One can compute several measures of relative gap that are common in the literature and practice of traffic assignment. The novelty of the results obtained demonstrates that this method is efficient even though it was not considered to be so in previous work.

It obtains very fine solutions of traffic assignment problems which exhibit relative gaps of the order of 10^-6. The method as well as extensive computational results are presented. The test problems originate from transportation planning practice on five continents.

Some examples of the computational times and comparative results with the linear approximation (F&W) method are given below:

Medium size network of 3,000 links (Winnipeg):

F&W 500 iter's 18.40 s. Abs Gap 128.2
Pr.Gr.50 iter's 9.17 s. Abs gap 9.6 Rel gap:0.0000096

Large size network of 30,000 links (Sydney):

F&W 500 iter's 2275.0 s. Abs Gap 2175.77
Pr.Gr. 40 iter's 1338.7 s. Abs gap 78.02 Rel gap: 0.0000028

For the latter network a solution equivalent to 500 iterations of F&W is obtained after 10 iterations of the projected gradient method after 842 s. Similar results were obtained on other large scale networks.


The performance of this new algorithm is compared as well to the Bar Gera origin based method to which it compares favorably.

Publisher

Association for European Transport