A PATH-BASED GRADIENT PROJECTION ALGORITHM: EFFECTS OF EQUILIBRATION WITH A RESTRICTED PATH SET UNDER TWO FLOW UPDATE POLICIES

In the network traffic assignment problem, it is generally believed that the minimum number of paths defining an equilibrium solution can be obtained by repeatedly equilibrating the set paths generated thus far in each iteration before creating new ones in the column generation phase. This scheme aims to minimize the number of shortest path calculations by only bringing in paths with greater potential to cause a reduction in the objective and at the same time retaining the existing paths in the path set. Using the path-based gradient projection (GP) algorithm, the restricted path equilibrium scheme was tested in two flow update policies: all-at-once and one-at-a-time. Discussed is also the applicability of implementing other known traffic assignment algorithms with these two flow update policies. The GP works well with the one-at-a-time flow update for both large and small networks without the need to employ the restricted path equilibration scheme.