Computational Study of a Path-Based Algorithm and Its Variants for Static Traffic Assignment

Recent research has indicated that advances in computer memory have made the use of path-based algorithms in urban traffic networks a possibility. The path-based gradient projection (GP) offers significant benefits in computation times over the conventional Frank-Wolfe algorithm and may be especially suited for real-time applications. The computational results from applying GP to networks of up to 4,900 nodes, as well as the performance of different variants of GP, are discussed. Also discussed is the sensitivity of the results to parameters such as the number of destinations and the level of congestion. The variants of the basic GP algorithm examined are intended to further improve the per-iteration performance of the algorithm for larger networks. These variants include a GP version with a modified first derivative update and different versions that use line-search techniques, including a boundary stopping method. The results establish that GP indicates substantial benefits even for larger networks. The modifications, while they do improve the computation times per GP iteration, affect the convergence quality of the algorithm, indicating that the earlier GP algorithm is a better alternative for both large and small networks.