This paper takes a fresh look at the arguments against path-enumeration algorithms for the traffic assignment problem and provides the results of a gradient projection method. The motivation behind the research is the orders of magnitude improvement in the availability of computer storage over the last decade. Faster assignment algorithms are necessary for real-time traffic assignment under several of the proposed Advanced Traffic Management System (ATMS) strategies, and path-based solutions are preferred. Our results show that gradient projection converges in 1/10 iterations than the conventional Frank-Wolfe algorithm. The computation time improvement is of the same order for small networks, but reduces as the network size increases. We discuss the computer implementation issues carefully, and provide schemes to achieve a 10-fold speed-up for larger networks also. We have used the algorithm for networks of up to 2000 nodes on a typical computer work station, and we discuss certain data structures to save storage and solve the assignment problem for even a 5000 node network.
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