The Ohio Department of Transportation (ODOT) uses benefit-cost analysis from the Ohio Statewide Travel Demand Model (OSTDM) as one of several criteria in their TRAC project evaluation process. Thus, the ability to produce stable, defensible benefit/cost ratios quickly is of critical importance. However, given the size of their statewide model highway network, ODOT had difficulty achieving assignment results stable enough for benefit/cost calculations. ODOT runs 500 iteration assignments using the Frank-Wolfe algorithm. After a runtime of 80 hours, this results in solutions with stable VHT in most, but not all, cases.

Investigating ways to speed up convergence revealed two very different issues. The first was that the assignments were not producing user equilibrium solutions because one of the conditions for the existence of user equilibrium had been violated by the use of caps on travel times produced by the volume delay functions. This seemingly innocuous constraint resulted in sometimes wildly unstable assignment results. However, removing it revealed the problem for which it had been added, namely a small number of extremely overloaded links representing only about 1% of the network produced 16 times as much VHT as the other 99% of the links and prevented convergence. Ultimately, editing to add more loading points to the network addressed this and resulted in faster and more stable solutions but this situation illustrates one of the pitfalls of the more aggregate zonal systems typical of statewide models.

The second aide in reducing runtimes and improving convergence came from testing alternative assignment algorithms. Testing determined that the Conjugate Frank-Wolfe, converged fastest in OSTDM’s modeling software when compared to traditional Frank-Wolfe, MSA, Bi-Conjugate Frank-Wolfe, and Gradient Projection. Origin-based assignments on a single processor in another software performed substantially faster still, however, this could be partially offset by the use of more processors in ODOT’s modeling cluster so conversion to this package was not pursued.

After both the network edits and the new algorithm, the original two-class assignment converges to relative gaps less than 1 x 10-4 (tighter than previously achievable at all) in less than 200 iterations and 14.5 hours of runtime. The faster runtimes have now created the possibility of judiciously adding vehicle classes and terms to the generalized cost function to provide more consistency between the assignment and benefit/cost analysis and more realistic toll choice modeling.