This document summarizes computational studies of two path-based traffic assignment algorithms: the disaggregate simplicial decomposition (DSD) algorithm and the gradient projection (GP) algorithm. The study used a large-scale real network in Chicago and five randomly generated networks. Results showed that the GP algorithm performed better than both versions of the DSD algorithm on all networks, finding solutions faster with fewer iterations. The GP algorithm was more efficient by maintaining a smaller set of active paths and avoiding expensive line searches through second derivative information. While DSD could find near-optimal solutions quickly, it took more time overall and maintained a larger set of paths in each iteration.