Update Strategies for Restricted Master Problems for User Equilibrium Traffic Assignment Problem

This paper aims to investigate how the trade-offs involved in the construction and solution of restrictive master problems for the user equilibrium traffic assignment problem may affect the overall convergence performance of the solution algorithms. Three strategies used to update user equilibrium path sets in path-based algorithms are examined: an origin–destination (O-D)-based strategy that updates the path set for each single O-D pair just before path flows are updated, an origin-based strategy that updates path sets for all O-D pairs associated with the same origin at once, and a simultaneous strategy that updates the path sets for all O-D pairs together. Three recently developed path-based algorithms to update the path sets by using three strategies are implemented for solution of the restrictive master problems. The implementation strategies are tested on medium to large real networks, and their relative performance characteristics are compared. The results show that the construction and update of the restrictive master problems by the different strategies have significant impacts on convergence as well as solution noise. The computational time for convergence under the simultaneous and origin-based strategies is significantly less than that under the O-D-based strategy. In addition, the solution obtained by adoption of the simultaneous strategy exhibits less noise than the other two strategies. These results provide important theoretical and practical insights into solution algorithms for the traffic assignment problem.