Accelerating strategies and computational studies of the Frank-Wolfe algorithm for the traffic assignment problem

An accelerating strategy to the well-known Frank-Wolfe algorithm for solution of the traffic assignment problem (TAP) is presented here. The Frank-Wolfe algorithm has been widely accepted and recognized by transportation researchers and practitioners as a state-of-the-practice solution method for TAP. With abundant numerical examples, the proposed accelerating strategy was compared with other accelerating methods, such as the parallel tangent technique, Fukushima direction, and Weintraub step size. The computational results successfully indicate that this new strategy is capable of obtaining highly accurate solutions with relatively moderate central processing unit time consumed. The computational results also indicate that the performance of this accelerating strategy is better than state-of-the-art algorithms, such as the restricted simplicial decomposition algorithm and the gradient projection algorithm. The proposed accelerating strategy is easy to implement and suitable for obtaining accurate solutions to TAP because of its economical memory requirement and stable performance, even when large and congested networks are considered.