Effects of Flow Update Strategies on Implementation of the Frank–Wolfe Algorithm for the Traffic Assignment Problem

Abstract

The Frank–Wolfe (FW) algorithm is the predominant algorithm used to solve traffic assignment problems in transportation planning studies. Despite its slow convergence, it remains the most popular choice among practitioners and researchers. One reason for its popularity is that it requires very modest memory storage, which allows planners to solve networks of realistic sizes. Computer random-access memory storage has become extremely cheap, and it is possible to store more information in the FW algorithm to improve the speed of convergence. This information may be required anyway in certain applications, such as optimal routing in route guidance systems, analysis of environmental impact, nonadditive traffic equilibrium problems, and origin-destination matrix estimation. Different flow update strategies are used to examine how to effectively utilize the additional information to improve the performance of the FW algorithm. Implementation of three flow update strategies in the FW algorithm is discussed. Numerical experiments are performed on four test networks of various sizes.