Implementing Frank-Wolfe Algorithm under Different Flow Update Strategies and Line Search Technologies

Abstract

Frank-Wolfe (FW) algorithm is widely used to solve traffic equilibrium assignment problems. It has the characteristics of simple implementation and modest memory requirement. However, it also faces some problems such as slow convergence, no providing path information, and so on. In order to improve its implementation efficiency, the FW algorithm is furthermore studied from three flow update strategies (all-at-once, one-origin-at-a-time, and one-OD-at-a-time) and different step search methods, which include deterministic line search methods (bisection method, golden-section method, and success-failure method) and nondeterministic line search methods (a search method on the basis of Wolfe-Powell convergent criterion and a nonmonotone line search method). Four different scales of transportation networks are used to test the different update strategies finally.