A Note on Bar-Gera's Algorithm for the Origin-Based Traffic Assignment Problem

Recently, Bar-Gera (Bar-Gera, H. 2002. Origin-based algorithm for the traffic assignment problem. Transportation Sci.36(4) 398–417) proposed a quasi-Newton method for the origin-based formulation of the user equilibrium traffic assignment problem. This note shows that Bar-Gera's algorithm may generate negative second-order derivative, leading to a “wrong search direction,” which compromises the overall convergence performance. We prove that this shortcoming can be overcome by approximating the second-order derivative with an upper bound. The revised algorithm not only fixes a theoretical flaw but indeed demonstrates more satisfying computational performance in numerical experiments. This note also offers a rigorous derivation of optimality conditions that synthesizes the results of the literature.