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Title: A Note on Bar-Gera's Algorithm for the Origin-Based Traffic Assignment Problem.
Authors: Yu (Marco) Nie
Abstract: 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.
Subjects: ORIGIN & destination traffic surveys; TRAFFIC estimation; ALGORITHMS; NEWTON-Raphson method; TRAFFIC assignment
Publication: Transportation Science, 2012, Vol 46, Issue 1, p27
ISSN: 1526-5447
Publication type: Academic Journal
DOI: 10.1287/trsc.1110.0371

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