A note on bar-Gera's algorithm for the origin-based traffic assignment problem

Yu Nie*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)27-38
Number of pages12
JournalTransportation Science
Issue number1
StatePublished - Feb 2012


  • Origin-based formulation
  • Quasi-Newton method
  • Traffic assignment
  • User equilibrium

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation


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