A semismooth Newton method for traffic equilibrium problem with a general nonadditive route cost

Meng Xu, Anthony Chen, Yunchao Qu, Ziyou Gao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

14 Citations (Scopus)


Computing traffic equilibria with a general nonadditive route cost disutility function is considered in this paper. Following the user equilibrium (UE) condition, that is, no driver can unilaterally change route to achieve less travel costs, the traffic equilibrium problem (TEP) can be formulated as a nonlinear complementary problem (NCP). In this paper, we propose a semismooth Newton method with a penalized Fischer-Burmeister (PFB) NCP function to solve the NCP formulation of the TEP, and also, we investigate the properties of the proposed method. Numerical results are provided and compared with the classical TEP with additive route cost functions. The results show the algorithm can achieved substantially better performance than the existing approaches. A sensitivity analysis is also conducted to examine the parameter of the proposed nonadditive route cost function.
Original languageEnglish
Pages (from-to)3048-3062
Number of pages15
JournalApplied Mathematical Modelling
Issue number6
Publication statusPublished - 1 Jun 2011
Externally publishedYes


  • Nonadditive cost
  • Nonlinear complementarity problem
  • Optimization
  • Traffic equilibrium problem

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

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