A self-adaptive gradient projection algorithm for the nonadditive traffic equilibrium problem

Anthony Chen, Zhong Zhou, Xiangdong Xu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

48 Citations (Scopus)


Gradient projection (GP) algorithm has been shown as an efficient algorithm for solving the traditional traffic equilibrium problem with additive route costs. Recently, GP has been extended to solve the nonadditive traffic equilibrium problem (NaTEP), in which the cost incurred on each route is not just a simple sum of the link costs on that route. However, choosing an appropriate stepsize, which is not known a priori, is a critical issue in GP for solving the NaTEP. Inappropriate selection of the stepsize can significantly increase the computational burden, or even deteriorate the convergence. In this paper, a self-adaptive gradient projection (SAGP) algorithm is proposed. The self-adaptive scheme has the ability to automatically adjust the stepsize according to the information derived from previous iterations. Furthermore, the SAGP algorithm still retains the efficient flow update strategy that only requires a simple projection onto the nonnegative orthant. Numerical results are also provided to illustrate the efficiency and robustness of the proposed algorithm.
Original languageEnglish
Pages (from-to)127-138
Number of pages12
JournalComputers and Operations Research
Issue number2
Publication statusPublished - 1 Feb 2012
Externally publishedYes


  • Gradient projection algorithm
  • Nonadditive route cost
  • Self-adaptive scheme
  • Traffic equilibrium problem

ASJC Scopus subject areas

  • Computer Science(all)
  • Modelling and Simulation
  • Management Science and Operations Research

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