A multiple-path gradient projection method for solving the logit-based stochastic user equilibrium model


  • Heqing Tan College of Civil and Transportation Engineering, Hohai University
  • Muqing Du College of Civil and Transportation Engineering, Hohai University
  • Chun-bin Yu College of Civil and Transportation Engineering, Hohai University




Transportation Planning, Traffic assignment, Stochastic User Equilibrium, Gradient Projection Method, Multiple Paths


This paper proposes a path-based algorithm for solving the well-known logit-based stochastic user equilibrium (SUE) problem in transportation planning and management. Based on the gradient projection (GP) method, the new algorithm incorporates a novel multiple-path gradient approach to generate the descent direction in consideration of many paths existing in every single origin-destination (O-D) pair. To apply the path-based algorithm, the SUE problem is reformulated as a variational inequality (VI), and a working path set is predetermined. The numerical experiments are conducted on the Winnipeg network where a large number of paths are provided. The results show the multiple-path gradient projection algorithm outperforms the original GP method. Three different step size strategies, including the fixed step size, self-regulated averaging and self-adaptive Armijo’s strategies, are involved to draw a more general conclusion. Also, the effects of the path number on computational performance are analyzed. The multiple-path gradient projection (MGP) method converges much faster than the GP method when the path set size gets large.


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How to Cite

Tan, H., Du, M., & Yu, C.- bin. (2020). A multiple-path gradient projection method for solving the logit-based stochastic user equilibrium model. Journal of Transport and Land Use, 13(1), 539-558. https://doi.org/10.5198/jtlu.2020.1600



Special Issue: Innovations for Transport Planning in China