Enhancing logit stochastic user equilibrium convergence in large‐scale networks via Barzilai–Borwein step size optimization

Traffic assignment serves as an important component in modeling flow distribution across infrastructure networks and supporting intelligent traffic management and urban planning. Fast algorithms for solving the stochastic user equilibrium (SUE) model are essential for enhancing computational performance and scalability of traffic assignment models applied to complex infrastructure networks. We augment the gradient projection (GP) algorithm for the SUE models through Barzilai–Borwein (BB) step size adaptation. For further optimizing computational performance, we explore iteration strategies within the GP algorithm: Jacobi parallelization, Gauss–Seidel sequential updating, and successive over‐relaxation (SOR) with dynamic relaxation. Global convergence of these iterative methods in solving the SUE problems is theoretically established, with convergence conditions for the SOR derived. The results demonstrate the BB step size's superior performance, compared to alternative step size methods, across all network scales, and it achieves the best stability when demand factors and the dispersion parameter increase.