An inertia-infused ADMM-based splitting algorithm with parallel computing for traffic assignment
Pengjie Liu, Hu Shao, Emily Zhu Fainman, Feng Shao, Shenheng Xu, Chunkai Tang · Transportation Letters · 2025
In this paper, we propose an inertia-infused alternating direction method of multipliers (ADMM)-based splitting algorithm for the origin-based traffic assignment problem. The method is framed as a sequential Gauss–Seidel update with Jacobi-type parallelization in each subproblem. A Nesterov-accelerated inertial strategy, using information from previous iterations, is applied before updating link flows. Within each decomposed block, link-flow subproblems are solved in parallel via the gradient projection method with inertia. In updating Lagrange multipliers, a nonnegative relaxation factor is incorporated to improve flexibility. Numerical experiments show that with properly chosen inertial and relaxation parameters, the proposed algorithm achieves superior performance compared with the original ADMM.