A novel flow update policy in solving traffic assignment problems: Successive over relaxation iteration method

• Published in: Transportation research. Part E, Logistics and transportation review Vol. 174; p. 103111
• Main Authors: Zhang, Honggang, Liu, Zhiyuan, Wang, Jian, Wu, Yunchi
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2023
• Subjects: Gradient projection algorithm; Successive over relaxation iteration method; User equilibrium; Gradient projection algorithm; Successive over relaxation iteration method; User equilibrium
• ISSN: 1366-5545; 1878-5794
• DOI: 10.1016/j.tre.2023.103111

•A novel flow update policy: successive over relaxation (SOR) iteration method.•The principle of employing the SOR method in the traffic assignment algorithms, e.g., the gradient projection (GP) algorithm.•Three important propositions of the GP-SOR algorithm.•Self-adaptive adjustment of the relaxation factor based on the Armijo Rule.•To validate the SOR method with much large-scale networks. This paper presents a novel flow update policy, namely the successive over relaxation (SOR) iteration method, which can be implemented in traffic assignment algorithms. Most existing solution algorithms for the user equilibrium traffic assignment problem (UE-TAP) mainly use two flow update policies: Jacobi and Gauss-Seidel iteration methods. The proposed flow update policy SOR can be a more efficient replacement. Following the path-based gradient projection (GP) algorithm, we developed a new method GP-SOR for the UE-TAP. This study first provides the complete procedure of applying the GP-SOR algorithm to solve the UE-TAP. Subsequently, a few properties of the proposed method are rigorously proven. However, empirical tests of the GP-SOR algorithm demonstrate serious oscillations and poor convergence. To cope with this problem, the Armijo Rule is employed to determine the relaxation factor, which substantially improves the convergence of GP-SOR algorithm. The preliminary numerical examples show that the GP-SOR algorithm has speedier convergence compared with the known alternatives, which is reflected by the evident reduction of the computing time and the number of iterations.