Linear regression parallel block coordinate descent method with Barzilai–Borwein steps for large-scale traffic assignment problems

Traffic assignment is the cornerstone of the conventional four-step transportation planning framework. As a fundamental technique for predicting network flow distribution, it is pivotal in optimizing transportation planning and infrastructure design. However, traditional traffic assignment algorithms have a high computational requirement when addressing increasingly large-scale problems driven by ever-growing travel demand and expanding network sizes in real-world applications, making the trade-off between computational efficiency and solution accuracy increasingly critical. This study proposes a novel linear regression parallel block descent (LR-PBCD) method to address this challenge. First, we comprehensively analyze origin–destination (OD) pair characteristics and path travel time distributions. We then apply a linear regression model that identifies hard-to-converge OD pairs, followed by a hierarchical decomposition strategy using parallel block coordinate descent. A gradient projection algorithm is implemented within each block that uses fixed-step updates for normal OD pairs and the Barzilai–Borwein steps algorithm for hard-to-converge OD pairs. Experimental validation on real-world networks demonstrates that the LR-PBCD method improves solution efficiency over conventional methods while maintaining solution precision, providing a computationally efficient paradigm for large-scale transportation network analysis.