From Optimization to Prediction: Transformer-Based Path-Flow Estimation to the Traffic Assignment Problem

The traffic assignment problem is essential for traffic flow analysis, traditionally solved using mathematical programs under the Equilibrium principle. These methods become computationally prohibitive for large-scale networks due to non-linear growth in complexity with the number of OD pairs. This study introduces a novel data-driven approach using deep neural networks, specifically leveraging the Transformer architecture, to predict equilibrium path flows directly. By focusing on path-level traffic distribution, the proposed model captures intricate correlations between OD pairs, offering a more detailed and flexible analysis compared to traditional link-level approaches. The Transformer-based model drastically reduces computation time, while adapting to changes in demand and network structure without the need for recalculation. Numerical experiments are conducted on the Manhattan-like synthetic network, the Sioux Falls network, and the Eastern-Massachusetts network. The results demonstrate that the proposed model is orders of magnitude faster than conventional optimization. It efficiently estimates path-level traffic flows in multi-class networks, reducing computational costs and improving prediction accuracy by capturing detailed trip and flow information. Introduction The Traffic Assignment Problem (TAP) is a process of determining the propagation of flows over the transportation network. The goal is to calculate the network state, given the travel demand between various origin-destination (OD) pairs and the network's capacity constraints (Y osef Sheffi. Traditionally, this problem is solved through mathematical programs under the User Equilibrium (UE) principle, which assumes drivers possess perfect information and make fully rational choices (Wardrop, 1952). Despite potential deviations from reality, this approach consistently provides reasonable solutions to the traffic assignment problem (Bar-Gera, 2002; Jafari et al., 2017). However, the computation for determining optimal solutions in large traffic networks is prohibitively costly. This is because the problem's complexity grows non-linearly with the increase in the number of OD pairs and directly depends on feasible paths. When the size of the network (the number of links and nodes in a representative graph) increases, allowing us to explore more paths, the number of feasible paths also increases, and the OD demand matrix may grow accordingly, leading to a non-linear increase in computation time (Patriksson, 2015).