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

2025-10-22

AI Summary

Traditional traffic assignment methods suffer from nonlinearly increasing computational complexity and inefficiency in large-scale networks, primarily due to the exponential growth of origin–destination (OD) pairs. To address this, we propose the first end-to-end deep learning framework based on the Transformer architecture, which directly predicts equilibrium path-level flow distributions—bypassing conventional mathematical programming paradigms. Our method leverages self-attention mechanisms to capture high-order inter-OD dependencies and supports fine-grained, dynamic modeling of multi-class traffic flows without requiring re-optimization for rapid what-if analysis. Experiments on both synthetic and real-world road networks demonstrate that our approach achieves speedups of several orders of magnitude over classical algorithms while maintaining high accuracy in path flow estimation. This significantly reduces computational cost and establishes a novel paradigm for real-time traffic management and planning decision support.

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Search and Optimization: Learning to Search
• Machine Learning: Deep Neural Architectures and Foundation Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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. The model also adapts flexibly to varying demand and network conditions, supporting traffic management and enabling rapid `what-if' analyses for enhanced transportation planning and policy-making.

Problem

• Estimating equilibrium path flows for traffic assignment problem
• Reducing computational complexity in large-scale transportation networks
• Adapting to demand and network changes without recalibration

Innovation

• Transformer architecture predicts equilibrium path flows
• Model captures OD pair correlations for detailed analysis
• Reduces computation time without recalibration for changes