Numerical algorithms for optimizing network traffic assignment problems: Optimization of a road network topology

This thesis provides a comprehensive exploration of networks, covering fundamental concepts to advanced topics with a specific focus on optimizing traffic assignment problems in transport networks. It examines the static network traffic assignment problem through a mathematical optimization model, providing detailed discussions on optimality and Karush-Kuhn-Tucker (KKT) conditions using the Lagrange function. In addition, the thesis proposes a neural network based on the Lagrange function to address the optimization problem. The local and Lyapunov stability of this neural network is thoroughly explained, while the dynamic nature of the neural network is addressed by solving it with Maple 2023 software and obtaining a numerical solution using Python 3. The changes in network traffic and flows over time are carefully analyzed. Findings and results are presented through figures, demonstrating that the neural network-based solution outperforms traditional methods significantly. Notably, the proposed neural network transforms a static network into a dynamic system, enhancing the capability to predict changes in traffic flows on routes and connections over time. Overall, the optimization method outlined in the thesis consistently delivers predictable and effecient results.