Simulated Bifurcation with High-dimensional Expansion for Traffic Signal Optimization on Real-world Networks

With accelerating urbanization and worsening traffic congestion, optimizing traffic signal systems to improve road throughput and alleviate congestion has become a critical issue. This study proposes a short-term traffic prediction model based on real-world road topologies and a typical four-way, eight-phase traffic signal control scheme. The model accounts for traffic flow disparities across directions and signal phase change frequencies, integrating these factors into an optimization objective for global traffic optimization. The structure of this objective function is similar to spin-glass systems in statistical physics. A Simulated Bifurcation optimization algorithm is introduced, with traditional simulated annealing as a benchmark. The results show that Simulated Bifurcation outperforms simulated annealing in both efficiency and effectiveness. Using real traffic flow and road network data from Beijing, we initialized the model and conducted numerical optimization experiments. The results indicate that Simulated Bifurcation significantly outperforms simulated annealing in computational efficiency, effectively solving combinatorial optimization problems with multiple spin interactions, and reducing the time complexity to $O(N^{1.35})$. This solution addresses the NP-hard problem of global traffic signal optimization. Importantly, the signal phase patterns generated by Simulated Bifurcation align with the operational requirements of real traffic signal systems, showcasing its potential in optimizing signal control for large, complex urban traffic networks. This work provides solid theoretical and practical foundations for future urban traffic management and intelligent transportation systems.