Quantum Annealing for Realistic Traffic Flow Optimization: Clustering and Data-Driven QUBO

TL;DR

This work reframes city-wide traffic flow optimization as a data-driven QUBO that encodes spatiotemporal congestion and travel-time penalties, with a dynamically calibrated penalty $\lambda$ to enforce single-route choices. It combines a scalable, data-driven workflow (OSM maps, Valhalla routing) with Leiden clustering to partition large problems and evaluate solutions using quantum annealing (QAHS/QPU) and classical solvers (Gurobi, CBC, SA, Tabu). Across small to very large-scale instances (up to 25,000 vehicles in multiple cities), hybrid quantum–classical approaches achieve near-optimal solutions within ~1% of Gurobi and deliver substantial congestion reductions (up to ~25% relative to shortest-path baselines). The study demonstrates quantum readiness for realistic traffic optimization, highlights the importance of map topology and QUBO density on performance, and outlines practical pathways for real-time, congestion-aware routing and integration with urban mobility platforms. Overall, the results suggest that quantum-enhanced optimization can meaningfully complement existing navigation services by balancing individual travel time with system-wide congestion metrics, even under real-world data and city-scale constraints.

Abstract

Managing city traffic is a complex NP-hard problem where traditional methods often fail to scale. We present a data-driven approach that reformulates traffic optimization as a Quadratic Unconstrained Binary Optimization, capturing both congestion reduction and travel-time efficiency. The model integrates simulated realistic mobility data, multiple routing alternatives, and analytically derived penalty constraints. To address large networks, we apply Leiden clustering to preserve critical congestion patterns while reducing problem size. Benchmarking on up to 25,000 vehicles shows that hybrid quantum annealing achieves near-optimal solutions within 1% of the classical solver Gurobi while reducing congestion by up to 25%.

Figures (9)

• Figure 1: High-level workflow of the traffic optimization. Dashed node indicates an optional step.
• Figure 2: Average objective value (energy) versus number of vehicles ($n$) for each solver; tested for $\approx 100$ instances per $n$. Gurobi consistently returns the lowest energy, with Tabu tracking closely. SA and CBC diverge slightly as $n$ increases and QA QPU achieves the hightest energies.
• Figure 3: Average objective value (energy) versus number of vehicles ($n$) for each solver in medium-scale instances. Gurobi consistently achieves the lowest energy. QAHS tracks closely, while SA and Tabu increasingly diverge as $n$ grows.
• Figure 4: Relationship between solver performance and QUBO density. Each point represents a simulation, with color encoding the QAHS--Gurobi energy gap. QAHS is closest to optimal in denser formulations (blue points) and diverges modestly in sparse formulations (redder points).
• Figure 5: Comparison of solver performance across city networks. Cardiff’s uniform grid-like topology produces smaller QAHS--Gurobi gaps, while Košice’s irregular layout results in larger deviations.