Quantum and classical approaches to the optimization of highway platooning: the two-vehicle matching problem

Abstract

Aerodynamic drag reduction on highways through vehicle platooning is a well-known concept, but it has not yet seen systematic uptake, arguably because of significant technological and legislative obstacles. As a low-tech entry point to real multi-vehicle platooning, "Windbreaking-as-a-Service" (WaaS) was introduced recently. Here we use a QUBO formulation to study classical metaheuristics such as simulated annealing and tabu search, together with emerging quantum heuristics including quantum annealing and variants of the Quantum Approximate Optimization Algorithm (QAOA). These heuristic solvers do not guarantee optimality, but they traverse the same higher-order landscape using polynomial memory. They can also be parallelized aggressively, and efficient classical post-processing can be used in hybrid workflows to return only valid schedules. This paper therefore positions QUBO as a common language that allows heterogeneous classical, quantum, and hybrid solvers to address the optimization of highway platooning.

Figures (8)

• Figure 1: Schematic energy landscape under two penalty-weight regimes. Left: if $\lambda_3$ is too small, infeasible configurations can "cheat" by lowering $E_{\text{cost}}$ enough to overcome penalties. Right: if $\lambda_3$ is very large, infeasible states are pushed far above the feasible manifold, but feasible energies compress into an almost flat plateau, reducing cost discrimination among valid matchings.
• Figure 2: “Solver-zoo” benchmark. Every solver is run on the same fixed problem sets (yellow), and all outputs are funneled into one common metric panel (purple) for direct comparison.
• Figure 3: Summary of solver performance metrics for 10 problem instances in the benchmark suite in Sec. \ref{['sec:dataset']}. For a more detailed view of the benchmark results underlying these plots and Figs. \ref{['fig:eta_threeplots']}, we refer the reader to the Supplementary Material App. \ref{['app:app']}. It provides the full benchmarking tables for all instance sizes, including the raw and derived quantities used in the plots. These supplementary tables provide a reproducible reference for comparing the classical, quantum, and hybrid solvers.
• Figure 4: Schematic linear--ramp QAOA schedule. The cost angles $\gamma_{\ell}$ increase linearly with the layer index $\ell$ while the mixer angles $\beta_{\ell}$ decrease linearly without instance--specific angle optimization.
• Figure 5: QAOA cost landscape approximation for the linear--ramp schedule. The contour plot shows the Gaussian–process surrogate of the depth-$p$ objective $F_p(\Delta\gamma,\Delta\beta)$ over the two ramp parameters. Red markers indicate the QAOA evaluations used to train the surrogate, while the black cross marks the predicted minimum $(\Delta\gamma^\star, \Delta\beta^\star)$ that defines the final linear schedule.