A Quadratic Unconstrained Binary Optimization (QUBO) Model for Elevation‐Aware Vehicle Routing: Optimizing Fuel Consumption and Traffic Congestion

ABSTRACT This study formulates a novel, elevation‐aware Quadratic Unconstrained Binary Optimization (QUBO) model for multi‐vehicle route optimization that simultaneously reduces fuel consumption and traffic congestion. Candidate routes are generated using a gradient‐corrected Dijkstra algorithm, and route selection is optimized by minimizing a rigorously constructed QUBO Hamiltonian that incorporates fuel cost, route overlap, and constraint satisfaction. Extensive numerical validation is performed using classical annealing simulations across multiple regions with diverse topographical and road network characteristics, including San Francisco. The results demonstrate that incorporating elevation information significantly reduces fuel consumption, while the proposed overlap penalty effectively mitigates congestion. A clear trade‐off between overlap reduction and fuel efficiency is quantitatively characterized. The mathematical consistency of the formulation is ensured through a theoretically derived penalty coefficient, which guarantees constraint satisfaction and stable optimization behavior. Scaling experiments further reveal the limitations of classical solvers as the number of candidate routes increases, highlighting the importance of robust QUBO formulations and motivating future implementation on quantum processing units. Overall, this work establishes a validated and theoretically sound QUBO framework for sustainable transportation optimization and provides a reliable performance baseline for future quantum hardware–based investigations.