Hybrid Optimization QAOA for Scalable Vehicle Scheduling Problems

Abstract

Optimization of vehicle-to-station assignments under capacity and distance constraints represents a challenging combinatorial problem relevant to automated planning, logistics, and autonomous mobility systems. Classical methods such as Mixed Integer Linear Programming (MILP) or metaheuristics often struggle to scale efficiently with problem dimensionality, motivating the exploration of hybrid quantum-classical paradigms. This paper presents a normalized Quantum Approximate Optimization Algorithm (QAOA) framework tailored for constrained assignment problems, where vehicle-station distances are encoded into a normalized cost Hamiltonian. Capacity violations and unused resources are incorporated through dynamically scaled penalty terms, producing a cost landscape that effectively guides the quantum search process. The proposed pipeline integrates parameter optimization using COBYLA to refine the QAOA angles, ensuring convergence toward low-cost feasible configurations. Experimental simulations in Cirq on a 10-qubit system demonstrate that the normalized QAOA pipeline consistently identifies near-optimal assignments while substantially reducing the combinatorial search space. These results provide empirical evidence for the viability of hybrid QAOA formulations in real-world planning and scheduling scenarios, establishing a foundation for future implementations on noisy intermediatescale quantum (NISQ) hardware.