Solving Capacitated Vehicle Routing Problem with Quantum Alternating Operator Ansatz and Column Generation

Abstract: This study proposes a hybrid quantum-classical approach to solving the Capacitated Vehicle Routing Problem (CVRP) by integrating the Column Generation (CG) method with the Quantum Alternating Operator Ansatz (QAOAnsatz). The CG method divides the CVRP into the reduced master problem, which finds the best combination of the routes under the route set, and one or more subproblems, which generate the routes that would be beneficial to add to the route set. This method is iteratively refined by adding new routes identified via subproblems and continues until no improving route can be found. We leverage the QAOAnsatz to solve the subproblems. Our algorithm restricts the search space by designing the QAOAnsatz mixer Hamiltonian to enforce one-hot constraints. Moreover, to handle capacity constraints in QAOAnsatz, we employ an Augmented Lagrangian-inspired method that obviates the need for additional slack variables, reducing the required number of qubits. Experimental results on small-scale CVRP instances (up to 6 customers) show that QAOAnsatz converges more quickly to optimal routes than the standard QAOA approach, demonstrating the potential of this hybrid framework in tackling real-world logistical optimization problems on near-term quantum hardware.