Applying quantum approximate optimization to the heterogeneous vehicle routing problem

Quantum computing offers new heuristics for combinatorial problems. With small- and intermediate-scale quantum devices becoming available, it is possible to implement and test these heuristics on small-size problems. A candidate for such combinatorial problems is the \ac{HVRP}: the problem of finding the optimal set of routes, given a heterogeneous fleet of vehicles with varying loading capacities, to deliver goods to a given set of customers. In this work, we investigate the potential use of a quantum computer to find approximate solutions to the \ac{HVRP} using the quantum approximate optimization algorithm (QAOA). For this purpose we formulate a mapping of the \ac{HVRP} to an Ising Hamiltonian and simulate the algorithm on problem instances of up to 21 qubits. We find that the number of qubits needed for this mapping scales quadratically with the number of customers. We compare the performance of different classical optimizers in the QAOA for varying problem size of the \ac{HVRP}, finding a trade-off between optimizer performance and runtime.