Quantum Annealing of Vehicle Routing Problem with Time, State and Capacity

Abstract

We propose a brand-new formulation for capacitated vehicle routing problem (CVRP) as a quadratic unconstrained binary optimization (QUBO). The formulated CVRP is equipped with time-table which describes time-evolution of each vehicle. Therefore, various constraints associated with time can be successfully realized. Similarly, constraints of capacities are also introduced, where capacitated quantities are allowed to increase and decrease according to the cities in which vehicles arrive. As a bonus of capacity-qubits, one can also obtain a description of state, which allows us to set various traveling rules, depending on the state of each vehicle. As a consistency check, the proposed QUBO formulation is also evaluated using a quantum annealing machine, D-Wave 2000Q.