Summary
Planning drone deliveries is hard because drones have limits like how much weight they can carry and how far they can fly, making the planning math quite complex. The authors studied a method that first uses regular computers to rule out impossible delivery plans before using special quantum-inspired methods to choose the best plan. They found that filtering out unworkable missions classically greatly reduces the size of the problem and speeds up finding good routes. The quantum method tried didn’t perform as well on bigger problems, showing that the main improvement comes from the classical filtering step. This helps make drone delivery planning easier and faster.
What this means in practice
- •For drone fleet operators: Implement preprocessing to remove infeasible missions, speeding up drone route selection through reduced optimization problems.
- •For logistics software developers: Incorporate hybrid quantum-classical methods that preprocess constraints before applying optimization, improving solution speed on small drone delivery instances.
Abstract
Drone-delivery planning combines routing decisions with operational constraints such as payload capacity and limited onboard energy, resulting in combinatorial optimization problems that can become costly to encode directly in binary form. This work investigates a hybrid quantum--classical approach in which candidate drone missions are generated and evaluated classically before constructing a quadratic unconstrained binary optimization (QUBO) model for mission selection. Payload- and energy-infeasible missions are removed during preprocessing, while the reduced QUBO is solved using exact enumeration, simulated annealing (SA), and the Quantum Approximate Optimization Algorithm (QAOA), with mixed-integer linear programming (MILP) used as a classical reference. Experiments on controlled synthetic delivery instances evaluate solution quality, the effect of preprocessing, and computational scaling. Exact QUBO optimization reproduces the MILP optimum on the evaluated small instances, while SA achieves $100\%$ feasibility with a median optimality gap of $0\%$. Combined payload-and-energy preprocessing reduces the mean number of QUBO variables by $29.60\%$ and quadratic interactions by $49.20\%$, while reducing mean SA runtime by $31.26\%$. In contrast, the evaluated shallow statevector-based QAOA configuration achieves lower feasibility and is restricted to small QUBO instances. These results indicate that, in the considered setting, the main practical benefit of the hybrid architecture comes from classical feasibility preprocessing that reduces the binary search space before QUBO-based optimization.