Quantum-Based k-Coverage Optimization for UAV-Aided Search and Rescue Missions
In large-scale disaster scenarios, rapid localization of missing persons is a critical challenge for search-and-rescue (SAR) operations. Unmanned aerial vehicles (UAVs) equipped with radio frequency (RF) receivers can support RF-based localization by collecting signals emitted from mobile devices at spatially distributed sensing locations. This paper addresses the resulting waypoint-selection problem: determining a minimum set of UAV waypoints that provides at least threefold coverage of every potential target location. We formulate this task as an extended k-coverage problem that independently defines the UAV-navigable and target regions, and derive an exact-penalty quadratic unconstrained binary optimization (QUBO) formulation with a sufficient penalty condition that preserves feasibility and minimum waypoint cardinality. The QUBO is mapped to an Ising-form cost Hamiltonian and evaluated using the quantum approximate optimization algorithm (QAOA) on both a noise-free simulator and IBM's 127-qubit Eagle processor. On the tested simulator instances, QAOA recovers the known minimum-cardinality solutions. Across the rectangular hardware test cases, the mean 3-coverage ratio exceeded 95%. In the campus-scale evaluation, ten hardware executions achieved 99.3% mean 3-coverage with a 90% feasible-run rate, while the shortest feasible flight path was up to 37.0% shorter than those of the deterministic grid-based baselines. Additional comparisons with classical optimization and learning-based baselines are provided, together with computational and quantum-resource analyses for larger generated instances. These results establish an exact QUBO representation for RF-based SAR waypoint selection and characterize its implementation on current gate-based quantum hardware.