Certified-Robust Multi-Objective UAV Routing for Military Resupply under Nonlinear Energy Dynamics: An Adaptive Physics-Informed Approach
Abstract
Abstract In this paper, we study the scheduling of military unmanned aerial vehicle (UAV) resupply missions under three coupled sources of uncertainty: flight-time variability, operational risk, and nonlinear battery-energy depletion. Unlike standardrobust vehicle routing, we introduce a physical state, the battery energy level, that depletes according to Peukert’s law rather than a linear cost. We formulate a tri-objective robust routing model minimizing mission duration, cumulative risk under a budgeted-uncertainty set, and worst-case terminal energy shortfall, subject to payload-capacity and coverage constraints. To solve it, we propose Adaptive PINN, a physics-informed neural network (PINN) framework in which a shared trunk feeds an assignment head predicting the terminal routing distribution and an energy head predicting the battery trajectory, trained against the Peukert-law residual, with objective and physics/task weights adapted during training. A certified repair layer, built on a closed-form energy recursion exact for any Peukert exponent and checkable in linear time, restores worst-case feasibility of every returned schedule in finitely many moves. We validate the closed-form recursion against numerical integration and benchmark the recovered Pareto front against exact enumeration on small instances, leaving evaluation of the trained network and comparison against an evolutionary baseline at scale as immediate next steps. MSC Classification: 90B06 , 90C29 , 90C17…
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