A Maximum Entropy Approach to Joint Obstacle-Aware Routing and Facility Location in UAV Networks Under Energy Constraints

Abstract

This paper addresses the critical challenge of obstacle-aware path planning and energy-constrained facility location in Uncrewed Aerial Vehicle (UAV) networks, essential for applications like delivery services, agriculture, and emergency response. We propose a novel Maximum Entropy Principle (MEP)-based framework that simultaneously optimizes UAV routes and the strategic placement of charging facilities, including Uncrewed Ground Vehicles (UGVs), under battery constraints. By reformulating the problem, our method reduces the dimensionality of the optimization space compared to conventional approaches, enabling faster optimization and improved solution quality. The simulation results show that our method delivers high-quality solutions for complex scenarios under various constraints, achieving on average a nearly 30\times lower cost than existing metaheuristics while running significantly faster, and maintaining an optimality gap of less than 3% relative to the exact solver baseline. This work advances the theoretical foundation of coordinated UAV–UGV operations and presents a practical framework for efficient multi-objective network planning.