Multi-UAV path planning considering multiple energy consumptions via an improved bee foraging learning particle swarm optimization algorithm

With the advancement of unmanned aerial vehicle (UAV) technology, UAVs, such as multi-rotor drones, have found widespread application in wireless sensor networks. In scenarios where multiple UAVs collaborate to gather sensor data from the field, it is essential to establish a path planning model that incorporates an accurate energy consumption model for these UAVs. The power consumption of a multi-rotor drone varies depending on its flight state. When UAVs traverse various locations, it is not only the power required for steady-level flight that must be considered, but also the power necessary for acceleration, deceleration, climbing, and turning. This paper presents a path planning model for multiple UAVs, termed the Multi-UAV Path Planning Considering Multiple Energy Consumptions (MUAVPP-MEC). The solution derived adheres to the constraint that UAV flight energy consumption should not exceed the maximum stored energy, with the goal of minimizing the total flight time across all UAV paths. To tackle the MUAVPP-MEC, this study proposes an improved Bee Foraging Learning Particle Swarm Optimization algorithm (IBFLPSO), which integrates the bee-foraging algorithm into the particle swarm optimization framework. The IBFLPSO facilitates an efficient real-number encoding and greedy segmenting sequence decoding strategy, translating the solution space of the problem into the search space of the algorithm. To improve the optimization capabilities of the algorithm, IBFLPSO utilizes the energy-constrained 2-opt as a local search operator. In Experiment 1, the proposed model and algorithm are validated through three distinct case studies, demonstrating the stability and efficacy of the methods. It is clearly observed that as the number of collection points increases, both the total cruising time and energy consumption of the model rise significantly, thus confirming the accuracy of the model. In Experiment 2, when compared with four other algorithms, IBFLPSO outperforms them in both the optimal and average solutions. Specifically, the optimal solution of IBFLPSO is 54.64%, 49.45%, 25.78%, and 22.92% better than those of the traditional PSO algorithm, PSO-2OPT algorithm, GA, and BFLPSO, respectively. © The Author(s) 2025.