This study develops an MTSP model for multi-UAV delivery optimization from a central hub, proposing a hybrid algorithm that integrates genetic simulated annealing-enhanced clustering with an improved Hopfield neural network to minimize the total flight distance. The proposed methodology initially employs an enhanced fuzzy C-means clustering technique integrated with genetic simulated annealing (GSA) to effectively partition the MTSP formulation into multiple discrete traveling salesman problem (TSP) instances. The subsequent phase implements an enhanced Hopfield neural network (HNN) architecture incorporating three key modifications: data normalization procedures, adaptive step-size control mechanisms, and simulated annealing integration, collectively improving the TSP solution quality and computational efficiency. The proposed algorithm’s effectiveness is validated through comprehensive case studies, demonstrating significant performance improvements in the computational efficiency and solution quality compared to conventional methods. The results show that during clustering, the improved clustering algorithm is more stable in its clustering effect. With regard to path optimization, the improved neural network algorithm has a higher computational efficiency and makes it easier to obtain the global optimal solution. Compared with the genetic algorithm and ant colony algorithm, its iteration times, path length, and delivery time are reduced to varying degrees. To sum up, the hybrid optimization algorithm has obvious advantages for solving a multi-UAV collaborative distribution path optimization problem.

With the increasing application of unmanned vehicles in logistics delivery, more and more researchers are paying attention to improving delivery efficiency, improving delivery service levels and reducing costs. This research considers the unmanned vehicle delivery problem with time windows, where the delivery must be completed within the required time window, otherwise there will be a penalty and a penalty cost will be incurred. And considering the limited range of the unmanned vehicle's battery, whether it needs to enter the charging station for charging or not, the model is established based on the minimum running cost and penalty cost. And a genetic algorithm is designed. Finally, the effectiveness of the model and algorithm is verified by examples.