Multi-Objective Trajectory Planning Method for Air–Ground Collaborative Logistics UAVs Under Preemptive Scheduling

Multi-UAVs cooperative task allocation and path planning for low-altitude logistics

To address the challenges of collaborative task allocation and path planning for multiple logistics unmanned aerial vehicles (UAVs) in urban low-altitude environments, this paper proposes a bilevel nested joint optimization method based on reinforcement learning and a graph search algorithm to enhance the efficiency of collaborative last-mile delivery by multiple logistics UAVs while reducing flight risks. The proposed method constructs a bilevel architecture system based on a task allocation and decision-making model and a path planning model. The upper-level model holistically considers the demands of three stakeholders—government (safety), customers (timeliness), and UAV enterprises (economy)—at the macro level. Then, based on real-time order information and UAV status, a multi-objective optimization and constraint model is constructed under complex dynamic environments. A multi-agent proximal policy optimization algorithm is employed to achieve rapid dynamic task allocation and decision-making. The lower-layer model utilizes the upper-level allocation results combined with detailed environmental information to plan safe and efficient flight paths for each UAV at the micro level. It employs an improved jumping-point search algorithm for refined path optimization. A loop feedback mechanism is designed to facilitate information exchange between layers, thereby coupling the task allocation and path planning processes to achieve collaborative optimization of upper- and lower-level task allocation and decision-making. This method effectively addresses complex logistics delivery scenarios, enhancing the overall efficiency and robustness of the delivery system. Simulation experiments comprehensively consider path influences from flexible open-area delivery, varying numbers of distribution centers and UAVs, and on-demand rush orders. Tests conducted in medium- and high-density environments demonstrate the proposed model and algorithm’s significant superiority in dynamic complex scenarios. Even when confronted with complex environments and dynamic order scenarios, it consistently generates highly applicable UAV flight paths.

A Multi-Objective Optimization Framework Combining NSGA-II and MOPSO for UAV Path Planning

A multi-objective intelligent optimization algorithm, the wise wayfinding algorithm (WWA), which integrates mechanisms from non-dominated sorting genetic algorithm II and multi-objective particle swarm optimization (MOPSO) and exhibits favorable convergence and robust solution distribution on standard benchmark functions (ZDT, DTLZ, UF).

A Multi-UAV Planning Framework for Task Allocation, Route Optimization and Trajectory Smoothing

A Multi-UAV Planning Framework for Task Allocation, Route Optimization and Trajectory Smoothing for static environments with known obstacle geometry is presented and results demonstrate that the proposed hierarchical formulation is computationally effective, physically consistent, and well suited to multi-UAV mission planning.

Immune-enhanced NSGA-II for multi-objective multi-UAV disaster relief material distribution

In disaster-relief logistics, disrupted ground transportation networks and the limited payload and endurance of UAVs make it difficult to allocate emergency materials across geographically dispersed demand points. This study formulates a capacity-constrained bi-objective multi-UAV material distribution problem that simultaneously minimizes total flight distance and workload imbalance. Each demand point is served by one UAV in a single-trip route, and route feasibility is evaluated under payload-capacity and maximum route-distance constraints. To solve this constrained discrete optimization problem, we propose an immune-enhanced NSGA-II algorithm, referred to as INSGA-II. The algorithm represents each solution using an integer assignment vector and a priority vector for route decoding, and integrates immune cloning, stimulation-guided clone allocation, and a linearly decreasing mutation probability to improve the exploration of non-dominated allocation-routing solutions. Comparative experiments were conducted over 30 independent runs against standard NSGA-II, MOEA/D, Weighted-GA, and Weighted-ACO using hypervolume (HV), inverted generational distance (IGD), and runtime as evaluation metrics. INSGA-II achieved the highest mean HV of 0.895 and the lowest mean IGD of 0.184 among the compared algorithms, showing favorable average Pareto-front approximation performance in the tested scenario. Its average runtime was higher than NSGA-II and MOEA/D due to additional immune and repair operations, but lower than Weighted-GA and Weighted-ACO in the tested setting. The results suggest that INSGA-II provides quality-oriented Pareto trade-off solutions for capacity-constrained multi-UAV disaster-relief material distribution.

Centralized Scheduling and Distributed Trajectory Optimization for Cooperative Mapping with Multiple PX4-Based VTOL UAVs

A Trajectory Planning Method for UAVs in Dynamic Multi-Threat Environments Based on a Dynamic Multi-Objective Crow Search Algorithm

Trajectory planning, which determines a route from a starting position to a target position within a given airspace, is critical to unmanned aerial vehicle (UAV) mission execution. Many existing meta-heuristic approaches to three-dimensional (3D) trajectory planning aggregate competing requirements into a weighted cost and may suffer from limited adaptability when the environment changes. This paper formulates 3D UAV trajectory planning in dynamic multi-threat environments as a dynamic bi-objective optimization problem and proposes a multi-swarm dynamic multi-objective crow search algorithm (MDMCSA). The proposed method organizes objective-oriented swarms within a cooperative search framework and facilitates information exchange through archive sharing, thereby coordinating the search process among different objectives. The memory-time and diverse behavior strategies adjust search behaviors and solution perturbation to balance convergence and diversity. A hybrid change response strategy combines historical information reuse with diversity restoration after dynamic changes. Comparative experiments on dynamic benchmark problems and UAV trajectory planning scenarios demonstrate competitive convergence and adaptation performance, together with a favorable trade-off between solution quality and computational cost. Incremental ablation and parameter-sensitivity analyses further indicate the cumulative benefit of the integrated design and the stable performance of the selected parameter configuration across the tested settings.