A Guided Collaborative Optimization Framework for the Stability-Constrained UAV Routing and Three-Dimensional Loading Problem

The joint optimization of routing and three-dimensional loading is a highly complex NP-hard combinatorial problem, particularly when stringent center-of-gravity (CoG) stability constraints are required for unmanned aerial vehicle (UAV) operations. Existing algorithms typically adopt a route-first, load-second evaluation strategy for these interconnected components, often yielding distance-optimal yet physically infeasible solutions. To address this bottleneck, this paper formulates the Three-Dimensional Loading-Constrained UAV Routing Problem (3DLC-UAVRP), integrating unloading sequence consistency, spatial packing feasibility, and CoG deviation control into the routing decision process. A guided collaborative optimization framework, GLS-WSCPA, is proposed, coupling an Improved White Shark Optimization (IWSO) algorithm for global route exploration with a Human-like Divide-and-Conquer Packing Strategy (HLDCPS) for spatial arrangement. Unlike conventional decoupled approaches that treat loading feasibility as a post hoc filter, a Center-of-Gravity-Guided Path Adjustment (CGPA) and Local Loading Repair (LLR) mechanism is introduced to establish a dynamic feedback loop between routing search and loading evaluation, so that CoG violations are actively translated into guided routing perturbations rather than simply triggering solution rejection. Experimental results demonstrate that GLS-WSCPA generally achieves better solutions than the compared algorithms across the tested problem scales, with the performance gap tending to widen as the instance size increases within the tested range. Ablation studies verify the complementary roles of CGPA and LLR, and sensitivity analysis confirms that moderately relaxing payload and CoG constraints reduces routing distance within safety boundaries. Case analysis shows that the proposed method reduces fleet size by 20% and total delivery distance by 6.85% compared to traditional decoupled strategies.