Symmetry-Inspired Dung Beetle Optimizer for 3D UAV Path Planning with Structural-Invariance-Aware Grouping

Metaheuristic methods for three-dimensional (3D) unmanned aerial vehicle (UAV) path planning often suffer from premature convergence and reduced accuracy in complex high-dimensional spaces, in which waypoint-based decision variables exhibit structured dependencies and segment-level regularities. In a symmetry-inspired operational sense, these regularities can be interpreted as exploitable dependency patterns across path segments and permutation invariance among homogeneous UAVs, which are often overlooked by standard algorithms. The paper proposes an enhanced dung beetle optimizer (LEDBO) that integrates interaction-aware variable handling, adaptive role regulation, and a fitness-state-driven hybrid search mechanism. Correlation-based variable grouping clusters dependent waypoints into segments to exploit statistical dependency patterns among waypoint-coordinate variables and enhance local refinement. A three-level adaptive role-regulation scheme adjusts search behaviors according to convergence status and population diversity, thereby mitigating stagnation. Meanwhile, a fitness-state-driven hybrid engine combines Nelder–Mead local refinement with Lévy-flight global exploration to balance exploitation and exploration across stages. Experiments on the CEC2017 benchmark suite and complex 3D UAV path-planning simulations demonstrate that LEDBO achieves better solution quality, convergence behavior, and robustness than representative metaheuristics, producing smoother, shorter, and safer trajectories. The results suggest that incorporating interaction-aware variable grouping and adaptive search regulation can improve UAV path planning and related high-dimensional continuous optimization tasks.