Coupled Lévy-Convolutional Differential Evolution: An adaptive framework for UAV path planning in complex urban environments

Three-dimensional UAV path planning in complex urban environments is a high-dimensional and non-convex optimization problem involving multiple coupled constraints. Although adaptive differential evolution algorithms have shown promising performance in solving such problems, they may still encounter search imbalance, premature convergence, and path oscillations when facing dense obstacles and deceptive fitness landscapes. To address these challenges, this paper proposes a Coupled Lévy-Convolutional Differential Evolution algorithm (CLC-DE). First, a probabilistically mixed dual-strategy evolutionary mode is designed to balance rapid convergence with robust exploration. Second, an Adaptive Coupled-Convolutional Mechanism (ACCM) is introduced to perform differentiated corrections according to the spatial distribution of stagnant individuals. Specifically, for discrete individuals located far from promising regions, a Convolutional Filtering Mutation (CFM) operator is employed to suppress random perturbations and guide a smoother return toward effective search regions. For individuals aggregated near local optima, a Coupled Lévy Search (CLS) operator incorporates long-tailed jumps and non-axial coupling transformations to enhance local-optimum avoidance. Experimental results on the CEC2017 benchmark suite demonstrate that CLC-DE achieves superior convergence accuracy and stability compared with several classical and advanced algorithms. Further UAV path planning simulations in complex urban environments show that CLC-DE can generate relatively short, safe, and smooth paths while satisfying obstacle-avoidance and kinematic constraints. These results indicate that the proposed method enhances the capability of differential evolution in solving high-dimensional constrained optimization problems and provides a promising optimization framework for autonomous UAV path planning in complex urban airspace. The source code of CLC-DE is available at: https://github.com/zhbyes/CLCDE.