<p>This article introduces an adaptive hierarchical differential gray wolf optimization (DGWO) algorithm, a hybrid approach that combines the exploration capabilities of the gray wolf optimization algorithm with the utilization capabilities of the differential evolution algorithm. The DGWO algorithm aims to overcome the limitations of traditional optimization algorithms, such as premature convergence and slow convergence rates, by integrating various innovative mechanisms. These mechanisms include the dynamic adjustment of the convergence factor α in GWO, the β wolf position spiral update mechanism inspired by the whale optimization algorithm (WOA), and the adaptive switching mechanism that switches between exploration and development stages based on population diversity and the frequency of optimal solution updates. Additionally, the algorithm uses tent chaotic mapping for population initialization to enhance diversity and employs a directed local search strategy in the later optimization stages to improve solution accuracy. Extensive experimental evaluations of various benchmark functions, including unimodal, multimodal, and composite functions, have shown that DGWO significantly outperforms traditional GWO, DE, and other advanced algorithms in terms of convergence speed, accuracy, and stability. The effectiveness of this algorithm has been further validated through its practical application in UAV swarm path planning and multi-story building framework optimization, achieving excellent results in minimizing total path length, avoiding collisions, and reducing structural weight. Overall, the DGWO algorithm is a powerful and versatile optimization tool, well-suited for complex real-world problems, with potential for future expansion to tackle ultra-high-dimensional issues and dynamic environments.</p>