<p>This paper proposes an improved black-winged kite algorithm with multiple strategies (IGFM-BKA) to address two critical limitations in the original black-winged kite optimization algorithm (BKA): inadequate balance between exploration and exploitation during the attack phase resulting in limited search capability and low convergence accuracy, and insufficient population diversity during the migration phase leading to slow convergence speed and susceptibility to local optima. Our enhancement implements three strategic modifications across different algorithmic stages. During the attack phase, an adaptive weight strategy is incorporated to dynamically balance exploration and exploitation, thereby enhancing convergence precision and global search capability. For the migration phase, a multi-directional flipping strategy (GBKA) is adopted to significantly increase population diversity and accelerate convergence speed. Furthermore, a differential evolution strategy with vertical crossover (FMBKA) is introduced to promote information exchange among population members and prevent the algorithm from trapped in local optima. The synergistic integration of these three strategies substantially improves the overall algorithmic performance. Comprehensive evaluations were conducted using 18 classical benchmark functions alongside test suites from CEC2017 and CEC2022 to validate the effectiveness and advancement of the proposed IGFM-BKA. Detailed convergence analysis and Wilcoxon rank-sum test comparisons with other state-of-the-art algorithms demonstrate the superior convergence performance and robustness of our approach. Furthermore, the algorithm was successfully applied to optimize a complex three-dimensional path planning model for unmanned aerial vehicles. Experimental results confirm that IGFM-BKA achieves the lowest comprehensive cost while generating smooth and collision-free flight trajectories, providing an efficient solution for UAV navigation in complex environments and fully validating its significant practical value in real-world applications. Furthermore, the computational intensity of evaluating complex cost functions in high-dimensional search spaces, coupled with the real-time demands of drone navigation in dynamic environments, makes high-performance computing (HPC) capabilities an essential requirement. The proposed IGFM-BKA possesses parallelizable characteristics, making it an ideal solution for distributed and parallel processing.</p>