Abstract: The original black-winged kite algorithm (BKA) has several drawbacks such as easy to fall into local optima and insufficient convergence accuracy, an improved BKA (IBKA) based on the adaptive inertia weight was proposed. Firstly, the population is initialized using the Fuch chaotic mapping strategy to enhance population diversity. Secondly, an adaptive weight is incorporated into the attack behavior of the black-winged kite to better balance local exploitation and global exploration capabilities. Finally, Lévy flight operator is introduced into the migration behavior of the black-winged kite to effectively strengthen the algorithm's global search ability. 29 CEC2017 test functions are solved by using IBKA, BKA, whale optimization algorithm (WOA), zebra optimization algorithm (ZOA), sine cosine algorithm (SCA), and dung beetle optimization (DBO). The results demonstrate that IBKA exhibits superior convergence speed and accuracy compared with BKA, WOA, ZOA, SCA, and DBO. Additionally, the effectiveness of IBKA in solving practical engineering optimization problems is verified through the resolution of three engineering design constraint optimization problems.