Approximate multi-degree reduction of disk Wang-Bézier generalized ball curves via improved black-winged kite algorithm

This study proposed an efficient optimization approach for the degree reduction approximation of disk Wang-Bézier generalized ball (DWBGB) curves, utilizing an improved black-winged kite algorithm (IBKA). A constrained optimization model was developed based on the geometric characteristics of DWBGB curves, accompanied by a novel error metric for degree reduction evaluation. The original BKA was enhanced in three key aspects. First, a Sobol sequence paired with opposition-based learning was utilized to optimize the initial population distribution, markedly improving diversity and quality. Second, an adaptive spiral search mechanism was incorporated to bolster local exploitation. Third, the foraging strategy of the parrot algorithm was integrated to enhance global exploration and optimization efficiency. Evaluations conducted on the IEEE CEC-2020 benchmark test suite indicated that IBKA surpassed ten leading intelligent optimization algorithms in convergence speed, solution precision, and stability. When applied to DWBGB curve degree reduction across four test cases, IBKA demonstrated superior approximation accuracy and convergence stability compared to four representative algorithms. Relative to the original BKA, IBKA yielded improvements of 53.85%, 80.89%, and 36.18% in mean error, standard deviation, and minimum error, respectively, confirming its efficacy and superiority in addressing the multi-degree reduction problem for DWBGB curves.