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

Xia Wang; Feng Zou; Weilin Zhang; Huogen Yang; Xia Wang; Feng Zou; Weilin Zhang; Huogen Yang

doi:10.3934/math.2025742

AIMS Mathematics

2025, Volume 10, Issue 7: 16570-16596. doi: 10.3934/math.2025742

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Research article

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

1.
School of Science, Jiangxi University of Science and Technology, Ganzhou, Jiangxi 341000, China
2.
Jiangxi Provincial Key Laboratory of Multidimensional Intelligent Perception and Control, Jiangxi University of Science and Technology, Ganzhou, Jiangxi 341000, China

Received: 22 May 2025 Revised: 04 July 2025 Accepted: 18 July 2025 Published: 23 July 2025
MSC : 65D15, 65D17, 90C59

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.
- disk Wang-Bézier curve,
- multi-degree reduction approximation,
- black-winged kite algorithm,
- adaptive spiral strategy,
- parrot algorithm
Citation: Xia Wang, Feng Zou, Weilin Zhang, Huogen Yang. Approximate multi-degree reduction of disk Wang-Bézier generalized ball curves via improved black-winged kite algorithm[J]. AIMS Mathematics, 2025, 10(7): 16570-16596. doi: 10.3934/math.2025742

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Abstract

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.

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