Approximate Multi-Degree Reduction of SG-Bézier Curves Using the Grey Wolf Optimizer Algorithm

Hu, Gang; Qiao, Yu; Qin, Xinqiang; Wei, Guo

doi:10.3390/sym11101242

Cited by 6 publications

(5 citation statements)

References 32 publications

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“…Grey wolf optimizer (GWO) has gained significant attention in recent years due to its flexibility, scalability, and few parameters [ 61 ]. It is applied in various applications such as gait analysis [ 62 ], structural strain reconstruction [ 63 ], engines [ 64 ], renewable energy systems [ 65 ], robotics [ 66 ], deep learning [ 67 ], wireless sensor networks [ 68 ], smart grid [ 69 ], medical [ 70 ], and energy management [ 71 ]. Even though GWO has been utilized in different applications, due to the complexity of real-world optimization problems, various improvements have been made in GWO in terms of updating mechanisms, hybridization, encoding schemes, multi-objective, and new operators.…”

Section: Introductionmentioning

confidence: 99%

Variants of Chaotic Grey Wolf Heuristic for Robust Identification of Control Autoregressive Model

et al. 2023

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In this article, a chaotic computing paradigm is investigated for the parameter estimation of the autoregressive exogenous (ARX) model by exploiting the optimization knacks of an improved chaotic grey wolf optimizer (ICGWO). The identification problem is formulated by defining a mean square error-based fitness function between true and estimated responses of the ARX system. The decision parameters of the ARX model are calculated by ICGWO for various populations, generations, and noise levels. The comparative performance analyses with standard counterparts indicate the worth of the ICGWO for ARX model identification, while the statistical analyses endorse the efficacy of the proposed chaotic scheme in terms of accuracy, robustness, and reliability.

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Section: Introductionmentioning

confidence: 99%

Variants of Chaotic Grey Wolf Heuristic for Robust Identification of Control Autoregressive Model

et al. 2023

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“…Thus, for data conversation and transmission between various models, we properly investigated the degree reduction/elevation of curves. For the degree reduction of curves, the three methods were proposed based on the least square theory [22][23][24][25], the algebraic method [26][27][28][29][30], and the intelligent optimization algorithm based methods, in which the problem of degree reduction is formulated as an optimization one and is solved by incorporating intelligent optimization algorithms [31][32][33][34]. In 2019, based on the genetic simulated annealing algorithm, Lu and Qin [31] realized the multi-degree reduction approximation of the S-λ curve for the first time.…”

Section: Introductionmentioning

confidence: 99%

“…In 2019, based on the genetic simulated annealing algorithm, Lu and Qin [31] realized the multi-degree reduction approximation of the S-λ curve for the first time. Hu et al [32] studied the problem of approximate multi-degree reduction for SG-Bézier curves using the grey wolf optimizer algorithm, and achieved a good degree reduction effect. After that, Qin et al [33] further extended the method in literature [32] to the degree reduction of SG-Bézier surfaces.…”

Section: Introductionmentioning

confidence: 99%

“…Hu et al [32] studied the problem of approximate multi-degree reduction for SG-Bézier curves using the grey wolf optimizer algorithm, and achieved a good degree reduction effect. After that, Qin et al [33] further extended the method in literature [32] to the degree reduction of SG-Bézier surfaces. Guo et al [33] improved the whale optimization algorithm by using the skewed normal cloud and applied it to solve the problem of degree reduction for S-λ curve.…”

Section: Introductionmentioning

confidence: 99%

“…Guo et al [33] improved the whale optimization algorithm by using the skewed normal cloud and applied it to solve the problem of degree reduction for S-λ curve. Compared with the first two methods, the third kind of method in [31][32][33][34] is more convenient to be used for the multiple-degree reduction of different types of curves. Moreover, these methods based on intelligent optimization algorithms seem simpler, by which global optimal degree reduced curves can be obtained intelligently, avoiding complicated theoretical derivation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Degree Reduction of Q-Bézier Curves via Squirrel Search Algorithm

Liu

Abbas

et al. 2021

Mathematics

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Q-Bézier curves find extensive applications in shape design owing to their excellent geometric properties and good shape adjustability. In this article, a new method for the multiple-degree reduction of Q-Bézier curves by incorporating the swarm intelligence-based squirrel search algorithm (SSA) is proposed. We formulate the degree reduction as an optimization problem, in which the objective function is defined as the distance between the original curve and the approximate curve. By using the squirrel search algorithm, we search within a reasonable range for the optimal set of control points of the approximate curve to minimize the objective function. As a result, the optimal approximating Q-Bézier curve of lower degree can be found. The feasibility of the method is verified by several examples, which show that the method is easy to implement, and good degree reduction effect can be achieved using it.

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Degree reduction of ball Said‐Ball surfaces using an enhanced coot optimization algorithm

Hu,

Dou,

2023

Math Methods in App Sciences

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Degree reduction of ball Said‐Ball (BSB) surface is a complex and unsolved problem in computer‐aided design (CAD) and computer graphics (CG), which has potential application prospects in many engineering fields of geometric modeling. In this paper, the degree reduction of BSB surface is transformed into the optimization problems of center surface and radius function, and the improved coot optimization algorithm is used to solve it. An effective method to solve the degree reduction of BSB surface by intelligent optimization algorithm is proposed. Firstly, the degree reduction of BSB surface is decomposed into center surface reduction and radius function reduction, and the objective function and constraint conditions are determined according to the optimization idea, then the degree reduction optimization model of center surface and radius function is established. Secondly, an enhanced coot (ECOOT for short) algorithm is proposed, which combines chain strategy, dispersed foraging strategy, and quadratic interpolation strategy. Compared with the original algorithm, ECOOT algorithm has better convergence performance and higher calculation accuracy. Finally, the proposed ECOOT algorithm is used to solve the degree reduction optimization model, and the optimal center surface and minimum distance radius function of the BSB surface after degree reduction are obtained. The experimental results show that the ECOOT algorithm can effectively solve the problem of degree reduction for BSB surface, the degree reduction error is reduced by about 20% compared to the original COOT algorithm, and is superior to other intelligent optimization algorithms in accuracy, robustness, and convergence.

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Approximate Multi-Degree Reduction of SG-Bézier Curves Using the Grey Wolf Optimizer Algorithm

Cited by 6 publications

References 32 publications

Variants of Chaotic Grey Wolf Heuristic for Robust Identification of Control Autoregressive Model

Variants of Chaotic Grey Wolf Heuristic for Robust Identification of Control Autoregressive Model

Degree Reduction of Q-Bézier Curves via Squirrel Search Algorithm

Degree reduction of ball Said‐Ball surfaces using an enhanced coot optimization algorithm

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