Chen Kang, Chen Liuxin, Hu Gang
Unmanned System Research Institute, Northwestern Polytechnical University, Xi'an 710072, China.
Xi'an Jingkai No. 1 Primary School, Xi'an 710018, China.
Biomimetics (Basel). 2023 Aug 18;8(4):377. doi: 10.3390/biomimetics8040377.
With the rapid development of the geometric modeling industry and computer technology, the design and shape optimization of complex curve shapes have now become a very important research topic in CAGD. In this paper, the Hybrid Artificial Hummingbird Algorithm (HAHA) is used to optimize complex composite shape-adjustable generalized cubic Ball (CSGC-Ball, for short) curves. Firstly, the Artificial Hummingbird algorithm (AHA), as a newly proposed meta-heuristic algorithm, has the advantages of simple structure and easy implementation and can quickly find the global optimal solution. However, there are still limitations, such as low convergence accuracy and the tendency to fall into local optimization. Therefore, this paper proposes the HAHA based on the original AHA, combined with the elite opposition-based learning strategy, PSO, and Cauchy mutation, to increase the population diversity of the original algorithm, avoid falling into local optimization, and thus improve the accuracy and rate of convergence of the original AHA. Twenty-five benchmark test functions and the CEC 2022 test suite are used to evaluate the overall performance of HAHA, and the experimental results are statistically analyzed using Friedman and Wilkerson rank sum tests. The experimental results show that, compared with other advanced algorithms, HAHA has good competitiveness and practicality. Secondly, in order to better realize the modeling of complex curves in engineering, the CSGC-Ball curves with global and local shape parameters are constructed based on SGC-Ball basis functions. By changing the shape parameters, the whole or local shape of the curves can be adjusted more flexibly. Finally, in order to make the constructed curve have a more ideal shape, the CSGC-Ball curve-shape optimization model is established based on the minimum curve energy value, and the proposed HAHA is used to solve the established shape optimization model. Two representative numerical examples comprehensively verify the effectiveness and superiority of HAHA in solving CSGC-Ball curve-shape optimization problems.
随着几何建模行业和计算机技术的快速发展，复杂曲线形状的设计与形状优化现已成为计算机辅助几何设计（CAGD）中一个非常重要的研究课题。本文采用混合人工蜂鸟算法（HAHA）对复杂的复合形状可调广义三次Ball曲线（简称为CSGC - Ball曲线）进行优化。首先，人工蜂鸟算法（AHA）作为一种新提出的元启发式算法，具有结构简单、易于实现的优点，能够快速找到全局最优解。然而，它仍存在局限性，如收敛精度低和易陷入局部最优的倾向。因此，本文在原始AHA的基础上提出HAHA，结合基于精英反向学习策略、粒子群优化算法（PSO）和柯西变异，以增加原始算法的种群多样性，避免陷入局部最优，从而提高原始AHA的精度和收敛速度。使用25个基准测试函数和CEC 2022测试套件来评估HAHA的整体性能，并使用弗里德曼检验和威尔克森秩和检验对实验结果进行统计分析。实验结果表明，与其他先进算法相比，HAHA具有良好的竞争力和实用性。其次，为了更好地实现工程中复杂曲线的建模，基于SGC - Ball基函数构造了具有全局和局部形状参数的CSGC - Ball曲线。通过改变形状参数，可以更灵活地调整曲线的整体或局部形状。最后，为了使构造的曲线具有更理想的形状，基于曲线能量值最小化建立了CSGC - Ball曲线形状优化模型，并使用所提出的HAHA来求解所建立的形状优化模型。两个代表性数值例子全面验证了HAHA在解决CSGC - Ball曲线形状优化问题中的有效性和优越性。
