随着几何造型行业和计算机技术的迅速发展,复杂曲线形状的设计和形状优化现在已经成为CAGD中一个非常重要的研究课题。在本文中,混合人工蜂鸟算法(HAHA)用于优化复杂复合形状可调广义立方球(CSGC-Ball,简而言之)曲线。首先,人工蜂鸟算法(AHA),作为一种新提出的元启发式算法,结构简单,易于实现,能快速找到全局最优解。然而,仍然有局限性,如收敛精度低,容易陷入局部优化。因此,本文在原有AHA的基础上提出了HAHA,结合精英对立学习策略,PSO,和柯西突变,为了增加原始算法的种群多样性,避免陷入局部优化,从而提高了原始AHA的精度和收敛速度。25个基准测试函数和CEC2022测试套件用于评估HAHA的整体性能,并使用Friedman和Wilkerson秩和检验对实验结果进行统计分析。实验结果表明,与其他高级算法相比,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基函数构造具有全局和局部形状参数的CSGC-Ball曲线。通过更改形状参数,曲线的整体或局部形状可以更灵活地调整。最后,为了使构造的曲线具有更理想的形状,建立了基于最小曲线能量值的CSGC-Ball曲线形状优化模型,并利用提出的HAHA对建立的外形优化模型进行求解。两个具有代表性的数值算例全面验证了HAHA在求解CSGC-Ball曲线形状优化问题中的有效性和优越性。
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.