Curvature lines are special and important curves on surfaces. It is of great significance to construct developable surface interpolated on curvature lines in engineering applications. In this paper, the shape optimization of generalized cubic ball developable surface interpolated on the curvature line is studied by using the improved reptile search algorithm. Firstly, based on the curvature line of generalized cubic ball curve with shape adjustable, this paper gives the construction method of SGC-Ball developable surface interpolated on the curve. Secondly, the feedback mechanism, adaptive parameters and mutation strategy are introduced into the reptile search algorithm, and the Feedback mechanism-driven improved reptile search algorithm effectively improves the solving precision. On IEEE congress on evolutionary computation 2014, 2017, 2019 and four engineering design problems, the feedback mechanism-driven improved reptile search algorithm is compared with other representative methods, and the result indicates that the solution performance of the feedback mechanism-driven improved reptile search algorithm is competitive. At last, taking the minimum energy as the evaluation index, the shape optimization model of SGC-Ball interpolation developable surface is established. The developable surface with the minimum energy is achieved with the help of the feedback mechanism-driven improved reptile search algorithm, and the comparison experiment verifies the superiority of the feedback mechanism-driven improved reptile search algorithm for the shape optimization problem.

曲率线是曲面上特殊且重要的曲线。曲率线插值构造可展开曲面在工程应用中具有重要意义。本文利用改进的爬虫搜索算法，研究曲率线上插值的广义立方球可展曲面的形状优化问题。首先，基于形状可调的广义三次球曲线的曲率线，给出了在曲线上插值的SGC-Ball可展开曲面的构造方法。其次，在爬虫搜索算法中引入反馈机制、自适应参数和变异策略，反馈机制驱动的改进爬虫搜索算法有效提高了求解精度。在2014、2017、2019年IEEE进化计算大会上以及四个工程设计问题上，将反馈机制驱动的改进爬虫搜索算法与其他代表性方法进行了比较，结果表明反馈机制驱动的改进爬虫搜索的求解性能算法具有竞争力。最后，以最小能量为评价指标，建立了SGC-Ball插值可展曲面形状优化模型。借助反馈机制驱动的改进爬虫搜索算法实现了能量最小的可展曲面，并通过对比实验验证了反馈机制驱动的改进爬虫搜索算法对于形状优化问题的优越性。