Abstract: Curvature lines are special and important curves on surfaces. It is of great signifcance 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 efectively 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 verifes the superiority of the feedback mechanism-driven improved reptile search algorithm for the shape optimization problem.

Key words: Reptile search algorithm , · Feedback mechanism , · Adaptive parameter , · Mutation strategy , · SGC-Ball interpolation developable surface , · Shape optimization