Combined cubic generalized ball surfaces: Construction and shape optimization using an enhanced JS']JS algorithm

The construction and shape optimization of complex shape-adjustable surfaces is a crucial and intractable technique in Computer Aided geometric Design (CAGD), which has a wide range of application value in many product designs and manufacturing fields involving complex surfaces modeling. In this paper, a novel combined cubic generalized Ball (CCG-Ball, for short) surfaces is constructed and the shape optimization of CCG-Ball surfaces is studied by an enhanced jellyfish search (JS) algorithm. First and foremost, we construct the CCG-Ball surfaces with multiple shape parameters based on a class of cubic generalized Ball basis functions, and then derive the conditions of G1 and G2 continuity for the surfaces. The shapes of CCG-Ball surfaces can be adjusted and optimized expediently by utilizing their shape parameters. Secondly, the shape optimization of CCG-Ball surfaces is mathematically an optimization problem that can be efficiently dealt with by swarm in-telligence algorithm. In this regard, an enhanced JS termed EJS algorithm, combined with sine and cosine learning factors, local escape operator, opposition-based learning and quasi-opposition learning strategies, is introduced to improve the convergence speed and calculation accuracy of the JS algorithm. Finally, by mini-mizing the energy of CCG-Ball surfaces as the evaluation standard, the shape optimization models of the surfaces with G1 and G2 geometric continuity are established, respectively. The EJS algorithm is utilized to solve the established models, and the CCG-Ball surfaces with minimum energy are obtained. The example results illustrate the ability of EJS algorithm in effectively solving the shape optimization problems of complex CCG-Ball surfaces.