An improved marine predators algorithm for shape optimization of developable Ball surfaces

The shape optimization of developable surfaces is a pivotal and knotty technique in CAD/CAM and used in many product manufacturing planning operations, e.g., for ships, aircraft wing, automobiles, garments, etc. In this paper, an improved marine predators algorithm (MPA) is used to optimize the shape of shape-adjustable generalized cubic developable Ball (SGCD-Ball, for short) surfaces. Firstly, to solve the problems of shape adjustment and optimization for developable surfaces, we present a class of novel shape-adjustable generalized cubic Ball basis functions, and then construct the SGCD-Ball surfaces with shape parameters by using the presented basis functions. The shapes of the surfaces can be adjusted and optimized expediently by using the shape parameters. Secondly, the shape optimization of developable surfaces is mathematically an optimization problem that can be effectively dealt with by swarm intelligence algorithm. In this regard, by incorporating a quasi-opposition strategy and a differential evolution algorithm to the MPA, an improved MPA called ODMPA is developed to increase the population diversity and enhance its capability of jumping out of the local minima. Furthermore, the superiority of the proposed ODMPA is verified by comparing with standard MPA, modified MPA and several well-known intelligent algorithms on 23 classical benchmark functions, the CEC’17 test suite and three engineering optimization problems, respectively. Finally, by minimizing the energy of the SGCD-Ball surfaces as the evaluation standard, the shape optimization models of the corresponding enveloping and spine curve developable surfaces are established. The ODMPA is utilized to solve the shape optimization models, and the SGCD-Ball surfaces with minimum energy are obtained. Some representative numerical examples demonstrate the superiority of the proposed ODMPA in effectively solving the shape optimization models in terms of precision and robustness.