Shape optimization of GHT-Bézier developable surfaces using particle swarm optimization algorithm

In the manufacturing process of free-form complex surfaces, various problems occur which degraded the performance and can be resolved by using an optimization technique. Thousands of real-world problems can be converted into optimization techniques with distinct objective functions to acquire the optimal solution. In this paper, an assembly of GHT-Bézier developable surfaces by using a nature-inspired particle swarm optimization technique combined with optimal parameters are constructed from two GHT-Bézier boundary curves to improve the efficiency of complex engineering products. For this purpose, the control points of GHT-Bézier surface are chosen as design variables. The objective function is defined as the developability degree of the ruled surface and the shape parameters are considered to be optimization variables. So, we search for the optimum shape control parameters within the value range of shape parameters by using the PSO technique, then the developable surfaces with highly accurate developability can be visualized. The modeling examples demonstrate the effectiveness of the proposed method with the fairness of the surfaces and its approximation to the original surface.