Multi-objective shape optimization of developable Bézier-like surfaces using non-dominated sorting genetic algorithm

Abstract

The shape optimization design of the developable surface is an important research topic in CAD/CAM, and it is widely used in engineering manufacturing. In this paper, NSGA-II (the elitist non-dominated sorting genetic algorithm) is used to study the multi-objective shape optimization problem of generalized cubic developable Bézier-like surfaces (GCDBLS, for short) to promote the application of GCDBLS in industrial software and engineering design. Firstly, the shape optimization of developable surfaces is transformed into the shape optimization of dyadic curves based on the point-to-plane duality theory. Secondly, a multi-objective shape parameter optimization model is developed based on three surface optimality criteria (the shortest arc length, the smallest energy, and the smallest curvature change rate of the dual curve). Finally, the results of shape parameter optimization of GCDBLS obtained by NSGA-II are compared with MSSA and MOGOA to verify the feasibility and superiority of NSGA-II in solving multi-objective shape optimization problems for developable surfaces and the flexibility of GCDBLS in the construction of developable surfaces.