The shape design and optimization of complex disk curves is a crucial and intractable technique in computer-aided design and manufacturing (CAD/CAM). Based on disk Wang-Ball (DWB) curves, this paper defines a novel combined disk Wang-Ball (CDWB) curve with constrained parameters and investigates the shape optimization of CDWB curves by using the multi-strategy ameliorated chameleon swarm algorithm (MCSA). Firstly, in order to meet the various shape design requirements, the CDWB curves consisting of DWB curves are defined, and the G and G geometric continuity conditions for the curves are derived. Secondly, the shape optimization of CDWB curves is considered as a minimization problem with curve energy as the objective, and an optimization model is developed under the constraints of the splicing conditions. Finally, the meta-heuristic algorithm MCSA is introduced to solve the established optimization model to obtain the minimum energy value, and its performance is verified by comparison with other algorithms. The results of representative numerical examples confirm the effectiveness and competitiveness of the MCSA for the CDWB curve shape optimization problems.
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