Enhanced Salp Swarm Algorithm for Optimizing the Shape of Developable Bézier-Like Surfaces

The shape optimization of developable surfaces is a key and difficult technology in CAD/CAM. This paper studies the shape optimization of generalized developable Bézier-like surfaces using the improved salp swarm algorithm. First, aiming at the problems of slow convergence speed and low calculation accuracy, quickly falling into the optimal local solution for the salp swarm algorithm, and by adjusting the control parameters, the added Morlet wavelet mutation strategy to the individual position updates operation. An improved salp swarm algorithm is proposed, called FMSSA for short. Numerical results show that FMSSA performed the best among 18 (78%) comparisons with other improved SSAs in the CEC2005 test set. In addition, FMSSA serves the best among 16 (69%) comparisons with other algorithms. Therefore, the convergence speed and computational accuracy of FMSSA are improved, and the computational results are significantly better than other intelligent algorithms. Second, according to the duality principle of point and plane, the shape optimization problem of generalized developable Bézier-like surface is transformed into the minimization problem of arc length, energy, and curvature change rate of the dual curve, and three shape optimization models of the developable surface are established. Finally, shape optimization of expandable surfaces is mathematically an optimization problem that the swarm intelligence algorithm can efficiently handle, so FMSSA is used to solve these three optimization models. Numerical experiments show that FMSSA obtains optimal generalized developable Bézier-like surfaces in solving these three optimization models, demonstrating the superiority of the proposed FMSSA in effectively solving the shape optimization models in terms of precision and robustness.