Shape optimization of generalized developable H-Bezier surfaces using adaptive cuckoo search algorithm

The shape optimization design of developable surface is a critical and intractable technique in CAD/CAM and used in many manufacturing planning operations. In this paper, we study shape optimization by using a new cuckoo search (CS) algorithm to promote the development of generalized developable H-Bezier surfaces (or GDHBS, for short). According to the duality between points and planes in 3D projective space, the GDHBS shape optimization problem is formulated as an arc length, energy and curvature variation minimization problem of dual curve, respectively. Then, an adaptive CS optimization algorithm is applied to the solutions of those GDHBS shape optimization models. Finally, we illustrate the effectiveness and performance of the proposed methods by some representative and convictive examples.