Engineering oriented shape optimization of GHT-Bézier developable surfaces using a meta heuristic approach with CAD/CAM applications.

Optimization techniques are particularly useful when designing different free-form surfaces and manufacturing products in the engineering and CAD/CAM fields. Recently, many real-world problems utilize optimization techniques with objective functions to get their desired solution. In this paper, the shape optimization of GHT-Bézier developable surfaces by using a meta-heuristic technique called Improved-Grey Wolf Optimization (I-GWO, in short) technique is presented. This Grey Wolf optimization algorithm impersonates the hunting tactics of grey wolves in nature. Three optimization models arc length (AL), minimum energy (En), and curvature variation energy (CVEn) of dual and interpolation curves, are used to formulate this technique. The shape control parameters are considered as optimization variables. So, our aim is to find the optimal shape control parameters by applying the I-GWO algorithm to the optimization models through an iterative process. By using the duality principle between the points and planes, the construction of GHT-Bézier developable surfaces is formulated by the optimal choice of shape parameters obtained from I-GWO technique. Furthermore, the developability degree of GHT-Bézier developable surfaces is also determined. Some applications of the proposed method are given and the effectiveness of this method is illustrated.