Optimized Packing Soft Convex Polygons

Packing soft convex polygons in an optimized convex container is considered. It is assumed that the soft polygonal object can change its shape in certain limits, while its area remains constant. Non-overlapping, containment, and area conservation constraints are formulated for soft polygonal objects, and a corresponding nonlinear programming model is presented. Numerical experiments for packing soft triangles and pentagons in optimized circular and quadratic containers are presented to demonstrate efficiency of the proposed approach.