Optimal packing of convex polygons defined by their vertices

In optimal packing problems, there is a set of small elements (load) to be arranged in one or more large objects (containers), fulfilling the non-overlapping conditions between the small elements and the containment conditions (the load does not exceed the dimensions of the container), in addition, there is an objective to optimize.

The main objective of this investigation is to find acceptable solutions in a reasonable time to the instances of the problem.
of packing convex polygons in convex containers (circular and circular sections) of variable dimensions, using an exact mathematical nonlinear programming model, defining polygons or items/loads by their vertices using a Lagrangian approach and convexity conditions. In addition to determining the effect on the packaging, having as control parameters the number of elements to be packaged, the type of element, and the type of container.