Largest Hexagon In A Circle What The Algorithm For 2 Dimensional Cutting Stock?

What the algorithm for 2 Dimensional Cutting Stock? - largest hexagon in a circle

I stand in front of a small IT project to identify the most effective, consisting of several different shapes (eg rectangle, triangle, hexagon, circle, etc.) on a large platter. Entrance is larger antenna (assuming that rectangular), the number of pieces cut, shape and size. The result is the configuration used for the provision of a large plate cutting for optimal space (eg, waste, and less Smales plate is used.)

What is the algorithm for this task?

thx all in advance.