Effective arrangement of two dimensional geometrical shapes (referred as 2D nesting), before to cut them out of a large sheet material, is a very important task in many industries such as sheet metal, cloth, leather, shipbuilding, aerospace, granite and paper; as it aims to the optimal utilization of the sheet material, targeting the substantial savings on the material cost. Since the requirement of two dimensional shapes to be cut may vary from the simple rectangular shapes to highly irregular shapes with a wide range of batch quantity, 2D nesting problem is mainly considered as the...