A GRASP Approach to the Nesting Problem

The nesting problem is a two-dimensional cutting and packing problem where the small pieces to cut have irregular shapes. The variant of the problem that we are going to deal with, which naturally arises in several industrial production processes (textile, garment, metalware, etc), considers only one big rectangular piece, the plate, with fixed width and infinite length. The objective will be the minimisation of the length of the plate that is used to produce a given set of small pieces. The nesting problem is also characterised by the intrinsic difficulty of dealing with geometry, once pieces are usually represented by non-convex polygons. The satisfaction of the no overlapping and containment constraints involve complex computations.