Algorithms for 2D nesting problem based on the no-fit polygon

Abstract

Strip-packing problem is apparent in textile industry where a set of items, i.e. cutting parts (2D convex or non-convex polygons) need to be placed on a rectangular container (fabric with an mxn area) so that cutting parts do not overlap and do not exceed the boundaries of the container. The goal is to find a placement that utilizes the area of a container. In this paper three methods (random search, greedy algorithm and genetic algorithm) are tested on sets of regular (convex polygons) and irregular (cutting parts) items. The goal is to find the optimal items placement that minimizes the cover area. In this paper a no-fit polygon (NFP) is used to assure two items touch without overlapping. NFP is constructed by rotating polygon B around a static polygon A in a way their edges always touch and never overlap. The result is a polygonal area enclosed by trajectory of rotating polygon's reference point which represents the overlapping area of A and B. Items touch if polygon B is placed on the NFP's border. Non-convex cutting parts are approximated with their convex hull since a NFP version for convex polygons is used in this paper.