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 m×n 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.

Efficient Free-Form Contour Packing Based on Code Matching Strategy

“…x After the parameters are calculated, the two contours are connected based on the coordinate transformation matrix using Eqs. (11) and (11). Where (x , y ) are new coordinates of the contour, (x, y) indicates the original coordinate of the contour.…”

“…An optimal position of the contours is then selected from these positions based on the principle of the lowest center of contour or the lowest height of packing. Examples of these methods include algorithms of no-fit polygons (NFP) [11] and discrete nesting and description of image pixels [12]. As the layout result of this method is affected by the rotating angle, the reduced angle is only considered to improve the material utilization, which results in the low efficiency of nesting.…”

Hyper-Heuristic Approach for Improving Marker Efficiency

“…Shape of polygons is often approximated in order to lower the execution time and computational complexity. If irregular polygons are used, they are often approximated with the bounding box [27] or a convex hull [28] to create simplified polygons with smaller number of vertices to lower the computational complexity. The disadvantage of this approach is the large amount of waste that occurs between the edges of the described rectangle and the approximated polygon.…”

Optimum placement of the cutting patterns on the leather with image processing and optimization

“…Bunların başında Tavlama Benzetimi [1][2][3][4] yöntemi gelmektedir. Tavlama Benzetimi yöntemini Genetik Algoritma [1][2]7], Tabu Arama [2], Guguk Kuşu Arama [5] ve Karınca Kolonisi Arama [8] yöntemleri takip etmektedir. Ayrıca optimizasyon yöntemleri ile hesaplama yaparken arama uzayını daraltmak ve en uygun yerleşimi bulmak için sıklıkla kullanılan bazı yöntemler bulunmaktadır.…”

“…Ayrıca optimizasyon yöntemleri ile hesaplama yaparken arama uzayını daraltmak ve en uygun yerleşimi bulmak için sıklıkla kullanılan bazı yöntemler bulunmaktadır. Bunlar Convex Hull [4,[6][7] ve No-Fit Polygon [9][10][11] yöntemleridir.…”