Solving Irregular Strip Packing Problems With Free Rotations Using Separation Lines

Solving nesting problems or irregular strip packing problems is to position polygons in a fixed width and unlimited length strip, obeying polygon integrity containment constraints and non-overlapping constraints, in order to minimize the used length of the strip. To ensure non-overlapping, we used separation lines. A straight line is a separation line if given two polygons, all vertices of one of the polygons are on one side of the line or on the line, and all vertices of the other polygon are on the other side of the line or on the line. Since we are considering free rotations of the polygons and separation lines, the mathematical model of the studied problem is nonlinear. Therefore, we use the nonlinear programming solver IPOPT (an algorithm of interior points type), which is part of COIN-OR. Computational tests were run using established benchmark instances and the results were compared with the ones obtained with other methodologies in the literature that use free rotation

Meta-heuristic Algorithms for Nesting Problem of Rectangular Pieces

Nesting problems consist of placing multiple items onto larger shapes finding a good arrangement. The goal of the nesting process is to minimize the waste of material. It is common to assume, as in the present work, that the stock sheet has fixed width and infinite height, since in the real world a company may have to cut pieces from a roll of material. The complexity of such problems is often faced with a two-stage approach, so-called \u201chybrid algorithm\u201d, combining a placement routine and a meta-heuristic algorithm. Starting from a given positioning sequence, the placement routine generates a non-overlapping configuration. The encoded solution is manipulated and modified by the meta-heuristic algorithm to generate a new sequence that brings to a better value of the objective function (in this case the height of the strip). The proposed method consists in placing the rectangles inside a strip and in combining the meta-heuristic algorithms with the No Fit Polygon algorithm. The software has been developed in Python language using proper libraries to solve the meta-heuristic techniques (Inspyred) and the geometric problems (Polygon). The results show the effectiveness of the proposed method; moreover, with regard to problems reported in literature employed as benchmark of the nesting algorithms, the degree of occupation values (Efficiency Ratio, ER) are shown to be higher than 90%

A scanline-based algorithm for the 2D free-form bin packing problem

Abstract This paper describes a heuristic algorithm for the two-dimensional free-form bin packing (2D-FBP) problem, which is also called the irregular cutting and packing, or nesting problem. Given a set of 2D free-form bins, which in practice may be plate materials, and a set of 2D free-form items, which in practice may be plate parts to be cut out of the materials, the 2D-FBP problem is to lay out items inside one or more bins in such a way that the number of bins used is minimized, and for each bin, the yield is maximized. The proposed algorithm handles the problem as a variant of the one-dimensional bin-packing problem; i.e., items and bins are approximated as sets of scanlines, and scanlines are packed. The details of the algorithm are given, and its application to a nesting problem in a shipbuilding company is reported. The proposed algorithm consists of the basic and the group placement algorithms. The basic placement algorithm is a variant of the first-fit decreasing algorithm which is simply extended from the one-dimensional case to the two-dimensional case by a novel scanline approximation. The group placement algorithm is an extension of the basic placement algorithm with recombination of input items. A numerical study with real instances shows that the basic placement algorithm has sufficient performance for most of the instances, however, the group placement algorithm is required when items must be aligned in columns. The qualities of the resulting layouts are good enough for practical use, and the processing times required for both algorithms are much faster than those by manual nesting. 1

A novel hybrid intelligence approach for 2D packing through Internet crowdsourcing

Packing problems on its current state are being utilized for wide area of industrial applications. The aim of present research is to create and implement an intelligent system that tackles the problem of 2D packing of objects inside a 2D container, such that objects do not overlap and the container area is to be maximized. The packing problem becomes easier, when regular/rectangular objects and container are used. In most of the practical situations, the usage of irregular objects comes to existence. To solve the packing problem of irregular objects inside a rectangular container, a hybrid intelligence approach is introduced in our proposed work. The combination of machine intelligence and human intelligence is referred as the hybrid intelligence or semi-automated approach in the proposed methodology. The incorporation of human intelligence in the outcome of machine intelligence is possible to obtain using the internet crowdsourcing as we wish to handle the packing problem through internet crowdsourcing involving rural people. The proposed methodology is tested on different standard data sets and it is observed that it has clear advantage over both manual as well as fully automated heuristic based methods in terms of time and space efficiency

Simulated Annealing Approach for Solving Stock Cutting Problem

The simulated annealing approach is applied to stock cutting. The conceptual approach proposed uses an energy function that measures the area of the rectangular enclosure of all the patterns to be nested, the level of similarity between pattern pairs, and the amount of overlap among patterns in evaluating various pattern configurations to be generated by the simulated annealing algorithm. Three methods for pattern configuration generation are considered. The first method uses heuristics to generate the initial configuration. The second and third methods use random selection and random placement of pattern