A new mixed-integer programming model for irregular strip packing based on vertical slices with a reproducible survey

The irregular strip-packing problem, also known as nesting or marker making, is defined as the automatic computation of a non-overlapping placement of a set of non-convex polygons onto a rectangular strip of fixed width and unbounded length, such that the strip length is minimized. Nesting methods based on heuristics are a mature technology, and currently, the only practical solution to this problem. However, recent performance gains of the Mixed-Integer Programming (MIP) solvers, together with the known limitations of the heuristics methods, have encouraged the exploration of exact optimization models for nesting during the last decade. Despite the research effort, the current family of exact MIP models for nesting cannot efficiently solve both large problem instances and instances containing polygons with complex geometries. In order to improve the efficiency of the current MIP models, this work introduces a new family of continuous MIP models based on a novel formulation of the NoFit-Polygon Covering Model (NFP-CM), called NFP-CM based on Vertical Slices (NFP-CM-VS). Our new family of MIP models is based on a new convex decomposition of the feasible space of relative placements between pieces into vertical slices, together with a new family of valid inequalities, symmetry breakings, and variable eliminations derived from the former convex decomposition. Our experiments show that our new NFP-CM-VS models outperform the current state-of-the-art MIP models. Finally, we provide a detailed reproducibility protocol and dataset based on our Java software library as supplementary material to allow the exact replication of our models, experiments, and results

Allocation of Two Dimensional Parts Using a Shape Reasoning Heuristic.

A technique is outlined for the allocation of irregular parts onto arbitrarily shaped resources. Placements are generated by matching complementary shapes between the unplaced parts and the remaining areas of the stock material. The part and resource profiles are characterized to varying levels of detail using geometric features . Information contained in the features is used at each stage of processing to intelligently select and place parts on the resource. Techniques for the efficient handling of complex profiles and other practical implementation issues are described. The utility of the proposed approach is verified using diverse problems from a marine fabrication facility. The formulation and performance of the method is contrasted to previously published works

Curve-Based Shape Matching Methods and Applications

One of the main cues we use in our everyday life when interacting with the environment is shape. For example, we use shape information to recognise a chair, grasp a cup, perceive traffic signs and solve jigsaw puzzles. We also use shape when dealing with more sophisticated tasks, such as the medical diagnosis of radiographs or the restoration of archaeological artifacts. While the perception of shape and its use is a natural ability of human beings, endowing machines with such skills is not straightforward. However, the exploitation of shape cues is important for the development of competent computer methods that will automatically perform tasks such as those just mentioned. With this aim, the present work proposes computer methods which use shape to tackle two important tasks, namely packing and object recognition. The packing problem arises in a variety of applications in industry, where the placement of a set of two-dimensional shapes on a surface such that no shapes overlap and the uncovered surface area is minimised is important. Given that this problem is NP-complete, we propose a heuristic method which searches for a solution of good quality, though not necessarily the optimal one, within a reasonable computation time. The proposed method adopts a pictorial representation and employs a greedy algorithm which uses a shape matching module in order to dynamically select the order and the pose of the parts to be placed based on the “gaps” appearing in the layout during the execution. This thesis further investigates shape matching in the context of object recognition and first considers the case where the target object and the input scene are represented by their silhouettes. Two distinct methods are proposed; the first method follows a local string matching approach, while the second one adopts a global optimisation approach using dynamic programming. Their use of silhouettes, however, rules out the consideration of any internal contours that might appear in the input scene, and in order to address this limitation, we later propose a graph-based scheme that performs shape matching incorporating information from both internal and external contours. Finally, we lift the assumption made that input data are available in the form of closed curves, and present a method which can robustly perform object recognition using curve fragments (edges) as input evidence. Experiments conducted with synthetic and real images, involving rigid and deformable objects, show the robustness of the proposed methods with respect to geometrical transformations, heavy clutter and substantial occlusion

Crowdsourcing solutions to 2D irregular strip packing problems from Internet workers

Many industrial processes require the nesting of 2D profiles prior to the cutting, or stamping, of components from raw sheet material. Despite decades of sustained academic effort algorithmic solutions are still sub-optimal and produce results that can frequently be improved by manual inspection. However the Internet offers the prospect of novel ‘human-in-the-loop’ approaches to nesting problems, that uses online workers to produce packing efficiencies beyond the reach of current CAM packages. To investigate the feasibility of such an approach this paper reports on the speed and efficiency of online workers engaged in the interactive nesting of six standard benchmark datasets. To ensure the results accurately characterise the diverse educational and social backgrounds of the many different labour forces available online, the study has been conducted with subjects based in both Indian IT service (i.e. Rural BPOs) centres and a network of homeworkers in northern Scotland. The results (i.e. time and packing efficiency) of the human workers are contrasted with both the baseline performance of a commercial CAM package and recent research results. The paper concludes that online workers could consistently achieve packing efficiencies roughly 4% higher than the commercial based-line established by the project. Beyond characterizing the abilities of online workers to nest components, the results also make a contribution to the development of algorithmic solutions by reporting new solutions to the benchmark problems and demonstrating methods for assessing the packing strategy employed by the best workers