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

MIP models for the irregular strip packing problem: new symmetry breaking constraints

The irregular strip packing problem consists in minimizing the length used to cut a set of pieces from a board with fixed width. Recently, a mixed integer programming model was proposed for the problem, but it may allow a large number of symmetric solutions. In this paper, new symmetry breaking constraints are proposed to improve the model. Computational experiments were performed for instances with convex pieces. The results show the proposed formulation is better than the previous one for most instances, since it improves lower bounds and reduces run-time and number of nodes explored to prove optimality

Making fish skin pattern-based garments: developing digital tools for the fashion industry based on Ainu fish skin robes and Japanese Kimono Patterns

Before the invention of synthetic fibres, people dressed in natural materials available in their environment such as skins and hides from local wildlife. The use of fish skin to create articles of clothing is an ancient tradition shared by Arctic societies along rivers and coasts, amongst them the Ainu Indigenous Peoples of Hokkaido Island (Japan). In this research we propose to use fish skin, a waste product of the food industry, as raw material for the fashion industry under the principles of zero waste. Throughout this project we recreated an Ainu fish skin robe, using digital tools and the material itself, as a means for gaining knowledge and experimenting with the use of fish skin for garment construction. The idea behind the project draws on the Ainu Indigenous Peoples’ subsistence resourcefulness and their heritage, with regards to traditional fish skin craft practices. The project thus connects between anthropology, ethnography, and craftsmanship with current interest in fashion sustainability, advanced digital technologies, and contemporary production processes in fashion. The Ainu garment is part of a study that hypothesises what would have happened if, during the Meji era, the Japanese, instead of making the Ainu shift from fishing to farming, had brought their own traditions, such as Katazome indigo dyeing, and blended them with the Ainu tradition of creating clothing from fish skin. The projects presented in this paper include a combination of different digital technologies and applications which were used to create a contemporary replica of an Ainu fish skin robe using a Japanese katazome indigo pattern. Firstly, we used the shape of an Ainu robe to create a fish skin module as a building block, and tested its relevancy for contemporary pattern making, and later introduced parametric design tools to test zero waste principals. We then used digital animation software to create an Ainu avatar and to recreate the fish skin garment situated in a virtual digital context. Finally following the digitally created garment, we have physically dyed in indigo the fish skins with Katazome stencils and lastly sewed a replica of the fish skin robe. The project aims to preserve traditional Ainu fish skin knowledge and introduce new advanced digital technology to enable the design and production of zero-waste fish skins for fashion

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

Making More Cars with Less Metal

Reducing sheet metal yield losses in automotive manufacturing would reduce material demand, providing environmental and financial benefits. This thesis explores material efficiency from four perspectives: 1. The opportunity for improvement: A part by part analysis of yield losses for every sheet metal component in a vehicle highlights nine material efficiency strategies. An industry study finds that on average only 56% of sheet metal purchased is used on the vehicle. Improving material utilisation to best practice of 70% would save £8 billion and 25 million tonnes of CO2 annually. 2. The potential to realise this opportunity: A design process to improve material efficiency is trialled within an automotive manufacturer and identifies opportunities of 20%. However, only 3% improvement is realised since the material efficiency opportunity is locked in at the start of the design process, where resource is not currently allocated. Earlier consideration of material utilisation is required. 3. Material efficiency within the circular economy: All existing metrics for recycling in sheet metal forming processes are mapped onto a diagram. A case study demonstrates that existing recycling metrics, do not promote the reduction of yield losses. Considering recycling process efficiencies rather than recycled content would enable recycling rates to be measured without penalising material efficiency. 4. Design for material efficiency: There are currently no suitable tools to inform process selection and geometry decisions for material efficiency. To address this, a novel set of experiments is conducted. These experiments identify a trend between the maximum draw depth and three critical radii. This trend could form a geometry based formability guideline which would enable design for material efficiency. Approaching material utilisation from these perspectives gives greater certainty of the saving opportunity for sheet metal material efficiency and clarifies the priority of material efficiency compared to other strategies to meet global climate change goals.Sponsored by Jaguar Land Rove

Indigenous Arctic Fish Skin Heritage: Sustainability, Craft and Material Innovation

The use of fish skin(1) for the construction of garments and accessories is an ancient tradition shared by coastal Arctic societies as a subsistence lifestyle(2) depending on aquatic resources for food and clothing. Arctic Indigenous(3) Peoples(4) need formidable resourcefulness to thrive in inhospitable ecosystems; fish skins provide them physical and spiritual protection(5). During the last century, they resisted not only colonisation and repression by humans but also dramatic ecological changes in seafood security. Fish skin craft became a way to communicate traditional knowledge where practical benefits combined cultural resilience(6). As market goods have replaced traditional fish skin clothing, the need for the skills required to create these items have diminished. The decrease of local natural resources also threatens the craft. The focus of this research is primarily to propose a vision of sustainability as an anthropological study of the resourcefulness and resilience of the Arctic Indigenous Peoples, their lifestyles, and fish skin practices. Secondarily it identifies the historical, cultural, environmental, and socioeconomic importance of fish skin as an innovative sustainable material, explored through the study of materials, processes and artefact analysis. Thirdly, the application of fish skin materials and craft practices has been tested through participatory workshops to explore how this material and the skill transmissions can contribute to sustainability practices in fashion. The contribution to knowledge is firstly the mapping of fish skin craft participatory practices with Artic Indigenous communities as this is the first time that such a survey has been undertaken. The material study of fish skin and its contribution to fashion sustainability forms a secondary contribution. 1 Within this thesis, the terms fish skin and fish leather are used to indicate different processes of the same material. Fish skin. Skin indicates the superficial dermis of an animal. In the thesis fish skin is referred as the historical raw material tanned following traditional methods: mechanical, oiling, smoking, bark, brain, urine, fish eggs and corn flour tanning. Fish Leather is used to indicate that the fish skin has passed one or more stages of industrial vegetable or chrome tanning production and is ready to be used to produce leather goods. 2 Subsistence activities of hunting, herding, fishing and gathering continue to be of major significance to the Indigenous Peoples of the Arctic in providing food, social relationships and cultural identity. 3 Indigenous Peoples are descent from the populations which inhabited a geographical region at the time of colonisation and who retain some or all of their own social, economic, cultural and political institutions. In this thesis, I use the terms ‘Indigenous’ and ‘Native’ interchangeably. In some countries, one of these terms may be favoured over the other. 4 The specific Arctic Indigenous groups with historical evidence of fish leather production are the Inuit, Yup’ik and Athabascan of Alaska and Canada; the various Siberian peoples, such as the Nivkh and Nanai; the Ainu from the Hokkaido Island in Japan and Sakhalin Island, Russia; the Hezhe from northeast China and the Saami of northern Scandinavia. 5 Arctic Indigenous Peoples believed that humans, animals and nature shared spiritual qualities. Arctic seamstresses decorated hunters’ fish skin clothing with motifs imbued with spirits, which gave protection from danger. 6 Arctic Indigenous Peoples have become a symbol of cultural resilience, actively adapting to colonisation, place dislocation due to land dispossession and resettlement, challenging the persistence of Indigenous knowledge systems