Two-Phase Approach to the Nesting problem with continuous rotations

Rocha, Pedro; Rodrigues, Rui; Gomes, António Alberto; Toledo, Franklina Maria Bragion de; Andretta, Marina

doi:10.1016/j.ifacol.2015.06.131

Cited by 7 publications

(7 citation statements)

References 8 publications

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“…These solutions can be used as an upper bound for the irregular strip packing problem with continuous rotations. Furthermore, many studies heuristically address the irregular strip packing problem considering continuous piece rotations to find good upper bounds [18,20].…”

Section: Boundsmentioning

confidence: 99%

“…Rocha et al [19] represented the pieces by sets of overlapping circles, aiming to achieve a certain degree of approximation while minimizing the necessary number of circles, allowing for any possible rotation. Rocha et al [20] proposed a two-phase approach to the nesting problem with continuous rotations based on a common compaction strategy which relies on the observable concept that the core structure of a layout is usually defined by the position and orientation of its largest pieces. Liao et al [18] proposed an algorithm to allocate irregular pieces in a rectangular sheet without overlapping based on the rubber band packing algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations

Cherri

Soler

2018

J Glob Optim

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The irregular strip packing problem consists of cutting a set of convex and nonconvex two-dimensional polygonal pieces from a board with a fixed height and infinite length. Owing to the importance of this problem, a large number of mathematical models and solution methods have been proposed. However, only few papers consider that the pieces can be rotated at any angle in order to reduce the board length used. Furthermore, the solution methods proposed in the literature are mostly heuristic. This paper proposes a novel mixed integer quadratically-constrained programming model for the irregular strip packing problem considering continuous rotations for the pieces. In the model, the pieces are allocated on the board using a reference point and its allocation is given by the translation and rotation of the pieces. To reduce the number of symmetric solutions for the model, sets of symmetry-breaking constraints are proposed. Computational experiments were performed on the model with and without symmetry-breaking constraints, showing that symmetry elimination improves the quality of solutions found by the solution methods. Tests were performed with instances from the literature. For two instances, it was possible to compare the solutions with a previous model from the literature and show that the proposed model is able to obtain numerically accurate solutions in competitive computational times.

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Section: Boundsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations

Cherri

Soler

2018

J Glob Optim

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“…The phi-function verifies overlap between items using mathematical equations defined over their dimensions. We can also highlight the studies carried out by Jones (2014) and Rocha et al (2015) in which overlapping is detected using circles placed inside the items.…”

Section: Computational Geometrymentioning

confidence: 99%

Mathematical models and heuristic methods for nesting problems

Mundim¹

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Irregular cutting and packing problems, with convex and non-convex polygons, are found in many industries such as metal mechanics, textiles, of shoe making, the furniture making and others. In this thesis we study the two-dimensional version of these problems, where we want to allocate a set of items, without overlap, inside one or more containers, limited or unlimited, so as to optimize an objective function. In this document we study the knapsack problem, placement problem, strip packing problem, cutting stock problem and bin packing problem. For these problems, the heuristic methods and mathematical programming models are proposed and presented very promising results, surpassing in many cases the best results in the specialized literature. This thesis is organized as follows. In Chapter 1, we present a review of the studied problems, the value proposition for this thesis with the main contributions and ideas. In Chapter 2, we propose a metaheursitic for the strip packing problem with irregular items and circles. Then, in Chapter 3, we present a generic heuristic for the allocation of irregular items that may be weakly or strongly heterogeneous and will be allocated in a container (output maximization problems) or multiple containers (input minimization problems). In Chapter 4, we propose a solution method for the cutting stock problem with deterministic demand and stochastic demand. In Chapters 5 and 6, we present mathematical programming models for the strip packing problem. Finally, in Chapter 7, we present a conclusion and a concise direction for future works.

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“…Quando os itens incluem bordas curvas, é comum aproximá-los por um polígono envolvente, em que uma série de tangentes à curva formam as bordas poligonais (veja um exemplo de um círculo aproximado por um polígono na Figura 4). Alguns trabalhos permitem que as bordas curvas sejam representadas em sua forma original e, para isto, os itens são representados como a união ou intersecção de objetos chamados primários, ou seja, círculos, retângulos, polígonos regulares, polígonos convexos e o complemento destas formas (STOYAN et al, 2001; Em outros trabalhos, a representação dos itens é feita pela inscrição ou cobertura de alguns círculos em cada item (JONES, 2013;ROCHA et al, 2015), veja um exemplo na Figura 7.…”

Section: Representação Dos Itensunclassified

“…• Uma ideia parecida à apresentada em (JONES, 2013) é usada em (ROCHA et al, 2015). Neste artigo, é apresentada uma abordagem para o ISPP que compacta os itens grandes em uma primeira fase, enquanto que em uma segunda fase, aloca os itens pequenos restantes entre os itens grandes, compactando todos os itens.…”

Section: Programação Não-linearunclassified

Resolução de problemas de empacotamento de itens irregulares usando técnicas de programação não-linear

Polo¹

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The irregular packing problems are cutting and packing problems, in which smaller irregular pieces (which we call items) should be packaged entirely in one large piece (which we call a plate), obeying non-overlapping constraints and minimizing the dimensions of the plate. To ensure non-overlapping, we make use of separation lines, that is, lines that separate one item from another. We present nonlinear programming models for problems of packing regular and irregular items that rotate freely. The items can be circles, convex and nonconvex polygons. The main advantage of the models is their simplicity, because they use only basic geometry concepts. We use the nonlinear programming algorithm IPOPT (an algorithm of interior points type), which is part of COIN-OR, to solve the problems. Computational tests were performed using known instances of the literature and the results were compared with results presented in the literature, obtained with other methodologies that also use free rotations, showing that our models are competitive. We also propose the use of separating parabola to avoid items overlaping in the models, which could provide greater computational eficiency as well as solutions with better quality.

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Two-Phase Approach to the Nesting problem with continuous rotations

Cited by 7 publications

References 8 publications

Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations

Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations

Mathematical models and heuristic methods for nesting problems

Resolução de problemas de empacotamento de itens irregulares usando técnicas de programação não-linear

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