A pairwise exact placement algorithm for the irregular nesting problem

Sato, Ayami; Martins, Thiago de Castro; Tsuzuki, Marcos de Sales Guerra

doi:10.1080/0951192x.2015.1033018

Cited by 18 publications

(10 citation statements)

References 17 publications

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“…They utilized a pairwise placement strategy to allocate items in exact placements. Simulated annealing algorithm was used to control placement sequence and search solution space [18].…”

Section: Literature Reviewmentioning

confidence: 99%

“…fill the stock sheet with items until the stock sheet is over 1/3 full (1. 4) record every item that does not fit (1.5) call Algorithm 2 (1.6) if the free area up to after a item could be placed then (1.7) reset = 0 and go to step (1.5) ( 1.8) call Algorithm 3 (1.9) if the free area up to after a combination of 2 items could be placed then (1.10) reset = 0 and go to step (1. for each ∈ \ do (11) if free area of stock sheet − area of the item and > percentage then (12) break (13) if item or the combination of item and do not fit OR area of item and > free area of stock sheet then (14) continue (15) if the item could be placed then (17) return (18) else remove the first item AND record the combination of the 2 items that does not fit if item does not fit OR area of item + 2 smallest items' area > free area of stock sheet then (4.5) continue (4.6) if this item could not be placed then (4. 7) record the item that could not be placed (4.8) else {select a second item ∈ \ } (4.9)…”

Section: The Proposed Selection Heuristic For Irregular 2dcspmentioning

confidence: 99%

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An Efficient Heuristic Approach for Irregular Cutting Stock Problem in Ship Building Industry

2016

Mathematical Problems in Engineering

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This paper presents an efficient approach for solving a real two-dimensional irregular cutting stock problem in ship building industry. Cutting stock problem is a common cutting and packing problem that arises in a variety of industrial applications. A modification of selection heuristic Exact Fit is applied in our research. In the case referring to irregular shapes, a placement heuristics is more important to construct a complete solution. A placement heuristic relating to bottom-left-fill is presented. We evaluate the proposed approach using generated instance only with convex shapes in literatures and some instances with nonconvex shapes based on real problem from ship building industry. The results demonstrate that the effectiveness and efficiency of the proposed approach are significantly better than some conventional heuristics.

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“…They utilized a pairwise placement strategy to allocate items in exact placements. Simulated annealing algorithm was used to control placement sequence and search solution space [18].…”

Section: Literature Reviewmentioning

confidence: 99%

Section: The Proposed Selection Heuristic For Irregular 2dcspmentioning

confidence: 99%

An Efficient Heuristic Approach for Irregular Cutting Stock Problem in Ship Building Industry

2016

Mathematical Problems in Engineering

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“…The layout positioning strategy determines the packing contour position and final outcomes of material requirement planning [8]. Irregular contour positioning strategies can be divided into transformation method and trial solution algorithm (TSA).…”

Section: Introductionmentioning

confidence: 99%

Efficient Free-Form Contour Packing Based on Code Matching Strategy

Guo

et al. 2019

IEEE Access

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Freeform surfaces exist widely in the stock cutting process of clinical prosthesis preparation, aviation, ship, and other manufacturing industries. The free-form contours of surfaces need to be packed before they are machined from raw materials. The existing methods search a contour position by rotating the contour and translating it to connect other contours for packing. The relative position between two contours will be changed after the rotation as the contour description is lack of geometric invariance. These methods easily miss the best layout position resulting in interspaces in the raw material. Moreover, this result seriously reduces the performance and efficiency of an automatic packing system. Therefore, a new packing algorithm is proposed in this paper by combining the geometric invariant description and coding matching for contours to solve the contour rotating and position connecting problems. The optimal position of a contour can be found directly and then connected by the extracted similar complement features of the contour. The experimental results show that the proposed method can greatly improve quality and efficiency of the layout, especially in the material utilization. INDEX TERMS Computer graphics, code matching, shape, free-form contour packing, freeman chain code, geometric invariant description, layout.

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“…Results for the 2D one-open dimension problem were divided into three groups: (i) comparison with approaches considering the same domain for the grid (set with 16 instances), in which the BRKGA was able to find an optimal solution for 8 instances and improve the results of two instances; (ii) comparison involving the hard and benchmark set of 15 ESICUP instances for which the BRKGA outperformed the approaches from Burke et al (2006), Pinheiro, Júnior and Saraiva (2015) and Sato, Martins and Tsuzuki (2015), while compared to Elkeran (2013) and Bennell and Song (2010) the BRKGA reached a difference concerning the solutions of 3.13% for Elkeran (2013) and 2.81% for Bennell and Song (2010), which are small values; and, (iii) new results for 12 instances with circles for which the literature could not resolve adequately. In the case of the 2D two-open dimension problem, we propose the first heuristic of the literature capable of solving medium and large-sized instances.…”

Section: Discussionmentioning

confidence: 99%

“…Furthermore, Bennell et al (2015) proposed a non-linear model that uses the phi-function concept to cluster pairs of irregular shaped items in the smallest circle, triangle or convex hull. Sato, Martins and Tsuzuki (2015) also proposed a pairwise placement heuristic, but considered the one-open dimension problem.…”

Section: Introductionmentioning

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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A pairwise exact placement algorithm for the irregular nesting problem

Cited by 18 publications

References 17 publications

An Efficient Heuristic Approach for Irregular Cutting Stock Problem in Ship Building Industry

An Efficient Heuristic Approach for Irregular Cutting Stock Problem in Ship Building Industry

Efficient Free-Form Contour Packing Based on Code Matching Strategy

Mathematical models and heuristic methods for nesting problems

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