A customized branch-and-bound approach for irregular shape nesting

Wang, Akang; Hanselman, Christopher L.; Gounaris, Chrysanthos E.

doi:10.1007/s10898-018-0637-y

Cited by 14 publications

(6 citation statements)

References 21 publications

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“…Burke et al (Burke et al, 2007) proposed an improved moving collision method for solving all placement positions between two polygons. Stoyan (Stoyan et al, 2016) and Akang Wang (Wang et al, 2018) improved the circular fill algorithm. They relaxed problems using quadratic programming for optimality.…”

Section: Collision Algorithmsmentioning

confidence: 99%

Two-dimensional irregular packing problems: A review

Guo

et al. 2022

Front. Mech. Eng.

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Two-dimensional (2D) irregular packing problems are widespread in manufacturing industries such as shipbuilding, metalworking, automotive production, aerospace, clothing and furniture manufacturing. Research on 2D irregular packing problems is essential for improving material utilization and industrial automation. Much research has been conducted on this problem with significant research results and certain algorithms. The work has made important contributions to solving practical problems. This paper reviews recent advances in the domain of 2D irregular packing problems based on a variety of research papers. We first introduce the basic concept and research background of 2D irregular packing problems and then summarize algorithms and strategies that have been proposed for the problems in recent years. Conclusion summarize development trends and research hotspots of typical 2D irregular shape packing problems. We hope that this review could provide guidance for researchers in the field of 2D irregular packing.

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Section: Collision Algorithmsmentioning

confidence: 99%

Two-dimensional irregular packing problems: A review

Guo

et al. 2022

Front. Mech. Eng.

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“…Second, the family of Constraint Programming (CP) models based on the NFP, whose pioneering work is introduced by Ribeiro et al [69], and subsequently improved by Carravilla et al [17], Ribeiro and Carravilla [68], and Cherri et al [21]. And third, Other models based on alternatives geometric representations and Non-Linear Programming (NLP) models, such as (3.a) the family of models based on Φ-functions, whose pioneering works are introduced by Stoyan et al [88], Chernov et al [19], and Stoyan et al [89]; (3.b) others non-linear models based on direct trigonometry introduced by Rocha et al [71], Cherri et al [24], and Peralta et al [64]; and finally, (3.c) the family of models based on circle coverings admitting free rotations, whose pioneering work is introduced by Jones [48] and subsequently refined by Rocha et al [72], Rocha et al [71], and Wang et al [92].…”

Section: Categorization Of Exact Mathematical Modelsmentioning

confidence: 99%

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

Lastra-Díaz¹,

Ortuño²

2022

Preprint

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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.

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“…Thus the algorithm efficiency is lower. Wang et al [17] proposed a customized branch-and-bound approach to address the nesting problem to guaranteed optimality of the layout, but the algorithm is very complex and difficult to apply in factories. In summary, the above algorithms have limitations in solving nesting problems because of defects of TSA and ignoring contour features.…”

Section: Related Researchmentioning

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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A customized branch-and-bound approach for irregular shape nesting

Cited by 14 publications

References 21 publications

Two-dimensional irregular packing problems: A review

Two-dimensional irregular packing problems: A review

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

Efficient Free-Form Contour Packing Based on Code Matching Strategy

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