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Raster penetration map applied to the irregular packing problem

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  • Sato, André Kubagawa
  • Martins, Thiago Castro
  • Gomes, Antonio Miguel
  • Tsuzuki, Marcos Sales Guerra

Abstract

Among the most complex problems in the field of 2-dimensional cutting & packing are irregular packing problems, in which items may have a more complex geometry. These problems are prominent in several areas, including, but not limited to, the textile, shipbuilding and leather industries. They consist in placing a set of items, whose geometry is often represented by simple polygons, into one or more containers such that there is no overlap between items and the utility rate of the container is maximized. In this work, the irregular strip packing problem, an irregular packing variant with a variable length container, is investigated. The placement space is reduced by adopting a rectangular grid and a full search is performed using preprocessed raster penetration maps to efficiently determine the new position of an item. Tests were performed using simple dotted board model cases and irregular strip packing benchmark instances. The comparison of our results with the state of the art solutions showed that the proposed algorithm is very competitive, achieving better or equal compaction in 9 out of 15 instances and improving the average density in 13 instances. Besides the contribution of the new best results, the proposed approach showed the advantage of adopting discrete placement, which can be potentially applied to other irregular packing problems.

Suggested Citation

  • Sato, André Kubagawa & Martins, Thiago Castro & Gomes, Antonio Miguel & Tsuzuki, Marcos Sales Guerra, 2019. "Raster penetration map applied to the irregular packing problem," European Journal of Operational Research, Elsevier, vol. 279(2), pages 657-671.
    • Handle: RePEc:eee:ejores:v:279:y:2019:i:2:p:657-671
    DOI: 10.1016/j.ejor.2019.06.008
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    2. Germán Pantoja-Benavides & David Álvarez-Martínez & Francisco Parreño Torres, 2024. "The Normalized Direct Trigonometry Model for the Two-Dimensional Irregular Strip Packing Problem," Mathematics, MDPI, vol. 12(15), pages 1-25, August.
    3. Umetani, Shunji & Murakami, Shohei, 2022. "Coordinate descent heuristics for the irregular strip packing problem of rasterized shapes," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1009-1026.
    4. Hu, Xiaoxuan & Zhu, Waiming & Ma, Huawei & An, Bo & Zhi, Yanling & Wu, Yi, 2021. "Orientational variable-length strip covering problem: A branch-and-price-based algorithm," European Journal of Operational Research, Elsevier, vol. 289(1), pages 254-269.
    5. Hatice ER, 2021. "Academic Aspect of the Leather Industry: An Interpretation from the Perspective of Business Science," Prizren Social Science Journal, SHIKS, vol. 5(1), pages 11-43, April.
    6. Lastra-Díaz, Juan J. & Ortuño, M. Teresa, 2024. "Mixed-integer programming models for irregular strip packing based on vertical slices and feasibility cuts," European Journal of Operational Research, Elsevier, vol. 313(1), pages 69-91.
    7. Cherri, Luiz Henrique & Carravilla, Maria Antónia & Ribeiro, Cristina & Toledo, Franklina Maria Bragion, 2019. "Optimality in nesting problems: New constraint programming models and a new global constraint for non-overlap," Operations Research Perspectives, Elsevier, vol. 6(C).

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