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Column-based strip packing using ordered and compliant containment

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Applied Computational Geometry Towards Geometric Engineering (WACG 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1148))

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Abstract

The oriented strip packing problem is very important to manufacturing industries: given a strip of fixed width and a set of many (> 100) nonconvex polygons with 1, 2, 4, or 8 orientations permitted for each polygon, find a set of translations and orientations for the polygons that places them without overlapping into the strip of minimum length. Heuristics are given for two versions of strip packing: 1) translation-only and 2) oriented. The first heuristic uses an algorithm we have previously developed for translational containment: given polygons P1, P2, ..., P k and a fixed container C, find translations for the polygons that place them into C without overlapping. The containment algorithm is practical for k ≤10. Two new containment algorithms are presented for use in the second packing heuristic. The first, an ordered containment algorithm, solves containment in time which is only linear in k when the polygons are a) “long” with respect to one dimension of the container and b) ordered with respect to the other dimension. The second algorithm solves compliant containment: given polygons P 1, P 2, ..., P l+k and a container C such that polygons P1, P2, ..., P l are already placed into C, find translations for Pl+1, Pl+2, ..., P l+k and a nonoverlapping translational motion of P1, P2, ..., P l that allows all l+k polygons to fit into the container without overlapping.

The performance of the heuristics is compared to the performance of commercial software and/or human experts. The results demonstrate that fast containment algorithms for modest values of k (k ≤10) are very useful in the development of heuristics for oriented strip packing of many (k ≫ 10) polygons.

This research was funded by the Textile/Clothing Technology Corporation from funds awarded by the Alfred P. Sloan Foundation and by NSF grants CCR-91-157993 and CCR-90-09272.

This research was funded by the Textile/Clothing Technology Corporation from funds awarded to them by the Alfred P. Sloan Foundation, by NSF grant CCR-91-157993, and by a subcontract of a National Textile Center grant to Auburn University, Department of Consumer Affairs.

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Authors and Affiliations

  1. Division of Applied Sciences, Harvard University, USA

    Karen Daniels

  2. Department of Math and Computer Science, University of Miami, USA

    Karen Daniels & Victor J. Milenkovic

Authors
  1. Karen Daniels
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  2. Victor J. Milenkovic
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Editor information

Ming C. Lin Dinesh Manocha

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© 1996 Springer-Verlag Berlin Heidelberg

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Daniels, K., Milenkovic, V.J. (1996). Column-based strip packing using ordered and compliant containment. In: Lin, M.C., Manocha, D. (eds) Applied Computational Geometry Towards Geometric Engineering. WACG 1996. Lecture Notes in Computer Science, vol 1148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014488

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  • DOI: https://doi.org/10.1007/BFb0014488

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61785-3

  • Online ISBN: 978-3-540-70680-9

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