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Column-based strip packing using ordered and compliant containment

  • Karen Daniels
  • Victor J. Milenkovic
Submitted Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1148)

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, ..., Pk 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 P1, P2, ..., Pl+k and a container C such that polygons P1, P2, ..., Pl are already placed into C, find translations for Pl+1, Pl+2, ..., Pl+k and a nonoverlapping translational motion of P1, P2, ..., Pl 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.

Keywords

Human Expert Cloth Utilization Fixed Width Strip Packing Strip Packing Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Karen Daniels
    • 1
    • 2
  • Victor J. Milenkovic
    • 2
  1. 1.Division of Applied SciencesHarvard UniversityUSA
  2. 2.Department of Math and Computer ScienceUniversity of MiamiUSA

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