Column-based strip packing using ordered and compliant containment

Karen Daniels, Victor Milenkovic

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

The oriented strip packingproblem 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 practica] 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,..., Pi+k and a container C such that polygons P1, P2,…, Pi are already placed into C, find translations for Pi+l, Pi+2,…, Pi+k and a nonoverlapping translationa] motion of P1, P2,…, Pi 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.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages91-107
Number of pages17
Volume1148
ISBN (Print)354061785X, 9783540617853
StatePublished - 1996
Event1st ACM Workshop on Applied Computational Geometry, WACG 1996 held as part of 2nd Federated Computing Research Conference, FCRC 1996 - Philadelphia, United States
Duration: May 27 1996May 28 1996

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1148
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other1st ACM Workshop on Applied Computational Geometry, WACG 1996 held as part of 2nd Federated Computing Research Conference, FCRC 1996
CountryUnited States
CityPhiladelphia
Period5/27/965/28/96

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

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  • Cite this

    Daniels, K., & Milenkovic, V. (1996). Column-based strip packing using ordered and compliant containment. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1148, pp. 91-107). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1148). Springer Verlag.