## 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 P_{1}, P_{2}…., P_{k} 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 P_{1}, P_{2},..., P_{i+k} and a container C such that polygons P_{1}, P_{2},…, P_{i} are already placed into C, find translations for P_{i+l}, P_{i+2},…, P_{i+k} and a nonoverlapping translationa] motion of P_{1}, P_{2},…, P_{i} 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 language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer Verlag |

Pages | 91-107 |

Number of pages | 17 |

Volume | 1148 |

ISBN (Print) | 354061785X, 9783540617853 |

State | Published - 1996 |

Event | 1st 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 1996 → May 28 1996 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1148 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 1st ACM Workshop on Applied Computational Geometry, WACG 1996 held as part of 2nd Federated Computing Research Conference, FCRC 1996 |
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Country | United States |

City | Philadelphia |

Period | 5/27/96 → 5/28/96 |

## ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science