Upper bounds for heuristic approaches to the strip packing problem
We consider the 2D and 3D strip packing problem (SPP): given a set of rectangular items and a strip, find the minimal height needed to pack all items. Rotation of the items is not permitted. We present an algorithm for the 2D SPP, which improves the packing of the well‐known FFDH heuristic and state...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Scheithauer, Guntram [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Rechteinformationen: |
Nutzungsrecht: 2014 The Authors. International Transactions in Operational Research © 2014 International Federation of Operational Research Societies Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main St, Malden, MA02148, USA. |
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| Schlagwörter: |
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| Systematik: |
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| Übergeordnetes Werk: |
Enthalten in: International transactions in operational research - Oxford : Wiley, 1994, 23(2016), 1-2, Seite 93-119 |
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| Übergeordnetes Werk: |
volume:23 ; year:2016 ; number:1-2 ; pages:93-119 |
| Links: |
|---|
| DOI / URN: |
10.1111/itor.12100 |
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| 520 | |a We consider the 2D and 3D strip packing problem (SPP): given a set of rectangular items and a strip, find the minimal height needed to pack all items. Rotation of the items is not permitted. We present an algorithm for the 2D SPP, which improves the packing of the well‐known FFDH heuristic and state theoretical results for this algorithm. Furthermore, we prove new upper bounds for the 3D SPP in special cases. Moreover, we present an implementation of the FFDH heuristic for the 3D case, which is used to construct a new algorithm, called COMB‐3D heuristic, with absolute performance ratio of at most 5. Based on the new algorithm, we also prove a general upper bound for the optimal height, which depends on the continuous lower bound and the maximum height lower bound, and we show that the combination of both lower bounds also has an absolute worst‐case performance ratio of at most 5. | ||
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10.1111/itor.12100 doi PQ20160212 (DE-627)OLC197130400X (DE-599)GBVOLC197130400X (PRQ)c2160-630dd35ecb4fc00280bc1e5c6b4e4b9639140d876148051e36eaf1f609bbe9830 (KEY)0238234220160000023000100093upperboundsforheuristicapproachestothestrippacking DE-627 ger DE-627 rakwb eng 510 DNB QA 10000 AVZ rvk 54.00 bkl Scheithauer, Guntram verfasserin aut Upper bounds for heuristic approaches to the strip packing problem 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We consider the 2D and 3D strip packing problem (SPP): given a set of rectangular items and a strip, find the minimal height needed to pack all items. Rotation of the items is not permitted. We present an algorithm for the 2D SPP, which improves the packing of the well‐known FFDH heuristic and state theoretical results for this algorithm. Furthermore, we prove new upper bounds for the 3D SPP in special cases. Moreover, we present an implementation of the FFDH heuristic for the 3D case, which is used to construct a new algorithm, called COMB‐3D heuristic, with absolute performance ratio of at most 5. Based on the new algorithm, we also prove a general upper bound for the optimal height, which depends on the continuous lower bound and the maximum height lower bound, and we show that the combination of both lower bounds also has an absolute worst‐case performance ratio of at most 5. Nutzungsrecht: 2014 The Authors. International Transactions in Operational Research © 2014 International Federation of Operational Research Societies Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main St, Malden, MA02148, USA. performance ratio strip packing problem cutting and packing Algorithms Heuristic Studies Operations research Packing problem Buchwald, Torsten oth Enthalten in International transactions in operational research Oxford : Wiley, 1994 23(2016), 1-2, Seite 93-119 (DE-627)182525775 (DE-600)1213721-2 (DE-576)045288984 0969-6016 nnns volume:23 year:2016 number:1-2 pages:93-119 http://dx.doi.org/10.1111/itor.12100 Volltext http://onlinelibrary.wiley.com/doi/10.1111/itor.12100/abstract http://search.proquest.com/docview/1729143725 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW GBV_ILN_26 GBV_ILN_4126 QA 10000 54.00 AVZ AR 23 2016 1-2 93-119 |
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10.1111/itor.12100 doi PQ20160212 (DE-627)OLC197130400X (DE-599)GBVOLC197130400X (PRQ)c2160-630dd35ecb4fc00280bc1e5c6b4e4b9639140d876148051e36eaf1f609bbe9830 (KEY)0238234220160000023000100093upperboundsforheuristicapproachestothestrippacking DE-627 ger DE-627 rakwb eng 510 DNB QA 10000 AVZ rvk 54.00 bkl Scheithauer, Guntram verfasserin aut Upper bounds for heuristic approaches to the strip packing problem 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We consider the 2D and 3D strip packing problem (SPP): given a set of rectangular items and a strip, find the minimal height needed to pack all items. Rotation of the items is not permitted. We present an algorithm for the 2D SPP, which improves the packing of the well‐known FFDH heuristic and state theoretical results for this algorithm. Furthermore, we prove new upper bounds for the 3D SPP in special cases. Moreover, we present an implementation of the FFDH heuristic for the 3D case, which is used to construct a new algorithm, called COMB‐3D heuristic, with absolute performance ratio of at most 5. Based on the new algorithm, we also prove a general upper bound for the optimal height, which depends on the continuous lower bound and the maximum height lower bound, and we show that the combination of both lower bounds also has an absolute worst‐case performance ratio of at most 5. Nutzungsrecht: 2014 The Authors. International Transactions in Operational Research © 2014 International Federation of Operational Research Societies Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main St, Malden, MA02148, USA. performance ratio strip packing problem cutting and packing Algorithms Heuristic Studies Operations research Packing problem Buchwald, Torsten oth Enthalten in International transactions in operational research Oxford : Wiley, 1994 23(2016), 1-2, Seite 93-119 (DE-627)182525775 (DE-600)1213721-2 (DE-576)045288984 0969-6016 nnns volume:23 year:2016 number:1-2 pages:93-119 http://dx.doi.org/10.1111/itor.12100 Volltext http://onlinelibrary.wiley.com/doi/10.1111/itor.12100/abstract http://search.proquest.com/docview/1729143725 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW GBV_ILN_26 GBV_ILN_4126 QA 10000 54.00 AVZ AR 23 2016 1-2 93-119 |
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10.1111/itor.12100 doi PQ20160212 (DE-627)OLC197130400X (DE-599)GBVOLC197130400X (PRQ)c2160-630dd35ecb4fc00280bc1e5c6b4e4b9639140d876148051e36eaf1f609bbe9830 (KEY)0238234220160000023000100093upperboundsforheuristicapproachestothestrippacking DE-627 ger DE-627 rakwb eng 510 DNB QA 10000 AVZ rvk 54.00 bkl Scheithauer, Guntram verfasserin aut Upper bounds for heuristic approaches to the strip packing problem 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We consider the 2D and 3D strip packing problem (SPP): given a set of rectangular items and a strip, find the minimal height needed to pack all items. Rotation of the items is not permitted. We present an algorithm for the 2D SPP, which improves the packing of the well‐known FFDH heuristic and state theoretical results for this algorithm. Furthermore, we prove new upper bounds for the 3D SPP in special cases. Moreover, we present an implementation of the FFDH heuristic for the 3D case, which is used to construct a new algorithm, called COMB‐3D heuristic, with absolute performance ratio of at most 5. Based on the new algorithm, we also prove a general upper bound for the optimal height, which depends on the continuous lower bound and the maximum height lower bound, and we show that the combination of both lower bounds also has an absolute worst‐case performance ratio of at most 5. Nutzungsrecht: 2014 The Authors. International Transactions in Operational Research © 2014 International Federation of Operational Research Societies Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main St, Malden, MA02148, USA. performance ratio strip packing problem cutting and packing Algorithms Heuristic Studies Operations research Packing problem Buchwald, Torsten oth Enthalten in International transactions in operational research Oxford : Wiley, 1994 23(2016), 1-2, Seite 93-119 (DE-627)182525775 (DE-600)1213721-2 (DE-576)045288984 0969-6016 nnns volume:23 year:2016 number:1-2 pages:93-119 http://dx.doi.org/10.1111/itor.12100 Volltext http://onlinelibrary.wiley.com/doi/10.1111/itor.12100/abstract http://search.proquest.com/docview/1729143725 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW GBV_ILN_26 GBV_ILN_4126 QA 10000 54.00 AVZ AR 23 2016 1-2 93-119 |
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10.1111/itor.12100 doi PQ20160212 (DE-627)OLC197130400X (DE-599)GBVOLC197130400X (PRQ)c2160-630dd35ecb4fc00280bc1e5c6b4e4b9639140d876148051e36eaf1f609bbe9830 (KEY)0238234220160000023000100093upperboundsforheuristicapproachestothestrippacking DE-627 ger DE-627 rakwb eng 510 DNB QA 10000 AVZ rvk 54.00 bkl Scheithauer, Guntram verfasserin aut Upper bounds for heuristic approaches to the strip packing problem 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We consider the 2D and 3D strip packing problem (SPP): given a set of rectangular items and a strip, find the minimal height needed to pack all items. Rotation of the items is not permitted. We present an algorithm for the 2D SPP, which improves the packing of the well‐known FFDH heuristic and state theoretical results for this algorithm. Furthermore, we prove new upper bounds for the 3D SPP in special cases. Moreover, we present an implementation of the FFDH heuristic for the 3D case, which is used to construct a new algorithm, called COMB‐3D heuristic, with absolute performance ratio of at most 5. Based on the new algorithm, we also prove a general upper bound for the optimal height, which depends on the continuous lower bound and the maximum height lower bound, and we show that the combination of both lower bounds also has an absolute worst‐case performance ratio of at most 5. Nutzungsrecht: 2014 The Authors. International Transactions in Operational Research © 2014 International Federation of Operational Research Societies Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main St, Malden, MA02148, USA. performance ratio strip packing problem cutting and packing Algorithms Heuristic Studies Operations research Packing problem Buchwald, Torsten oth Enthalten in International transactions in operational research Oxford : Wiley, 1994 23(2016), 1-2, Seite 93-119 (DE-627)182525775 (DE-600)1213721-2 (DE-576)045288984 0969-6016 nnns volume:23 year:2016 number:1-2 pages:93-119 http://dx.doi.org/10.1111/itor.12100 Volltext http://onlinelibrary.wiley.com/doi/10.1111/itor.12100/abstract http://search.proquest.com/docview/1729143725 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW GBV_ILN_26 GBV_ILN_4126 QA 10000 54.00 AVZ AR 23 2016 1-2 93-119 |
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510 DNB QA 10000 AVZ rvk 54.00 bkl Upper bounds for heuristic approaches to the strip packing problem performance ratio strip packing problem cutting and packing Algorithms Heuristic Studies Operations research Packing problem |
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Upper bounds for heuristic approaches to the strip packing problem |
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Upper bounds for heuristic approaches to the strip packing problem |
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Scheithauer, Guntram |
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upper bounds for heuristic approaches to the strip packing problem |
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Upper bounds for heuristic approaches to the strip packing problem |
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We consider the 2D and 3D strip packing problem (SPP): given a set of rectangular items and a strip, find the minimal height needed to pack all items. Rotation of the items is not permitted. We present an algorithm for the 2D SPP, which improves the packing of the well‐known FFDH heuristic and state theoretical results for this algorithm. Furthermore, we prove new upper bounds for the 3D SPP in special cases. Moreover, we present an implementation of the FFDH heuristic for the 3D case, which is used to construct a new algorithm, called COMB‐3D heuristic, with absolute performance ratio of at most 5. Based on the new algorithm, we also prove a general upper bound for the optimal height, which depends on the continuous lower bound and the maximum height lower bound, and we show that the combination of both lower bounds also has an absolute worst‐case performance ratio of at most 5. |
| abstractGer |
We consider the 2D and 3D strip packing problem (SPP): given a set of rectangular items and a strip, find the minimal height needed to pack all items. Rotation of the items is not permitted. We present an algorithm for the 2D SPP, which improves the packing of the well‐known FFDH heuristic and state theoretical results for this algorithm. Furthermore, we prove new upper bounds for the 3D SPP in special cases. Moreover, we present an implementation of the FFDH heuristic for the 3D case, which is used to construct a new algorithm, called COMB‐3D heuristic, with absolute performance ratio of at most 5. Based on the new algorithm, we also prove a general upper bound for the optimal height, which depends on the continuous lower bound and the maximum height lower bound, and we show that the combination of both lower bounds also has an absolute worst‐case performance ratio of at most 5. |
| abstract_unstemmed |
We consider the 2D and 3D strip packing problem (SPP): given a set of rectangular items and a strip, find the minimal height needed to pack all items. Rotation of the items is not permitted. We present an algorithm for the 2D SPP, which improves the packing of the well‐known FFDH heuristic and state theoretical results for this algorithm. Furthermore, we prove new upper bounds for the 3D SPP in special cases. Moreover, we present an implementation of the FFDH heuristic for the 3D case, which is used to construct a new algorithm, called COMB‐3D heuristic, with absolute performance ratio of at most 5. Based on the new algorithm, we also prove a general upper bound for the optimal height, which depends on the continuous lower bound and the maximum height lower bound, and we show that the combination of both lower bounds also has an absolute worst‐case performance ratio of at most 5. |
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Upper bounds for heuristic approaches to the strip packing problem |
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