Optimized Packing Clusters of Objects in a Rectangular Container
A packing (layout) problem for a number of clusters (groups) composed of convex objects (e.g., circles, ellipses, or convex polygons) is considered. The clusters have to be packed into a given rectangular container subject to nonoverlapping between objects within a cluster. Each cluster is represent...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2019
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| Subjects: | |
| Online Access: | http://eprints.uanl.mx/23313/1/23313.pdf |
| _version_ | 1824416836429545472 |
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| author | Romanova, Tatiana Pankratov, Alexander Litvinchev, Igor Pankratova, Yu Urniaieva, I. |
| author_facet | Romanova, Tatiana Pankratov, Alexander Litvinchev, Igor Pankratova, Yu Urniaieva, I. |
| author_sort | Romanova, Tatiana |
| collection | Repositorio Institucional |
| description | A packing (layout) problem for a number of clusters (groups) composed of convex objects (e.g., circles, ellipses, or convex polygons) is considered. The clusters have to be packed into a given rectangular container subject to nonoverlapping between objects within a cluster. Each cluster is represented by the convex hull of objects that form the cluster. Two clusters are said to be nonoverlapping if their convex hulls do not overlap. A cluster is said to be entirely in the container if so is its convex hull. All objects in the cluster have the same shape (different sizes are allowed) and can be continuously translated and rotated. The objective of optimized packing is constructing a maximum sparse layout for clusters subject to nonoverlapping and containment conditions for clusters and objects. Here the term sparse means that clusters are sufficiently distant one from another. New quasi-phi-functions and phi-functions to describe analytically nonoverlapping, containment and distance constraints for clusters are introduced. The layout problem is then formulated as a nonlinear nonconvex continuous problem. A novel algorithm to search for locally optimal solutions is developed. Computational results are provided to demonstrate the efficiency of our approach. This research is motivated by a container-loading problem; however similar problems arise naturally in many other packing/cutting/clustering issues. |
| format | Article |
| id | eprints-23313 |
| institution | UANL |
| language | English |
| publishDate | 2019 |
| publisher | Hindawi Publishing Corporation |
| record_format | eprints |
| spelling | eprints-233132024-12-11T16:22:34Z http://eprints.uanl.mx/23313/ Optimized Packing Clusters of Objects in a Rectangular Container Romanova, Tatiana Pankratov, Alexander Litvinchev, Igor Pankratova, Yu Urniaieva, I. TA Ingeniería General y Civil A packing (layout) problem for a number of clusters (groups) composed of convex objects (e.g., circles, ellipses, or convex polygons) is considered. The clusters have to be packed into a given rectangular container subject to nonoverlapping between objects within a cluster. Each cluster is represented by the convex hull of objects that form the cluster. Two clusters are said to be nonoverlapping if their convex hulls do not overlap. A cluster is said to be entirely in the container if so is its convex hull. All objects in the cluster have the same shape (different sizes are allowed) and can be continuously translated and rotated. The objective of optimized packing is constructing a maximum sparse layout for clusters subject to nonoverlapping and containment conditions for clusters and objects. Here the term sparse means that clusters are sufficiently distant one from another. New quasi-phi-functions and phi-functions to describe analytically nonoverlapping, containment and distance constraints for clusters are introduced. The layout problem is then formulated as a nonlinear nonconvex continuous problem. A novel algorithm to search for locally optimal solutions is developed. Computational results are provided to demonstrate the efficiency of our approach. This research is motivated by a container-loading problem; however similar problems arise naturally in many other packing/cutting/clustering issues. Hindawi Publishing Corporation 2019 Article PeerReviewed text en cc_by_nc_nd http://eprints.uanl.mx/23313/1/23313.pdf http://eprints.uanl.mx/23313/1.haspreviewThumbnailVersion/23313.pdf Romanova, Tatiana y Pankratov, Alexander y Litvinchev, Igor y Pankratova, Yu y Urniaieva, I. (2019) Optimized Packing Clusters of Objects in a Rectangular Container. Mathematical Problems in Engineering, 2019. pp. 1-12. ISSN 1024-123X http://doi.org/10.1155/2019/4136430 doi:10.1155/2019/4136430 |
| spellingShingle | TA Ingeniería General y Civil Romanova, Tatiana Pankratov, Alexander Litvinchev, Igor Pankratova, Yu Urniaieva, I. Optimized Packing Clusters of Objects in a Rectangular Container |
| thumbnail | https://rediab.uanl.mx/themes/sandal5/images/online.png |
| title | Optimized Packing Clusters of Objects in a Rectangular Container |
| title_full | Optimized Packing Clusters of Objects in a Rectangular Container |
| title_fullStr | Optimized Packing Clusters of Objects in a Rectangular Container |
| title_full_unstemmed | Optimized Packing Clusters of Objects in a Rectangular Container |
| title_short | Optimized Packing Clusters of Objects in a Rectangular Container |
| title_sort | optimized packing clusters of objects in a rectangular container |
| topic | TA Ingeniería General y Civil |
| url | http://eprints.uanl.mx/23313/1/23313.pdf |
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