A Model-Based Heuristic for Packing Soft Rotated Rectangles in an Optimized Convex Container with Prohibited Zones
Packing soft rectangular objects in an optimized convex container is considered. Each soft rectangle can be freely translated and rotated, has a fixed area, and its dimensions can vary in certain limits. The convex container may have prohibited zones where allocation of the objects is not allowed. T...
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| author | Oksana Melashenko Tetyana Romanova Igor Litvinchev Carlos Gustavo Martínez Gomez Rui Yang Bingtao Sun |
| author_facet | Oksana Melashenko Tetyana Romanova Igor Litvinchev Carlos Gustavo Martínez Gomez Rui Yang Bingtao Sun |
| author_sort | Oksana Melashenko |
| collection | DOAJ |
| description | Packing soft rectangular objects in an optimized convex container is considered. Each soft rectangle can be freely translated and rotated, has a fixed area, and its dimensions can vary in certain limits. The convex container may have prohibited zones where allocation of the objects is not allowed. The soft rectangles must be arranged completely inside the container; mutual intersection and overlapping with prohibited zones is not allowed. The objective is to minimize a certain metric characteristic of the container. The corresponding nonlinear mathematical problem is formulated using the phi-function technique to present non-overlapping and containment conditions. A model-based heuristic is proposed to find reasonable solutions to the problem. Numerical results are provided for triangular, circular, and scaled polygonal containers to validate the model and demonstrate the proposed approach’s efficiency. |
| format | Article |
| id | doaj-art-7bd2e6b3bd7042f28b3f40e05fdc67eb |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-7bd2e6b3bd7042f28b3f40e05fdc67eb2025-08-20T02:12:30ZengMDPI AGMathematics2227-73902025-01-0113349310.3390/math13030493A Model-Based Heuristic for Packing Soft Rotated Rectangles in an Optimized Convex Container with Prohibited ZonesOksana Melashenko0Tetyana Romanova1Igor Litvinchev2Carlos Gustavo Martínez Gomez3Rui Yang4Bingtao Sun5A. Pidgorny Institute of Power Machines and Systems of the National Academy of Sciences of Ukraine, 61046 Kharkiv, UkraineA. Pidgorny Institute of Power Machines and Systems of the National Academy of Sciences of Ukraine, 61046 Kharkiv, UkraineFaculty of Mechanical and Electrical Engineering, Autonomous University of Nuevo Leon, Monterrey 66455, MexicoFaculty of Mechanical and Electrical Engineering, Autonomous University of Nuevo Leon, Monterrey 66455, MexicoCollege of Mechanical and Electrical Engineering, Pingyang Institute of Intelligent Manufacturing, Wenzhou University, Wenzhou 325035, ChinaCollege of Mechanical and Electrical Engineering, Pingyang Institute of Intelligent Manufacturing, Wenzhou University, Wenzhou 325035, ChinaPacking soft rectangular objects in an optimized convex container is considered. Each soft rectangle can be freely translated and rotated, has a fixed area, and its dimensions can vary in certain limits. The convex container may have prohibited zones where allocation of the objects is not allowed. The soft rectangles must be arranged completely inside the container; mutual intersection and overlapping with prohibited zones is not allowed. The objective is to minimize a certain metric characteristic of the container. The corresponding nonlinear mathematical problem is formulated using the phi-function technique to present non-overlapping and containment conditions. A model-based heuristic is proposed to find reasonable solutions to the problem. Numerical results are provided for triangular, circular, and scaled polygonal containers to validate the model and demonstrate the proposed approach’s efficiency.https://www.mdpi.com/2227-7390/13/3/493packingsoft rectangular objectscontainer with prohibited zonesnonlinear optimization |
| spellingShingle | Oksana Melashenko Tetyana Romanova Igor Litvinchev Carlos Gustavo Martínez Gomez Rui Yang Bingtao Sun A Model-Based Heuristic for Packing Soft Rotated Rectangles in an Optimized Convex Container with Prohibited Zones Mathematics packing soft rectangular objects container with prohibited zones nonlinear optimization |
| title | A Model-Based Heuristic for Packing Soft Rotated Rectangles in an Optimized Convex Container with Prohibited Zones |
| title_full | A Model-Based Heuristic for Packing Soft Rotated Rectangles in an Optimized Convex Container with Prohibited Zones |
| title_fullStr | A Model-Based Heuristic for Packing Soft Rotated Rectangles in an Optimized Convex Container with Prohibited Zones |
| title_full_unstemmed | A Model-Based Heuristic for Packing Soft Rotated Rectangles in an Optimized Convex Container with Prohibited Zones |
| title_short | A Model-Based Heuristic for Packing Soft Rotated Rectangles in an Optimized Convex Container with Prohibited Zones |
| title_sort | model based heuristic for packing soft rotated rectangles in an optimized convex container with prohibited zones |
| topic | packing soft rectangular objects container with prohibited zones nonlinear optimization |
| url | https://www.mdpi.com/2227-7390/13/3/493 |
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