A Model-Based Heuristic for Packing Soft Rotated Rectangles in an Optimized Convex Container with Prohibited Zones

Oksana Melashenko, Tetyana Romanova (), Igor Litvinchev (), Carlos Gustavo Martínez Gomez, Rui Yang and Bingtao Sun
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Oksana Melashenko: A. Pidgorny Institute of Power Machines and Systems of the National Academy of Sciences of Ukraine, 61046 Kharkiv, Ukraine
Tetyana Romanova: A. Pidgorny Institute of Power Machines and Systems of the National Academy of Sciences of Ukraine, 61046 Kharkiv, Ukraine
Igor Litvinchev: Faculty of Mechanical and Electrical Engineering, Autonomous University of Nuevo Leon, Monterrey 66455, Mexico
Carlos Gustavo Martínez Gomez: Faculty of Mechanical and Electrical Engineering, Autonomous University of Nuevo Leon, Monterrey 66455, Mexico
Rui Yang: College of Mechanical and Electrical Engineering, Pingyang Institute of Intelligent Manufacturing, Wenzhou University, Wenzhou 325035, China
Bingtao Sun: College of Mechanical and Electrical Engineering, Pingyang Institute of Intelligent Manufacturing, Wenzhou University, Wenzhou 325035, China

Mathematics, 2025, vol. 13, issue 3, 1-21

Abstract: 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.

Keywords: packing; soft rectangular objects; container with prohibited zones; nonlinear optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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