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

Author

Listed:
  • 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
    Leeds University Business School, University of Leeds, Maurice Keyworth Building, Leeds LS2 9JT, UK
    Faculty of Computer Science, Kharkiv National University of Radio Electronics, 61166 Kharkiv, Ukraine)

  • Igor Litvinchev

    (Faculty of Mechanical and Electrical Engineering, Autonomous University of Nuevo Leon, Monterrey 66455, Mexico
    College of Mechanical and Electrical Engineering, Pingyang Institute of Intelligent Manufacturing, Wenzhou University, Wenzhou 325035, China)

  • 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)

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.

Suggested Citation

  • Oksana Melashenko & Tetyana Romanova & Igor Litvinchev & Carlos Gustavo Martínez Gomez & Rui Yang & Bingtao Sun, 2025. "A Model-Based Heuristic for Packing Soft Rotated Rectangles in an Optimized Convex Container with Prohibited Zones," Mathematics, MDPI, vol. 13(3), pages 1-21, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:493-:d:1581583
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