IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i17p2670-d1465683.html
   My bibliography  Save this article

Optimizing Two-Dimensional Irregular Pattern Packing with Advanced Overlap Optimization Techniques

Author

Listed:
  • Longhui Meng

    (School of Mechanical and Power Engineering, Nanjing Tech University, Nanjing 211816, China)

  • Liang Ding

    (Nanjing WIT Science & Technology Co., Ltd., Nanjing 210012, China)

  • Aqib Mashood Khan

    (College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)

  • Ray Tahir Mushtaq

    (Bio-Additive Manufacturing University-Enterprise Joint Research Center of Shaanxi Province, Department of Industrial Engineering, Northwestern Polytechnical University, Xi’an 710072, China)

  • Mohammed Alkahtani

    (Department of Industrial Engineering, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia)

Abstract

This research introduces the Iterative Overlap Optimization Placement (IOOP) method, a novel approach designed to enhance the efficiency of irregular pattern packing by dynamically optimizing overlap ratios and pattern placements. Utilizing a modified genetic algorithm, IOOP addresses the complexities of arranging irregular patterns in a given space, focusing on improving spatial and material efficiency. This study demonstrates the method’s superiority over the traditional Size-First Non-Iterative Overlap Optimization Placement technique through comparative analysis, highlighting significant improvements in spatial utilization, flexibility, and material conservation. The effectiveness of IOOP is further validated by its robustness in handling diverse pattern groups and its adaptability in adjusting pattern placements iteratively. This research not only showcases the potential of IOOP in manufacturing and design processes requiring precise spatial planning but also opens avenues for its application across various industries, underscoring the need for further exploration into advanced technological integrations for tackling complex spatial optimization challenges.

Suggested Citation

  • Longhui Meng & Liang Ding & Aqib Mashood Khan & Ray Tahir Mushtaq & Mohammed Alkahtani, 2024. "Optimizing Two-Dimensional Irregular Pattern Packing with Advanced Overlap Optimization Techniques," Mathematics, MDPI, vol. 12(17), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2670-:d:1465683
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/17/2670/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/17/2670/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Akang Wang & Christopher L. Hanselman & Chrysanthos E. Gounaris, 2018. "A customized branch-and-bound approach for irregular shape nesting," Journal of Global Optimization, Springer, vol. 71(4), pages 935-955, August.
    2. Leandro R. Mundim & Marina Andretta & Maria Antónia Carravilla & José Fernando Oliveira, 2018. "A general heuristic for two-dimensional nesting problems with limited-size containers," International Journal of Production Research, Taylor & Francis Journals, vol. 56(1-2), pages 709-732, January.
    3. Martinez-Sykora, A. & Alvarez-Valdes, R. & Bennell, J.A. & Ruiz, R. & Tamarit, J.M., 2017. "Matheuristics for the irregular bin packing problem with free rotations," European Journal of Operational Research, Elsevier, vol. 258(2), pages 440-455.
    4. Cherri, Luiz H. & Mundim, Leandro R. & Andretta, Marina & Toledo, Franklina M.B. & Oliveira, José F. & Carravilla, Maria Antónia, 2016. "Robust mixed-integer linear programming models for the irregular strip packing problem," European Journal of Operational Research, Elsevier, vol. 253(3), pages 570-583.
    5. Yuriy Stoyan & Alexander Pankratov & Tatiana Romanova, 2016. "Cutting and packing problems for irregular objects with continuous rotations: mathematical modelling and non-linear optimization," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(5), pages 786-800, May.
    6. Tatiana Romanova & Alexander Pankratov & Igor Litvinchev & Sergiy Plankovskyy & Yevgen Tsegelnyk & Olga Shypul, 2021. "Sparsest packing of two-dimensional objects," International Journal of Production Research, Taylor & Francis Journals, vol. 59(13), pages 3900-3915, July.
    7. Abeysooriya, Ranga P. & Bennell, Julia A. & Martinez-Sykora, Antonio, 2018. "Jostle heuristics for the 2D-irregular shapes bin packing problems with free rotation," International Journal of Production Economics, Elsevier, vol. 195(C), pages 12-26.
    8. Luiz H. Cherri & Adriana C. Cherri & Edilaine M. Soler, 2018. "Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations," Journal of Global Optimization, Springer, vol. 72(1), pages 89-107, September.
    9. Alvarez-Valdes, R. & Martinez, A. & Tamarit, J.M., 2013. "A branch & bound algorithm for cutting and packing irregularly shaped pieces," International Journal of Production Economics, Elsevier, vol. 145(2), pages 463-477.
    10. Luiz Henrique Cherri & Adriana Cristina Cherri & Maria Antónia Carravilla & José Fernando Oliveira & Franklina Maria Bragion Toledo & Andréa Carla Gonçalves Vianna, 2018. "An innovative data structure to handle the geometry of nesting problems," International Journal of Production Research, Taylor & Francis Journals, vol. 56(23), pages 7085-7102, December.
    11. Elkeran, Ahmed, 2013. "A new approach for sheet nesting problem using guided cuckoo search and pairwise clustering," European Journal of Operational Research, Elsevier, vol. 231(3), pages 757-769.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lastra-Díaz, Juan J. & Ortuño, M. Teresa, 2024. "Mixed-integer programming models for irregular strip packing based on vertical slices and feasibility cuts," European Journal of Operational Research, Elsevier, vol. 313(1), pages 69-91.
    2. Germán Pantoja-Benavides & David Álvarez-Martínez & Francisco Parreño Torres, 2024. "The Normalized Direct Trigonometry Model for the Two-Dimensional Irregular Strip Packing Problem," Mathematics, MDPI, vol. 12(15), pages 1-25, August.
    3. Igor Kierkosz & Maciej Łuczak, 2019. "A one-pass heuristic for nesting problems," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(1), pages 37-60.
    4. Leao, Aline A.S. & Toledo, Franklina M.B. & Oliveira, José Fernando & Carravilla, Maria Antónia & Alvarez-Valdés, Ramón, 2020. "Irregular packing problems: A review of mathematical models," European Journal of Operational Research, Elsevier, vol. 282(3), pages 803-822.
    5. Cherri, Luiz Henrique & Carravilla, Maria Antónia & Ribeiro, Cristina & Toledo, Franklina Maria Bragion, 2019. "Optimality in nesting problems: New constraint programming models and a new global constraint for non-overlap," Operations Research Perspectives, Elsevier, vol. 6(C).
    6. Sato, André Kubagawa & Martins, Thiago Castro & Gomes, Antonio Miguel & Tsuzuki, Marcos Sales Guerra, 2019. "Raster penetration map applied to the irregular packing problem," European Journal of Operational Research, Elsevier, vol. 279(2), pages 657-671.
    7. Luiz H. Cherri & Adriana C. Cherri & Edilaine M. Soler, 2018. "Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations," Journal of Global Optimization, Springer, vol. 72(1), pages 89-107, September.
    8. Qiang Luo & Yunqing Rao, 2022. "Improved Sliding Algorithm for Generating No-Fit Polygon in the 2D Irregular Packing Problem," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    9. Bennell, J.A. & Cabo, M. & Martínez-Sykora, A., 2018. "A beam search approach to solve the convex irregular bin packing problem with guillotine guts," European Journal of Operational Research, Elsevier, vol. 270(1), pages 89-102.
    10. Akang Wang & Christopher L. Hanselman & Chrysanthos E. Gounaris, 2018. "A customized branch-and-bound approach for irregular shape nesting," Journal of Global Optimization, Springer, vol. 71(4), pages 935-955, August.
    11. Nascimento, Paulo Jorge & Silva, Cristóvão & Antunes, Carlos Henggeler & Moniz, Samuel, 2024. "Optimal decomposition approach for solving large nesting and scheduling problems of additive manufacturing systems," European Journal of Operational Research, Elsevier, vol. 317(1), pages 92-110.
    12. Jie Fang & Yunqing Rao & Xusheng Zhao & Bing Du, 2023. "A Hybrid Reinforcement Learning Algorithm for 2D Irregular Packing Problems," Mathematics, MDPI, vol. 11(2), pages 1-17, January.
    13. Hagspihl, Thomas & Kolisch, Rainer & Fontaine, Pirmin & Schiffels, Sebastian, 2024. "Apron layout planning–Optimal positioning of aircraft stands," Transportation Research Part B: Methodological, Elsevier, vol. 179(C).
    14. Hu, Xiaoxuan & Zhu, Waiming & Ma, Huawei & An, Bo & Zhi, Yanling & Wu, Yi, 2021. "Orientational variable-length strip covering problem: A branch-and-price-based algorithm," European Journal of Operational Research, Elsevier, vol. 289(1), pages 254-269.
    15. Demiröz, Barış Evrim & Altınel, İ. Kuban & Akarun, Lale, 2019. "Rectangle blanket problem: Binary integer linear programming formulation and solution algorithms," European Journal of Operational Research, Elsevier, vol. 277(1), pages 62-83.
    16. Cherri, Luiz H. & Mundim, Leandro R. & Andretta, Marina & Toledo, Franklina M.B. & Oliveira, José F. & Carravilla, Maria Antónia, 2016. "Robust mixed-integer linear programming models for the irregular strip packing problem," European Journal of Operational Research, Elsevier, vol. 253(3), pages 570-583.
    17. Kimms, Alf & Király, Hédi, 2023. "An extended model formulation for the two-dimensional irregular strip packing problem considering general industry-relevant aspects," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1202-1218.
    18. Yainier Labrada-Nueva & Martin H. Cruz-Rosales & Juan Manuel Rendón-Mancha & Rafael Rivera-López & Marta Lilia Eraña-Díaz & Marco Antonio Cruz-Chávez, 2021. "Overlap Detection in 2D Amorphous Shapes for Paper Optimization in Digital Printing Presses," Mathematics, MDPI, vol. 9(9), pages 1-22, May.
    19. Juan Lu & Chengyi Ou & Chen Liao & Zhenkun Zhang & Kai Chen & Xiaoping Liao, 2021. "Formal modelling of a sheet metal smart manufacturing system by using Petri nets and first-order predicate logic," Journal of Intelligent Manufacturing, Springer, vol. 32(4), pages 1043-1063, April.
    20. Parreño, F. & Alvarez-Valdes, R., 2021. "Mathematical models for a cutting problem in the glass manufacturing industry," Omega, Elsevier, vol. 103(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2670-:d:1465683. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.