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A Literature Review on Circle and Sphere Packing Problems: Models and Methodologies

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  • Mhand Hifi
  • Rym M'Hallah

Abstract

This paper reviews the most relevant literature on efficient models and methods for packing circular objects/items into Euclidean plane regions where the objects/items and regions are either two- or three-dimensional. These packing problems are NP hard optimization problems with a wide variety of applications. They have been tackled using various approaches-based algorithms ranging from computer-aided optimality proofs, to branch-and-bound procedures, to constructive approaches, to multi-start nonconvex minimization, to billiard simulation, to multiphase heuristics, and metaheuristics.

Suggested Citation

  • Mhand Hifi & Rym M'Hallah, 2009. "A Literature Review on Circle and Sphere Packing Problems: Models and Methodologies," Advances in Operations Research, Hindawi, vol. 2009, pages 1-22, July.
    • Handle: RePEc:hin:jnlaor:150624
    DOI: 10.1155/2009/150624
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    Cited by:

    1. Andreas Fischer & Igor Litvinchev & Tetyana Romanova & Petro Stetsyuk & Georgiy Yaskov, 2023. "Quasi-Packing Different Spheres with Ratio Conditions in a Spherical Container," Mathematics, MDPI, vol. 11(9), pages 1-19, April.
    2. Andreas Fischer & Igor Litvinchev & Tetyana Romanova & Petro Stetsyuk & Georgiy Yaskov, 2024. "Packing spheres with quasi-containment conditions," Journal of Global Optimization, Springer, vol. 90(3), pages 671-689, November.
    3. Oslandsbotn, Andreas & Kereta, Željko & Naumova, Valeriya & Freund, Yoav & Cloninger, Alexander, 2022. "StreaMRAK a streaming multi-resolution adaptive kernel algorithm," Applied Mathematics and Computation, Elsevier, vol. 426(C).
    4. Hifi, Mhand & Yousef, Labib, 2019. "A local search-based method for sphere packing problems," European Journal of Operational Research, Elsevier, vol. 274(2), pages 482-500.
    5. Ambros Gleixner & Stephen J. Maher & Benjamin Müller & João Pedro Pedroso, 2020. "Price-and-verify: a new algorithm for recursive circle packing using Dantzig–Wolfe decomposition," Annals of Operations Research, Springer, vol. 284(2), pages 527-555, January.
    6. Frank J. Kampas & János D. Pintér & Ignacio Castillo, 2023. "Model Development and Solver Demonstrations Using Randomized Test Problems," SN Operations Research Forum, Springer, vol. 4(1), pages 1-15, March.
    7. Xiangyang Huang & LiGuo Huang, 2023. "Spreading Points Using Gradient and Tabu," SN Operations Research Forum, Springer, vol. 4(2), pages 1-11, June.
    8. Igor Litvinchev & Andreas Fischer & Tetyana Romanova & Petro Stetsyuk, 2024. "A New Class of Irregular Packing Problems Reducible to Sphere Packing in Arbitrary Norms," Mathematics, MDPI, vol. 12(7), pages 1-17, March.
    9. Silva, Allyson & Coelho, Leandro C. & Darvish, Maryam & Renaud, Jacques, 2022. "A cutting plane method and a parallel algorithm for packing rectangles in a circular container," European Journal of Operational Research, Elsevier, vol. 303(1), pages 114-128.
    10. Ryu, Joonghyun & Lee, Mokwon & Kim, Donguk & Kallrath, Josef & Sugihara, Kokichi & Kim, Deok-Soo, 2020. "VOROPACK-D: Real-time disk packing algorithm using Voronoi diagram," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    11. Akang Wang & Chrysanthos E. Gounaris, 2021. "On tackling reverse convex constraints for non-overlapping of unequal circles," Journal of Global Optimization, Springer, vol. 80(2), pages 357-385, June.

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