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Packing Compaction Algorithm for Rectangular Cutting and Orthogonal Packing Problems

  • V. A. Chekanin
  • A. V. Chekanin
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

Abstract

The rectangular cutting and orthogonal packing problems which have many practical applications in industry and engineering are considered. Increasing the density of placement schemes leads to reducing the material usage in solving the rectangular cutting problems and reducing the unused resources at solving the orthogonal packing problems. This article contains the description of the developed packing compaction algorithm and its investigation. This algorithm uses six object selection rules, which select objects from a container for deleting and subsequent reallocation of them into freed spaces of the container. The packing compaction algorithm iteratively applies a one-pass heuristic algorithm which finds the best placement of the deleted objects in order to increase the density of the result packing. The effectiveness of the application of the proposed algorithm is investigated on the standard two-dimensional strip packing problems which are the rectangular cutting problems with only one container of a fixed width and an infinite length. Based on the test results, the effective sequence of application of the proposed rules used as the part of the packing algorithm was determined. The packing compaction algorithm is implemented in a general form which makes it possible for application in the rectangular cutting and orthogonal packing problems of arbitrary dimension.

Keywords

Compaction algorithm Packing Packing problem Rectangular cutting Optimization 

References

  1. 1.
    Wascher G, Haubner H, Schumann H (2007) An improved typology of cutting and packing problems. EJOR 183(3):1109–1130CrossRefGoogle Scholar
  2. 2.
    Johnson DS (2012) A brief history of NP-completeness, 1954–2012. Doc Math Extra Volume ISMP 359–376Google Scholar
  3. 3.
    Chekanin VA, Chekanin AV (2014) Development of the multimethod genetic algorithm for the strip packing problem. Appl Mech Mater 598:377–381CrossRefGoogle Scholar
  4. 4.
    Goncalves JF, Resende MGC (2013) A biased random key genetic algorithm for 2D and 3D bin packing problems. Int J Prod Econ 145(2):500–510CrossRefGoogle Scholar
  5. 5.
    Kierkosz I, Luczak M (2014) A hybrid evolutionary algorithm for the two-dimensional packing problem. Cent Eur J Oper Res 22(4):729–753MathSciNetCrossRefGoogle Scholar
  6. 6.
    Leung SCH, Zhang DF, Zhou CL, Wu T (2012) A hybrid simulated annealing metaheuristic algorithm for the two-dimensional knapsack packing problem. Comput Oper Res 39(1):64–73CrossRefGoogle Scholar
  7. 7.
    Bortfeldt A, Wascher G (2013) Constraints in container loading—a state-of-the-art review. EJOR 229(1):1–20MathSciNetCrossRefGoogle Scholar
  8. 8.
    Fekete SP, Schepers J, van der Veen JC (2007) An exact algorithm for higher-dimensional orthogonal packing. Oper Res 55(3):569–587MathSciNetCrossRefGoogle Scholar
  9. 9.
    Lins L, Lins S, Morabito R (2002) An n-tet graph approach for non-guillotine packings of n-dimensional boxes into an n-container. EJOR 141(2):421–439MathSciNetCrossRefGoogle Scholar
  10. 10.
    Westerlund J, Papageorgiou LG, Westerlund T (2007) A MILP model for N-dimensional allocation. Comput Chem Eng 31(12):1702–1714CrossRefGoogle Scholar
  11. 11.
    Chekanin VA, Chekanin AV (2015) An efficient model for the orthogonal packing problem. Adv Mech Eng 22:33–38zbMATHGoogle Scholar
  12. 12.
    Chekanin VA, Chekanin AV (2016) Implementation of packing methods for the orthogonal packing problems. J Theor Appl Inf Technol 88(3):421–430zbMATHGoogle Scholar
  13. 13.
    Chekanin AV, Chekanin VA (2014) Effective data structure for the multidimensional orthogonal bin packing problems. Adv Mater Res 962–965:2868–2871CrossRefGoogle Scholar
  14. 14.
    Chekanin VA, Chekanin AV (2014) Improved data structure for the orthogonal packing problem. Adv Mater Res 945–949:3143–3146CrossRefGoogle Scholar
  15. 15.
    Chekanin VA, Chekanin AV (2017) Algorithms and methods in multidimensional orthogonal packing problems. Int J Appl Eng Res 12(6):1009–1019zbMATHGoogle Scholar
  16. 16.
    Berkey O, Wang P (1987) Two-dimensional finite bin-packing algorithms. J Oper Res Soc 38(5):423–429CrossRefGoogle Scholar
  17. 17.
    Martello S, Vigo D (1998) Exact solution of the two-dimensional finite bin packing problem. Manag Sci 44(3):388–399CrossRefGoogle Scholar
  18. 18.
    Chekanin VA, Chekanin AV (2015) Development of optimization software to solve practical packing and cutting problems. Adv Intell Syst Res 123:379–382Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Moscow State University of Technology “STANKIN”MoscowRussia

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