Skip to main content

Deleting Objects Algorithm for the Optimization of Orthogonal Packing Problems

  • Chapter
  • First Online:

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Abstract

This paper considers the orthogonal packing problem that is a problem of placing all given orthogonal objects into a minimal set of orthogonal containers in the form of parallelepipeds of arbitrary dimension. It proposes an algorithm for deleting objects with the aim of effectively managing free spaces in containers. This algorithm provides a possibility of realization of heuristic methods, which are based on excluding some placed objects from a container and consequently filling the freed spaces within it more rationally.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Bortfeldt A, Wascher G (2013) Constraints in container loading—a state-of-the-art review. EJOR 229(1):1–20

    Article  MathSciNet  MATH  Google Scholar 

  2. Chekanin VA, Chekanin AV (2012) Researching of genetic methods to optimize the allocation of rectangular resources. In: Proceedings of 2nd international scientific conference on modern engineering: science and education, Izd-vo Politekhn. un-ta, SPb, pp 798–804 (in Russian)

    Google Scholar 

  3. Chekanin VA, Chekanin AV (2013) Improved packing representation model for the orthogonal packing problem. Appl Mech Mater 390:591–595

    Article  MATH  Google Scholar 

  4. Chekanin VA, Chekanin AV (2014) Development of the multimethod genetic algorithm for the strip packing problem. Appl Mech Mater 598:377–381

    Article  MATH  Google Scholar 

  5. Chekanin VA, Chekanin AV (2015) Data structure for the three dimensional orthogonal packing problem. Vestnik MSTU “STANKIN” (Vestnik MGTU “STANKIN”) 1:112–116 (in Russian)

    Google Scholar 

  6. Chekanin VA (2014) Library class for solving packing problems via evolutionary algorithms In: Proceedings of 4th international scientific conference on modern engineering: science and education. Izd-vo Politekhn. un-ta, SPb, pp 789–796 (in Russian)

    Google Scholar 

  7. Chekanin VA, Chekanin AV (2015) An efficient model for the orthogonal packing problem. Adv Mech Eng 22:33–38

    MATH  Google Scholar 

  8. Chekanin VA, Chekanin AV (2015) Development of optimization software to solve practical packing and cutting problems. Adv Intell Syst Res 123:379–382

    Google Scholar 

  9. Chekanin VA, Chekanin AV (2016) New effective data structure for multidimensional optimization orthogonal packing problems. In: Advances in mechanical engineering. Springer International Publishing, pp 87–92

    Google Scholar 

  10. Crainic TG, Perboli G, Tadei R (2008) Extreme point-based heuristics for three-dimensional bin packing. INFORMS J Comput 20(3):368–384

    Article  MathSciNet  MATH  Google Scholar 

  11. Fekete SP, Schepers J, van der Veen JC (2007) An exact algorithm for higher-dimensional orthogonal packing. Oper Res 55(3):569–587

    Article  MathSciNet  MATH  Google Scholar 

  12. Filippova AS (2006) Modeling of evolution algorithms for rectangular packing problems based on block structure technology. In: Inf Technol (Informacionnye Tehnologii). Appendix, 32 p (in Russian)

    Google Scholar 

  13. Gao YQ, Guan HB, Qi ZW, Hou Y, Liu L (2013) A multi-objective ant colony system algorithm for virtual machine placement in cloud computing. J Comput Syst Sci 79(8):1230–1242

    Article  MathSciNet  MATH  Google Scholar 

  14. Goncalves JF, Resende MGC (2013) A biased random key genetic algorithm for 2d and 3d bin packing problems. Int J Prod Econ 145(2):500–510

    Article  Google Scholar 

  15. Johnson DS (2012) A brief history of NP-completeness, 1954–2012. Documenta Mathematica. Extra Volume ISMP, pp 359–376

    Google Scholar 

  16. 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):64–73

    Article  MATH  Google Scholar 

  17. Martinez MAA, Clautiaux F, Dell’Amico M, Iori M (2013) Exact algorithms for the bin packing problem with fragile objects. Discret Optim 10(3):210–223

    Article  MathSciNet  Google Scholar 

  18. Riff MC, Bonnaire X, Neveu B (2009) A revision of recent approaches for two-dimensional strip-packing problems. Eng Appl Artif Intell 22(4–5):823–827

    Article  Google Scholar 

  19. Wascher G, Haubner H, Schumann H (2007) An improved typology of cutting and packing problems. EJOR 183(3):1109–1130

    Article  MATH  Google Scholar 

  20. Westerlund J, Papageorgiou LG, Westerlund T (2007) A MILP model for N-dimensional allocation. Comput Chem Eng 31(12):1702–1714

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vladislav A. Chekanin .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Chekanin, V.A., Chekanin, A.V. (2017). Deleting Objects Algorithm for the Optimization of Orthogonal Packing Problems. In: Evgrafov, A. (eds) Advances in Mechanical Engineering. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-53363-6_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-53363-6_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53362-9

  • Online ISBN: 978-3-319-53363-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics