Skip to main content
SpringerLink
Log in
Book cover

International Scientific Conference “Intellectual Systems of Decision Making and Problem of Computational Intelligence”

ISDMCI 2019: Lecture Notes in Computational Intelligence and Decision Making pp 122–132Cite as

Configuration Spaces of Geometric Objects with Their Applications in Packing, Layout and Covering Problems

  • Conference paper
  • First Online:

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1020))

Abstract

The concept of spatial configuration is introduced as a mapping of a finite set of geometric objects into a partially ordered set of a certain structure subject to a given constraints. Depending on the choice of generalized variables, various classes of spatial configurations are investigated. New approaches have been proposed for an analytical description of the main constraints in the packing, layout and covering optimization problems. This approach is based on the use of a special class of functions defined on a set of generalized variables of the configuration space.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Fasano G (2015) A modeling-based approach for non-standard packing problems. Optim Pack Appl 105:67–85

    MathSciNet  MATH  Google Scholar 

  2. Fasano G (2013) A global optimization point of view for non-standard packing problems. J Global Optim 155(2):279–299

    Article  MathSciNet  Google Scholar 

  3. Sriramya P, Parvatha BV (2012) A state-of-the-art review of bin packing techniques. Eur J Sci Res 86(3):360–364

    Google Scholar 

  4. Hifi M, M’Hallah R (2009) A literature review on circle and sphere packing problems: model and methodologies. Adv Optim Res 2009:1–22

    MATH  Google Scholar 

  5. Wascher G et al (2007) An improved typology of cutting and packing problems. Eur J Oper Res 183:1109–1130

    Article  Google Scholar 

  6. Bortfeldt A, Wascher G (2013) Constraints in container loading: a state-of-the-art review. Eur J Oper Res 229(1):1–20

    Article  MathSciNet  Google Scholar 

  7. Fadel GM, Wiecek MM (2015) Packing optimization of free-form objects in engineering design. Optim Pack Appl 105:37–66

    MATH  Google Scholar 

  8. Yakovlev SV (2017) The method of artificial space dilation in problems of optimal packing of geometric objects. Cybern Syst Anal 53(5):725–732

    Article  Google Scholar 

  9. Sun Z-G, Teng H-F (2003) Optimal layout design of a satellite module. Eng Optim 35(5):513–529

    Article  Google Scholar 

  10. Coggan J, Shimada K, Yin S (2002) A survey of computational approaches to three-dimensional layout problems. CAD Comput Aided Des 34(8):597–611

    Article  Google Scholar 

  11. Tian T et al (2016) The multiple container loading problem with preference. Eur J Oper Res 248(1):84–94

    Article  MathSciNet  Google Scholar 

  12. Drira A, Pierreval H, Hajri-Gabouj S (2007) Facility layout problems: a survey. Ann Rev Control 31(2):255–267

    Article  Google Scholar 

  13. Stoyan YG, Semkin VV, Chugay AM (2014) Optimization of 3D objects layout into a multiply connected domain with account for shortest distances. Cybern Syst Anal 50(3):374–385

    Article  MathSciNet  Google Scholar 

  14. Grebennik IV et al (2018) Combinatorial configurations in balance layout optimization problems. Cybern Syst Anal 54(2):221–231

    Article  MathSciNet  Google Scholar 

  15. Yakovlev SV (1999) On a class of problems on covering of a bounded set. Acta Mathematica Hungarica 53(3):253–262

    MathSciNet  Google Scholar 

  16. Stoyan YG, Patsuk VM (2014) Covering a convex 3D polytope by a minimal number of congruent spheres. Int J Comput Math 91(9):2010–2020

    Article  MathSciNet  Google Scholar 

  17. Shekhovtsov SB, Yakovlev SV (1989) Formalization and solution of one class of covering problem in design of control and monitoring systems. Avtomatika i Telemekhanika 5:160–168

    MATH  Google Scholar 

  18. Kiseleva EM, Lozovskaya LI, Timoshenko EV (2009) Solution of continuous problems of optimal covering with spheres using optimal set-partition theory. Cybern Syst Anal 45(3):421–437

    Article  Google Scholar 

  19. Kiseleva EM, Koriashkina LS (2015) Theory of continuous optimal set partitioning problems as a universal mathematical formalism for constructing Voronoi diagrams and their generalizations. Cybern Syst Anal 51(3):325–335

    Article  MathSciNet  Google Scholar 

  20. Kiseleva EM, Prytomanova OM, Zhuravel SV (2018) Algorithm for solving a continuous problem of optimal partitioning with neurolinguistic identification of functions in target functional. J Autom Inform Sci 50(3):102–112

    Article  Google Scholar 

  21. Rvachov VL (1982) Theory R-function and its applications. Nauk. Dumka, Kiev

    Google Scholar 

  22. Stoyan YG, Yakovlev SV (2018) Configuration space of geometric objects. Cybern Syst Anal 54(5):716–726

    Article  MathSciNet  Google Scholar 

  23. Yakovlev SV (2018) On some classes of spatial configurations of geometric objects and their formalization. J Autom Inf Sci 50(9):38–50

    Article  Google Scholar 

  24. Berge C (1968) Principes de combinatoire. Dunod, Paris

    MATH  Google Scholar 

  25. Yakovlev S, Kartashov O (2018) System analysis and classification of spatial configurations. In: Proceedings of 2018 IEEE first international conference on system analysis and intelligent computing, SAIC 2018, Kyiv, pp 90–93

    Google Scholar 

  26. Kovalenko AA et al (2015) Balance layout problem for 3D-objects: mathematical model and solution methods. Cybern Syst Anal 51(4):556–565

    Article  MathSciNet  Google Scholar 

  27. Stoyan YuG, Sokolovskii VZ, Yakovlev SV (1982) Method of balancing rotating discretely distributed masses. Energomashinostroenie 2:4–5

    Google Scholar 

  28. Stoyan Yu, Romanova T, Pankratov A, Kovalenko A, Stetsyuk P (2016) Balance layout problems: mathematical modeling and nonlinear optimization. In: Space engineering. Modeling and optimization with case studies, vol 114, pp 369-400

    MATH  Google Scholar 

  29. Korte B, Vygen J (2018) Combinatorial optimization: theory and algorithms, 6th edn. Springer, New York

    Book  Google Scholar 

  30. Burkard RE (2013) Quadratic assignment problems. In: Handbook of combinatorial optimization, vol 5, no 1, pp 2741–2814

    Chapter  Google Scholar 

  31. Hulianytskyi L, Riasna I (2017) Formalization and classification of combinatorial optimization problems. In: Optimization and its applications, vol 130, pp 239–250. Springer

    Google Scholar 

  32. Yakovlev S (2017) Convex extensions in combinatorial optimization and their applications. In: Optimization and its applications, vol 130, pp 567–584. Springer

    Google Scholar 

  33. Yakovlev SV (1989) Bounds on the minimum of convex functions on Euclidean combinatorial sets. Cybernetics 25(3):385–391

    Article  MathSciNet  Google Scholar 

  34. Yakovlev SV, Pichugina OS (2018) Properties of combinatorial optimization problems over polyhedral-spherical sets. Cybern Syst Anal 54(1):99–109

    Article  Google Scholar 

  35. Yakovlev SV, Pichugina OS, Yarovaya OV (2019) Polyhedral spherical configuration in discrete optimization. J Autom Inf Sci 51(1):38–50

    Article  Google Scholar 

  36. Stoyan Y, Romanova T (2013) Mathematical models of placement optimization: two- and three-dimensional problems and applications. Model Optim Space Eng 73:363–388

    Article  Google Scholar 

  37. Bennell J et al (2010) Tools of mathematical modelling of arbitrary object packing problems. J Ann Oper Res 179(1):343–368

    Article  MathSciNet  Google Scholar 

  38. Yakovlev SV (2019) Formalization of spatial configuration optimization problems with a special function class. Cybern Syst Anal 55(4):512–523

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Aerospace University “Kharkiv Aviation Institute”, Kharkiv, Ukraine

    Sergiy Yakovlev

Authors
  1. Sergiy Yakovlev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sergiy Yakovlev .

Editor information

Editors and Affiliations

  1. Kherson National Technical University, Kherson, Ukraine

    Volodymyr Lytvynenko

  2. Jan Evangelista Purkyně University in Ústi and Labem, Usti and Labem, Czech Republic

    Sergii Babichev

  3. Lublin University of Technology, Lublin, Poland

    Waldemar Wójcik

  4. IT Step University, Lviv, Ukraine

    Olena Vynokurova

  5. Kherson National Technical University, Kherson, Ukraine

    Svetlana Vyshemyrskaya

  6. Kherson National Technical University, Kherson, Ukraine

    Svetlana Radetskaya

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Yakovlev, S. (2020). Configuration Spaces of Geometric Objects with Their Applications in Packing, Layout and Covering Problems. In: Lytvynenko, V., Babichev, S., Wójcik, W., Vynokurova, O., Vyshemyrskaya, S., Radetskaya, S. (eds) Lecture Notes in Computational Intelligence and Decision Making. ISDMCI 2019. Advances in Intelligent Systems and Computing, vol 1020. Springer, Cham. https://doi.org/10.1007/978-3-030-26474-1_9

Download citation

Publish with us

Policies and ethics

Search

Navigation