Skip to main content
Springer Nature Link
Log in

An Arrangement of a Family of Convex 3D Objects in a Minimum-Volume Container

  • Conference paper
  • First Online:
Smart Technologies in Urban Engineering (STUE 2024)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 1658))

Included in the following conference series:

  • 77 Accesses

Abstract

The paper is aiming to development of an approach for arrangement of assembled parts of complex geometry in the working area of 3D printer, considering standards of 3D printing. For an analytical description of industrial products of the complex shaped, a family of convex objects is used including spheres, cylinders, spherical cylinders, cones, truncated cones and spherical discs. Using the normalized quasi-phi-function of a general convex composed object, a mathematical model of the problem is presented in the form of a nonlinear programming problem. A solution strategy is developed that combines: obtaining feasible starting points, searching for local minima and choosing the best local minimum from those found at the previous stage. Numerical examples of packing 3D parts approximated by composed convex objects from the given family are provided and illustrated with figures. This study emphasizes the importance of further research and innovation in optimization of the technological process of 3D printing.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+
from $39.99 /Month
  • Starting from 10 chapters or articles per month
  • Access and download chapters and articles from more than 300k books and 2,500 journals
  • Cancel anytime
View plans

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
eBook
USD 169.00
Price excludes VAT (USA)
Softcover Book
USD 219.99
Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, books and news in related subjects, suggested using machine learning.

References

  1. Srivastava, M., Rathee, S.: Additive manufacturing: recent trends, applications and future outlooks. Prog. Addit. Manuf. 7, 261–287 (2022). https://doi.org/10.1007/s40964-021-00229-8

    Article  Google Scholar 

  2. Ehlers, T., Meyer, I., Oel, M., Bode, B., Gembarski, P.C., Lachmayer, R.: Effect-engineering by additive manufacturing. In: Lachmayer, R., Bode, B., Kaierle, S. (eds.) Innovative Product Development by Additive Manufacturing. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-05918-6_1

  3. Kaikai X., Yadong G., Qiang Z. Comparison of traditional processing and additive manufacturing technologies in various performance aspects: a review. Archiv. Civ. Mech. Eng. 23, 188 (2023). https://doi.org/10.1007/s43452-023-00699-3

  4. Kadir, A.Z.A., Yusof, Y., Wahab, M.S.: Additive manufacturing cost estimation models – a classification review. Int. J. Adv. Manuf. Technol. 107, 4033–4053 (2020). https://doi.org/10.1007/s00170-020-05262-5

    Article  Google Scholar 

  5. Yadav, D., Chhabra, D., Kumar, Garg R., Ahlawat, A., Phogat, A.: Optimization of FDM 3D printing process parameters for multi-material using artificial neural network. Mater. Today Proc. 21(3), 1583–1591 (2020). https://doi.org/10.1016/j.matpr.2019.11.225

  6. Tri, W., Hasan, M., Ismianti, I.: 3D print parameter optimization: a literature review. LPPM UPN “Veteran” Yogyakarta Conf. Ser. Proc. Eng. Sci. Ser. 1(1), 146–151 (2020). https://doi.org/10.31098/ess.vlil.105

  7. Araújo, L.J.P., Özcan, E., Atkin, J.A.D., Baumersumers, M.: Analysis of irregular three-dimensional packing problems in additive manufacturing: a new taxonomy and dataset. Int. Prod. Res. 57(18), 5920–5934 (2019). https://doi.org/10.1080/00207543.2018.1534016

    Article  Google Scholar 

  8. Leao, A., Toledo, F., Oliveira, J., Carravilla, M.: Irregular packing problems: a review of mathematical models. Eur. J. Oper. Res. 282(3), 803–822 (2020). https://doi.org/10.1016/j.ejor.2019.04.045

    Article  MathSciNet  Google Scholar 

  9. Zhao, J.: Meso-model optimization of composite propellant based on hybrid genetic algorithm and mass spring system. J. Phys. Conf. Ser. 2025(1), 012036 (2025). https://doi.org/10.1088/1742-6596/2025/1/012036

  10. Yuan, Y., Tole, K., Ni, F., He, K., Xiong, Z., Liu, J.: Adaptive simulated annealing with greedy search for the circle bin packing problem. Comput. Oper. Res. 144, 105826 (2022). https://doi.org/10.1016/j.cor.2022.105826

  11. Li, S., Wei, Y., Liu, X., Zhu, He., Zhaoxu, Yu.: A new fast ant colony optimization algorithm: the saltatory evolution ant colony optimization algorithm. Mathematics 10(6), 925 (2022). https://doi.org/10.3390/math10060925

    Article  Google Scholar 

  12. Blum, C., Blesa, M.J.: Probabilistic beam search for the longest common subsequence problem. In: Stützle, T., Birattari, M.H., Hoos, H. (eds.) Engineering Stochastic Local Search Algorithms. Designing, Implementing and Analyzing Effective Heuristics, SLS 2007. LNCS, vol. 4638. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74446-7_11

  13. Stoyan, Y., Romanova, T., Pankratov, A., Chugay, A.: Optimized object packings using quasi-phi-functions. Optim. Packag. Appl., 265–293 (2015). https://doi.org/10.1007/978-3-319-18899-7_13

  14. Yaskov, G., Romanova, T., Litvinchev, I., Shekhovtsov, S.: Optimal packing problems: from knapsack problem to open dimension problem. In: Vasant, P., Zelinka, I., Weber, GW. (eds.) Intelligent Computing and Optimization, ICO 2019. Advances in Intelligent Systems and Computing, vol. 1072. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-33585-4_65

  15. Kubach, T., Bortfeldt, A., Tilli, T., Gehring, H.: Greedy algorithms for packing unequal spheres into a cuboidal strip or a cuboid. Asia-Pacific J. Oper. Res. 28(06), 739–753 (2011). https://doi.org/10.1142/S0217595911003326

    Article  MathSciNet  Google Scholar 

  16. Romanova, T., Stoyan, Y., Pankratov, A., Litvinchev, I., Marmolejo, J.A.: Decomposition algorithm for irregular placement problems. In: Vasant, P., Zelinka, I., Weber, G.W. (eds.) Intelligent Computing and Optimization, ICO 2019. Advances in Intelligent Systems and Computing, vol. 1072, pp. 214–221. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-33585-4_21

  17. Romanova, T., Stetsyuk, P., Chugay, A.M.: Parallel computing technologies for solving optimization problems of geometric design. Cybern. Syst. Anal. 55, 894–904 (2019). https://doi.org/10.1007/s10559-019-00199-4

    Article  MathSciNet  Google Scholar 

  18. Stoian, Y. E., Chugay, A. M., Pankratov A. V., et al.: Two approaches to modeling and solving the packing problem for convex polytopes. Cybern. Syst. Anal. 54, 585–593 (2018). https://doi.org/10.1007/s10559-018-0059-3

  19. Wachter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106(1), 25–57 (2006). https://doi.org/10.1007/s10107-004-0559-y

    Article  MathSciNet  Google Scholar 

  20. Litvinchev, I.S.: Refinement of Lagrangian bounds in optimization problems, Comput. Math. Math. Phys. 47(7), 1101-1108 (2007). ISSN 0965-5425. https://doi.org/10.1134/S0965542507070032

  21. Litvinchev, I., Rangel, S., Saucedo, J.: A Lagrangian bound for many-to-many assignment problems. J. Comb. Optim. 19(3), 241–257 (2010). ISSN 1382-6905. https://doi.org/10.1007/s10878-008-9196-3

  22. Fasano, G.: Solving Non-standard Packing Problems by Global Optimization and Heuristics. Springer (2014)

    Google Scholar 

  23. Litvinchev, I., Lopez, F., Escalante, H.J., Mata, M.: A MILP bi-objective model for static portfolio selection of R&D projects with synergies. J. Comput. Syst. Sci. Int. 50(6), 942–952 (2011). ISSN 1064-2307. https://doi.org/10.1134/S1064230711060165

  24. Litvinchev, I., Ríos-Solís, Y., Ozdemir, D., Hernandez-Landa, L.: Multiperiod and stochastic formulations for a closed loop supply chain with incentives. J. Comput. Syst. Sci. Int. 53(2), 201–211 (2014). ISSN 1064-2307. https://doi.org/10.1134/S1064230714020129

  25. Romanova, T., et al.: European J. Oper. Res. 291(1), 84-100 (2021)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. A. Pidgorny Institute of Power Machines and Systems of the National Academy of Sciences of Ukraine, 2/10 Кomunal’nykiv St., Kharkiv, 61046, Ukraine

    Andrii Chuhai

  2. Simon Kuznets Kharkiv National University of Economics, 9-A Nauky Ave., Kharkiv, 61070, Ukraine

    Andrii Chuhai

  3. Kharkiv National University of Radio Electronics, 14 Nauky Avenue, Kharkiv, 61166, Ukraine

    Sergiy Shekhovtsov & Sergiy Maximov

  4. Autonomous University of Nuevo Leon (UANL), San Nicolas de los Garza, 66455, Monterrey, Mexico

    Carlos Gustavo Martinez Gomez

Authors
  1. Andrii Chuhai
    View author publications

    Search author on:PubMed Google Scholar

  2. Sergiy Shekhovtsov
    View author publications

    Search author on:PubMed Google Scholar

  3. Sergiy Maximov
    View author publications

    Search author on:PubMed Google Scholar

  4. Carlos Gustavo Martinez Gomez
    View author publications

    Search author on:PubMed Google Scholar

Corresponding author

Correspondence to Sergiy Shekhovtsov .

Editor information

Editors and Affiliations

  1. O.M. Beketov National University of Urban Economy in Kharkiv, Kharkiv, Ukraine

    Olga Arsenyeva

  2. Anatolii Pidhornyi Institute of Power Machines and Systems of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine

    Tetyana Romanova

  3. O.M. Beketov National University of Urban Economy in Kharkiv, Kharkiv, Ukraine

    Maria Sukhonos

  4. O.M. Beketov National University of Urban Economy in Kharkiv, Kharkiv, Ukraine

    Ihor Biletskyi

  5. O.M. Beketov National University of Urban Economy in Kharkiv, Kharkiv, Ukraine

    Yevgen Tsegelnyk

Rights and permissions

Reprints and permissions

Copyright information

© 2026 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Chuhai, A., Shekhovtsov, S., Maximov, S., Gomez, C.G.M. (2026). An Arrangement of a Family of Convex 3D Objects in a Minimum-Volume Container. In: Arsenyeva, O., Romanova, T., Sukhonos, M., Biletskyi, I., Tsegelnyk, Y. (eds) Smart Technologies in Urban Engineering. STUE 2024. Lecture Notes in Networks and Systems, vol 1658. Springer, Cham. https://doi.org/10.1007/978-3-032-06829-3_31

Download citation

Keywords

Publish with us

Policies and ethics