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Combinatorial Configurations in Balance Layout Optimization Problems

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Abstract

The balance layout optimization problem for a given set of 3D objects in a container divided by horizontal racks into subcontainers is considered. For analytical description of non-overlapping and containment constraints, the phi-function technique is used. Combinatorial configurations describing the combinatorial structure of the problem are defined. Based on the introduced configurations, a mathematical model is constructed that takes into account not only the placement constraints and mechanical properties of the system but also the combinatorial features of the problem associated with generation of partitions of the set of objects placed inside the subcontainers. A solution strategy is proposed. The results of numerical experiments are provided.

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References

  1. B. Chazelle, H. Edelsbrunner, and L. J. Guibas, “The complexity of cutting complexes,” Discrete & Computational Geometry, Vol. 4, No. 2, 139–181 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  2. N. Chernov, Y. Stoyan, T. Romanova, and A. Pankratov, “Phi-functions for 2D objects formed by line segments and circular arcs,” Advances in Operations Research, DOI:https://doi.org/10.1155/2012/346358 (2012).

  3. N. Chernov, Y. Stoyan, and T. Romanova, “Mathematical model and efficient algorithms for object packing problem,” Computational Geometry: Theory and Applications, Vol. 43, No. 5, 535–553 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  4. G. Fasano and J. D. Pintér (eds.), Modeling and Optimization in Space Engineering, Springer, Optimization and Its Applications, Vol. 73 (2013).

  5. C. Che, Y. Wang, and H. Teng, “Test problems for quasi-satellite packing: Cylinders packing with behavior constraints and all the optimal solutions known,” URL: http://www.optimizationonline.org/DB_HTML/2008/09/2093.html.

  6. G. Fasano and J. D. Pintér (eds.), Space Engineering. Modeling and Optimization with Case Studies, Springer Optimization and its Applications, Vol. 114 (2016).

  7. Z. Sun and H. Teng, “Optimal layout design of a satellite module,” Engineering Optimization, Vol. 35, No. 5, 513–530 (2003).

    Article  Google Scholar 

  8. K. Lei, “Constrained layout optimization based on adaptive particle swarm optimizer,” in: Zhihua Cai, Zhenhua Li, Zhuo Kang, and Yong Liu (eds.), Proc. ISICA 2009, Advances in Computation and Intelligence, LNCS, Vol. 5821, 434–442 (2009).

  9. Yu. Stoyan and T. Romanova, “Mathematical models of placement optimization: Two- and three-dimensional problems and applications,” in: G. Fasano and J. D. Pintér (eds.), Modeling and Optimization in Space Engineering, Springer Optimization and its Applications, Vol. 73, Chap. 15, 363–388 (2013).

  10. I. V. Sergienko and V. P. Shilo, Discrete Optimization Problems: Challenges, Methods, Solutions, and Analysis [in Russian], Naukova Dumka, Kyiv (2003).

    Google Scholar 

  11. N. V. Semenova and L. M. Kolechkina, Vector Discrete Optimization Problems on Combinatorial Sets: Methods of the Analysis and Solution [in Ukrainian], Naukova Dumka, (2009).

  12. A. A. Kovalenko, T. E. Romanova, and P. I. Stetsyuk, “Balance layout problem for 3D-objects: Mathematical model and solution methods,” Cybern. Syst. Analysis, Vol. 51, No. 4, 556–565 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  13. Yu. Stoyan, T. Romanova, A. Pankratov, A. Kovalenko, and P. Stetsyuk, “Modeling and optimization of balance layout problems,” in: G. Fasano and J. D. Pintér (eds.), Space Engineering. Modeling and Optimization with Case Studies, Springer Optimization and its Applications Vol. 114, 177–208 (2016).

  14. E. Reingold, J. Nievergelt, and N. Deo, Combinatorial Algorithms: Theory and Practice, Pearson Education (1977).

  15. Yu. G. Stoyan and I. V. Grebennik, “Description and generation of combinatorial sets having special characteristics,” Intern. J. of Biomedical Soft Computing and Human Sciences, Special Volume “Bilevel Programming, Optimization Methods, and Applications to Economics,” Vol. 18, No. 1, 83–88 (2013).

    Google Scholar 

  16. Yu. Stoyan, A. Pankratov, and T. Romanova, “Quasi-phi-functions and optimal packing of ellipses,” J. of Global Optimization, Vol. 65, No. 2, 283–307 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  17. I. Grebennik and O. Lytvynenko, “Random generation of combinatorial sets with special properties,” An Intern. Quarterly J. on Economics of Technology and Modelling Processes (ECONTECHMOD), Vol. 5, No. 4, 43–48 (2016).

    Google Scholar 

  18. A. Wachter and L. T. Biegler, “On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming,” Mathematical Programming, Vol. 106, No. 1, 25–57 (2006).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Kharkiv National University of Radio Electronics, Kharkiv, Ukraine

    I. V. Grebennik, A. A. Kovalenko & I. A. Urniaieva

  2. A. Podgorny Institute for Mechanical Engineering Problems, Kharkiv, Ukraine

    T. E. Romanova

  3. Kharkiv National University of Home Affairs, Kharkiv, Ukraine

    S. B. Shekhovtsov

Authors
  1. I. V. Grebennik
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  2. A. A. Kovalenko
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  3. T. E. Romanova
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  4. I. A. Urniaieva
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  5. S. B. Shekhovtsov
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Corresponding author

Correspondence to I. V. Grebennik.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 2, March–April, 2018, pp. 55–67.

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Grebennik, I.V., Kovalenko, A.A., Romanova, T.E. et al. Combinatorial Configurations in Balance Layout Optimization Problems. Cybern Syst Anal 54, 221–231 (2018). https://doi.org/10.1007/s10559-018-0023-2

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  • DOI: https://doi.org/10.1007/s10559-018-0023-2

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