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Parallel Computing Technologies for Solving Optimization Problems of Geometric Design

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Cybernetics and Systems Analysis Aims and scope

This paper describes the application of parallel computing technologies in systems with shared and distributed memory for solving optimization problems of geometric design. The first technology is based on the maximin properties of phi-functions for composite objects, and the second technology uses the multistart strategy and methods for minimizing nonsmooth functions. This allowed to several times reduce time expenditures for searching for locally optimum placements of 2D and 3D objects and to obtain better results as for the objective function value.

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References

  1. X. Liu, J. Liu, and A. Cao, “HAPE3D — a new constructive algorithm for the 3D irregular packing problem,” Frontiers Inf. Technol. Electronic Eng., Vol. 16, No. 5, 380–390 (2015).

  2. L. Guangqiang, Z. Fengqiang, Z. Rubo, Du Jialu Du., G. Chen, and Z. Yiran, “A parallel particle bee colony algorithm approach to layout optimization,” Journal of Computational and Theoretical Nanoscience, Vol. 13, No. 7, 4151–4157 (2016).

  3. K. Karabulut and M. A. Inceoglu, “Hybrid genetic algorithm for packing in 3D with deepest bottom left with fill method,” in: T. Yakhno (ed.), Advances in Information Systems ADVIS’2004; Lecture Notes in Computer Science, Vol. 3261, 441–450 (2004).

  4. I. Litvinchev, L. Infante, and L. Ozuna, “Approximate packing: integer programming models, valid inequalities and nesting,” in: G. Fasano and J. D. Pinter (eds.), Optimized Packings and Their Applications (Ser. Springer Optimization and Its Applications), Vol. 105, 187–205 (2015).

  5. I. Litvinchev, L. Infante, and L. Ozuna, “Packing circular-like objects in a rectangular container,” Journal of Computer and Systems Sciences International, Vol. 54, No. 2, 259–267 (2015).

  6. E. K. Burke, R. S. R. Hellier, G. Kendall, and G. Whitwell, “Irregular packing using the line and arc no-fit polygon,” Operations Research, Vol. 58, No. 4, 948–970 (2010).

  7. L. H. Cherri, L. R. Mundim, M. Andretta, F. M. Toledo, J. F. Oliveira, and M. A. Carravilla, “Robust mixed-integer linear programming models for the irregular strip packing problem,” European Journal of Operational Research, Vol. 253, 570–583 (2016).

  8. Yu. Stoyan and T. Romanova, “Mathematical models of placement optimization: Two- and three-dimensional problems and applications,” in: G. Fasano and J. D. Pinter (eds.), Modeling and Optimization in Space Engineering (Ser. Springer Optimization and Its Applications), Vol. 73, Springer, New York (2012).

  9. Yu. Stoyan and S. Yakovlev, “Configuration space of geometric objects,” Cybernetics and Systems Analysis, Vol. 54, No. 5, 716–726 (2018).

  10. Yu. Stoyan, A. Pankratov, and T. Romanova, “Placement problems for irregular objects: Mathematical modeling, optimization and applications,” in: S. Butenko, P. Pardalos, and V. Shylo (eds.), Optimization Methods and Applications: Modeling and Optimization in Space Engineering (Ser. Springer Optimization and Its Applications), Vol. 130, Springer, New York (2017), pp. 521–559.

  11. Yu. Stoyan and A. Chugay, “Mathematical modeling of the interaction of non-oriented convex polytopes,” Cybernetics and Systems Analysis, Vol. 48, No. 6, 837–845 (2012).

  12. Yu. Stoyan, A. Pankratov, and T. Romanova, “Cutting and packing problems for irregular objects with continuous rotations: Mathematical modeling and nonlinear optimization,” Journal of the Operational Research Society, Vol. 67, Iss. 5, 786–800 (2016).

  13. Yu. Stoyan, A. Pankratov, T. Romanova, A. Chugay, “Optimized object packings using quasi- phi-functions,” in: G. Fasano and J. D. Pinter (eds.), Optimized Packings and Their Applications (Ser. Springer Optimization and Its Applications), Vol. 105, Springer, New York (2015), pp. 265–291.

  14. Y. G. Stoyan and A. M. Chugay, “Packing different cuboids with rotations and spheres into a cuboid,” Advances in Decision Sciences (2014). URL: https://www.hindawi.com/journals/ads/2014/571743.

  15. Y. G. Stoyan, V. V. Semkin, and A. M. Chugay, “Modeling close packing of 3D objects,” Cybernetics and Systems Analysis, Vol. 52, No. 2, 296–304 (2016).

  16. Y. E. Stoian, A. M. Chugay, A. V. Pankratov, and T. E. Romanova, “Two approaches to modeling and solving the packing problem for convex polytopes,” Cybernetics and Systems Analysis, Vol. 54, No. 4, 585–593 (2018).

  17. T. Romanova, J. Bennell, Yu. Stoyan, and A. Pankratov, “Packing of concave polyhedra with continuous rotations using nonlinear optimization,” European Journal of Operational Research, Vol. 268, Iss. 1, P 37–53 (2018).

  18. A. Pankratov, T. Romanova, I. Litvinchev, “Packing ellipses in an optimized convex polygon,” Journal of Global Optimization (2019). https://doi.org/10.1007/s10898-019-00777-y.

  19. A. Pankratov, T. Romanova, and I. Litvinchev, “Packing ellipses in an optimized rectangular container,” Wireless Networks (2018). https://doi.org/10.1007/s11276-018-1890-1.

  20. T. Romanova, A. Pankratov, I. Litvinchev, Yu. Pankratova, and I. Urniaieva, “Optimized packing clusters of objects in a rectangular container,” Mathematical Problems in Engineering, Vol. 2019. Article ID 4136430. 12 p. https://doi.org/10.1155/2019/4136430.

  21. Y. Wang, C. L. Lin, and J. D. Miller, “3D image segmentation for analysis of multisize particles in a packed particle bed,” Powder Technology, Vol. 301, 160–168 (2016).

  22. S. X. Li, J. Zhao, P. Lu, and Y. Xie, “Maximum packing densities of basis 3D objects,” Chinese Science Bulletin, Vol. 55, Iss. 2, 114–119 (2010).

  23. A. Ramya and S. Vanapalli, “3D printing technologies in various applications,” International Journal of Mechanical Engineering and Technology, Vol. 7, No. 3, 396–409 (2016).

  24. M. Baumers, P. Dickens, C. Tuck, and R. Hague, “The cost of additive manufacturing: Machine productivity, economies of scale and technology-push,” Technological Forecasting & Social Change, Vol. 102, Iss. C, 193–201 (2016).

  25. V. V. Voyevodin and Vl. V. Voyevodin, Parallel Computations [in Russian], BHV-Petersburg, St. Petersburg (2002).

  26. Cluster complex of the Institute of Cybernetics. Cluster complex SKIT. URL: https://icybcluster.org.ua/.

  27. A. Chugay and Ye. Stoian, “Cluster packing of concave non-oriented polyhedra in a cuboid,” Advanced Information Systems, Vol. 2, No. 1, 16–21 (2018).

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

  29. Yu. Stoyan, T. Romanova, A. Pankratov, A. Kovalenko, and P. Stetsyuk, “Balance layout problems: Mathematical modeling and nonlinear optimization,” in: G. Fasano and J. Pintѐr (eds.), Space Engineering: Modeling and Optimization with Case Studies (Ser. Springer Optimization and its Applications), Vol. 114, pp. 369–400 Springer, New York (2016).

  30. P. Stetsyuk, T. Romanova, and G. Scheithauer, “On the global minimum in a balanced circular packing problem,” Optimization Letters, Vol. 10, Iss. 6, 1347–1360 (2016).

  31. P. I. Stetsyuk, “Shor’s r-algorithms: Theory and practice,” in: S. Butenko, P. M. Pardalos, and V. Shylo (eds.), Optimization Methods and Applications, In Honor of the 80th Birthday of Ivan V. Sergienko, Springer, New York (2017), pp. 495–520.

  32. P. I. Stetsyuk, “Theory and software implementations of Shor’s r-Algorithms,” Cybernetics and Systems Analysis, Vol. 53, No. 5, 692–703 (2017).

  33. P. I. Stetsyuk, Methods of Ellipsoids and r-Algorithms [in Russian], Eureka, Chisinau (2014).

  34. P. I. Stetsyuk and O. P. Lykhovyd, Computer program “A parallel algorithm for a balanced circular packing problem,” Certificate of Copyright Registration for Work No. 62184 of 10.20.2015, Ministry of Education and Science of Ukraine, State Department of Intellectual Property.

  35. A. P. Lykhovyd, “On implementation of parallel algorithm for solving balance circular packing problems,” in: Theory of Optimal Solutions, V. M. Glushkov Institute of Cybernetics of NAS of Ukraine, Kyiv (2015), pp. 154–159

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Authors and Affiliations

  1. A. Pidgorny Institute of Mechanical Engineering Problems, National Academy of Science of Ukraine, Kharkiv, Ukraine

    T. E. Romanova & A. M. Chugay

  2. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    P. I. Stetsyuk

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

    S. B. Shekhovtsov

Authors
  1. T. E. Romanova
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  2. P. I. Stetsyuk
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  3. A. M. Chugay
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  4. S. B. Shekhovtsov
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Correspondence to T. E. Romanova.

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Translated from Kibernetika i Sistemnyi Analiz, No. 6, November–December, 2019, pp. 17–29

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Romanova, T.E., Stetsyuk, P.I., Chugay, A.M. et al. 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

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  • DOI: https://doi.org/10.1007/s10559-019-00199-4

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