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Journal of Automation and Information Sciences
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ISSN Imprimir: 1064-2315
ISSN En Línea: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v51.i1.30
pages 26-40

Polyhedral-Spherical Configurations in Discrete Optimization Problems

Sergey V. Yakovlev
N.E. Zhukovskiy National Aerospace University "Kharkov Aviation Institute", Kharkov
Oxana S. Pichugina
N.E. Zhukovskiy National Aerospace University "Kharkov Aviation Institute", Kharkov
Olga V. Yarovaya
N.E. Zhukovskiy National Aerospace University "Kharkov Aviation Institute", Kharkov

SINOPSIS

A class of polyhedral-spherical configurations as finite point configurations inscribed into a hypersphere is defined. Approaches to determination of configuration parameters are proposed. The properties of optimization problems on polyhedral-spherical configurations are considered, the theorems on existence of convex extensions of functions are formulated and their minima are evaluated. The results are extended to the class of quadratic functions defined on permutation configurations.

REFERENCIAS

  1. Korte B., Vygen J., Combinatorial optimization: theory and algorithms, Springer, Heidelberg, New York, 2018. DOI: https://doi.org/10.1007/978-3-662-56039-6

  2. Papadimitriou C.H., Steiglitz K., Combinatorial optimization: algorithms and complexity, Dover Publications, Mineola, 2013.

  3. Pardalos P.M., Du D-Z., Graham R.L. (Eds.), Handbook of combinatorial optimization, Springer, New York, 2013. DOI: https://doi.org/10.1007/978-1-4419-7997-1

  4. Schrijver A., Combinatorial optimization: polyhedra and efficiency, Springer Science and Business Media, 2002.

  5. Burkard R.E., Quadratic assignment problems, Handbook of combinatorial optimization, 2013, 5, No. 1, 2741–2814. DOI: https://doi.org/10.1007/978-1-4419-7997-1_22

  6. Sergienko I.V., Shilo V.P., Modern approaches to solving complex discrete optimization problems, Journal of Automation and Information Sciences, 2016, 48, No. 1, 15–24. DOI: https://doi.org/ 10.1615/JAutomatInfScien.v48.i1.30

  7. Sergienko I.V., Hulianytskyi L.F., Sirenko S.I., Classification of applied methods of combinatorial optimization, Cybernetics and Systems Analysis, 2009, 45, No. 5, 732–741. DOI: https://doi.org/ 10.1007/s10559-009-9134-0

  8. Zgurovkiy M.Z., Pavlov A.A., Challenging problems of combinatorial optimization in planning and decision making [in Russian], Naukova dumka, Kiev, 2016.

  9. Semenova N.V., Kolechkina L.N., Nagornaya A.N., Solution and investigation of vector problems of combinatorial optimization on a set of polypermutations, Journal of Automation and Information Sciences, 2008, 40, No. 6, 27–42. DOI: https://doi.org/10.1615/JAutomatInfScien.v40.i12.30

  10. Hulianytskyi L., Riasna I., Formalization and classification of combinatorial optimization problems, Springer Optimization Methods and its Applications, 2017, 130, 239–250. DOI: https://doi.org/ 10.1007/978-3-319-68640-0_11

  11. Berge C., Principes de combinatoire, Dunod, Paris, 1968.

  12. Stoyan Yu.G., Yakovlev S.V., Mathematical models and optimization methods of geometric design [in Russian], Naukova dumka, Kiev, 1986.

  13. Stoyan Yu.G., Yemetz O.O., Theory and methods of Euclidean combinatorial optimization [in Ukrainian], Instytut systemnykh doslidzhen osvity, Kyiv, 1993.

  14. Stoyan Yu.G., Yakovlev S.V., Pichugina O.S., Euclidean combinatorial configurations [in Russian], Konstanta, Kharkov,2017.

  15. Pichugina O.S., Yakovlev S.V., Continuous functional representations in discrete optimization problems [in Russian], Zolotaya milya, Kharkov, 2018.

  16. Ferreira O.P., Iusem A.N., Németh S.Z., Concepts and techniques of optimization on the sphere, TOP, 2014, 22, No. 3, 1148–1170. DOI: https://doi.org/10.1007/s11750-014-0322-3

  17. Gräf M., Hielscher R, Fast global optimization on the torus, the sphere, and the rotation group, SIAM J. Optim., 2015, 25, No. 1, 540–563. DOI: http://doi.org/10.1137/130950070

  18. Yakovlev S.V., The theory of convex continuations of functions on vertices of convex polygons, Computational Mathematics and Mathematical Physics, 1994, 34, No. 7, 959–965, https://dl.acm.org/ citation.cfm?id=196926.

  19. Yakovlev S., Convex extensions in combinatorial optimization and their applications, Springer Optimization Methods and its Applications, 2017, 130, 567–584. DOI: http://doi.org/10.1007/ 978-3-319-68640-0_27

  20. Yakovlev S.V., Bounds on the minimum of convex functions on Euclidean combinatorial sets, Cybernetics, 1989, 25, No. 3, 385–391. DOI: http://dx.doi.org/10.1007/BF01069996

  21. Pichugina O.S., Yakovlev S.V., Continuous representations and functional extensions in combinatorial optimization, Cybernetics and Systems Analysis, 2016, 52, No. 6, 921–930, DOI:. DOI: http://doi.org/10.1007/ s10559-016-9894-2

  22. Pichugina O.S., Yakovlev S.V., Functional and analytic representations of the general permutations. Eastern-European Journal of Enterprise Technologies, 2016, 1, No. 4, 27–38. DOI: http://doi.org/ 10.15587/1729-4061.2016.58550

  23. Yakovlev S.V., Grebennik I.V., Localization of solutions of some problems of nonlinear integer optimization, Cybernetics and Systems Analysis, 1993, 29, No. 5, 727–734. DOI: https://doi.org/ 10.1007/BF01125802

  24. Stoyan Y.G., Yakovlev S.V., Parshin O.V., Quadratic optimization on combinatorial sets in , Cybernetics and Systems Analysis, 1991, 27, No. 4, 562–567, DOI:. DOI: http://dx.doi.org/10.1007/ BF01130367

  25. Yakovlev S.V., Pichugina O.S., Properties of combinatorial optimization problems over polyhedral-spherical sets, Cybernetics and Systems Analysis, 2018, 54, No. 1, 385–391. DOI: https://doi.org/ 10.1007/s10559-018-0011-6

  26. Pichugina O., Yakovlev S., Optimization on polyhedral-spherical sets: theory and applications, In 2017 IEEE First Ukraine Conference on Electrical and Computer Engineering (UKRCON). Proceedings, 2017, 1167–1175. DOI: https://doi.org/10.1109/UKRCON.2017.8100436

  27. Schneider P., Eberly D.H., Geometric tools for computer graphics, Morgan Kaufmann, Amsterdam, 2002.

  28. Yemelichev V.A., Kovalev M.M., Kravtsov M.K., Polyhedrons, graphs, optimization (combinatorial theory of polyhedrons) [in Russian], Nauka, Moscow, 1981.

  29. Stoyan Y.G., Yakovlev S.V., Emets O.A., Valuiskaya O.A., Construction of convex continuations for functions defined on hypersphere, Cybernetics and Systems Analysis, 1998, 34, No. 2, 176–184. DOI: https://doi.org/10.1007/BF02742066

  30. Yakovlev S., Pichugina O., Yarovaya O., On polyhedral-spherical configurations: modelling and optimization, In 2018 International Conference on Innovations in Engineering, Technology and Sciences (ICIETS). Proceedings, Karnataka, India, 2018, 100–105.

  31. Yakovlev S., Pichugina O., Yarovaya O., On optimization problems on the polyhedral-spherical configurations with their properties, In 2018 IEEE First International Conference on System Analysis and Intelligent Computing (SAIC 2018). Proceedings, Kyiv, 2018, 94–100. DOI: http://dx.doi.org/ 10.1109/SAIC.2018.8516801

  32. Yakovlev S.V., Valuiskaya O.A., Optimization of linear functions at the vertices of a permutation polyhedron with additional linear constraints, Ukrainian Mathematical Journal, 2001, 53, No. 9, 1535–1545. DOI: https://doi.org/10.1023/A:1014374926840

  33. Stoyan Y.G., Yakovlev S.V., Configuration space of geometric objects, Cybernetics and Systems Analysis, 2018, 54, No. 5, 716–726. DOI: https://doi.org/10.1007/s10559-018-0073-5

  34. Yakovlev S.V., On some classes of spatial configurations of geometric objects and their formalization, Journal of Automation and Information Sciences, 2018, 50, No. 5, 73–84. DOI: https://doi.org/ 10.1615/JAutomatInfScien.v50.i9.30

  35. Yakovlev S.V., The method of artificial space dilation in problems of optimal packing of geometric objects, Cybernetics and Systems Analysis, 2017, 53, No. 5, 725–731. DOI: https://doi.org/10.1007/ s10559-017-9974-y

  36. Yakovlev S., Kartashov O., System analysis and classification of spatial configurations, In 2018 IEEE First International Conference on System Analysis and Intelligent Computing (SAIC 2018). Proceedings, Kiev, 2018, 90–93. DOI: https://doi.org/10.1109/SAIC.2018.8516760

  37. I.V. Grebennik, A.A. Kovalenko, T.E. Romanova, I.A. Urniaieva, S.B. Shekhovtsov, Combinatorial configurations in balance layout optimization problems, Cybernetics and Systems Analysis, 2018, 54, No. 2, 221–231. DOI: https://doi.org/10.1007/s10559-018-0023-2

  38. Chernov N., Stoyan Y., Romanova T., Mathematical model and efficient algorithms for object packing problem, Computational Geometry: Theory and Applications, 2010, 43, No. 5, 535–553. DOI: https://doi.org/10.1016/j.comgeo.2009.12.003

  39. Yakovlev S.V., On a class of problems on covering of a bounded set, Acta Mathematica Hungarica. 1989, 53, No. 3, 253–262. DOI: https://doi.org/10.1007/BF01953365

  40. Shekhotsov S.B., Yakovlev S.V., Formalization and solution of one class of covering problem in design of control and monitoring systems, Avtomatica i telemekhanika, 1989, No. 5, 160–168.

  41. Stoyan Yu.G., Sokolovskii V.Z., Yakovlev S.V., Method of balancing rotating discretely distributed masses, Energomashinostroenie, 1982, No. 2, 4–5, https://www.osti.gov/etdeweb/biblio/6490782.

  42. Pichugina O., Placement problems in chip design: modeling and optimization, In 2017 IEEE 4th International Scientific-Practical Conference Problems of Infocommunications Science and Technology. Proceedings, Kharkiv, 2017, 465–473. DOI: https://doi.org/10.1109/INFOCOMMST. 2017.8246440

  43. Farzad B., Pichugina O., Koliechkina L., Multi-layer community detection, In 2018 International Conference on Control, Artificial Intelligence, Robotics and Optimization (ICCAIRO). Proceedings, Prague, 2018, 101–108.

  44. Gerasin S.N., Shlyakhov V.V., Yakovlev S.V., Set coverings and tolerance relations, Cybernetics and Systems Analysis, 2008, 43, No. 3, 333–340. DOI: https://doi.org/10.1007/s10559-008-9007-y

  45. Yakovlev S., Kartashov O., Yarovaya O., On class of genetic algorithms in optimization problems on combinatorial configuration, In 2018 IEEE XIІI International Scientific and Technical Conference on Computer Sciences and Information Technologies (CSIT 2018). Proceedings, Lviv, 2018, 374–377. DOI: https://doi.org/10.1109/STC-CSIT.2018.8526

  46. Yakovlev S., Kartashov O., Pichugina O., Koliechkina L., The Genetic Algorithms in Optimization Problem on Combinatorial Configurations, In 2018 International Conference on Innovations in Engineering, Technology and Sciences (ICIETS). Proceedings, Karnataka, India, 2018, 106–111.


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