Control Systems and Computers

https://doi.org/10.15407/csc.2020.02.023

Control Systems and Computers, 2020, Issue 2 (286), pp. 23-29.

UDK  364.2:331; 681.513

L.M. KOLIECHKINA, Doctor of Physical and mathematical sciences, Professor, University of Lodz, 22 Banaha st., Lodz, 90-238, Poland, lkoliechkina@gmail.com

 O.A. DVIRNA, PhD, Physical and mathematical, Assistant, Poltava University of Economics and Trade, 3 Koval st., Poltava, 36000, Ukraine, lenadvirna@gmail.com

A.M. NAHIRNA, PhD, Physical and mathematical, Associate Professor, National University of “Kyiv-Mohyla Academy”, 2 Skovoroda st. , Kyiv, 04070, Ukraine, naghirnaalla@ukr.net

CONSTRUCTION OF A MATHEMATICAL MODEL OF MULTIOBJECTIVE OPTIMIZATION ON PERMUTATIONS

The article is devoted to the problem of constructing and solving mathematical models of applied problems as multiobjective problems on combinatorial configurations. This question is an actual branch because any task of optimal design of complex economic and technical systems, technological devices, planning, and management etc. requires that the desired solution be found consider many criteria.

It is used transfer to Euclidian combinatorial configurations and using discrete optimizations methods. Method for solving such problems is considered and it includes the analysis of structural graph of Euclidean combinatorial configurations sets. These methods can be modified by combining with other multiobjective optimization approaches depending on the initial conditions of the problem.

Models for defining real estate contribution plans and production planning as multiobjective discrete problems are proposed. These models can be supplemented as needed by the required functions and, depending on the initial conditions, are presented as tasks on different sets of combinatorial configurations.

 Download full text! (On English!)

 Keywords: optimization problems, combinatorial configurations, Euclidean combinatorial set, optimization problems model, optimal solutions set.

1. Ehrgott, M., 2005. Multicriteria Optimization. Springer, Berlin: New York, 323 p.
2. Ehrgott, M., Gandibleux, X., 2003. “Multiobjective Combinatorial Optimization – Theory, Methodology, and Applications”. In: Ehrgott, M. and Gandibleux, X. (eds.) Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys, Springer US, pp. 369-444. 
   https://doi.org/10.1007/0-306-48107-3_8
3. Tymofiyeva, N.K., Grytsenko, V.I., 2017. “Combinatory in the Artificial Intellect Problems”. Upravlausie sistemi i masiny, 2, pp. 6-19, 37. (In Ukrainian).
4. Koliechkina, L., Pichugina, O., 2018. “Multiobjective Optimization on Permutations with Applications”. DEStech Transactions on Computer Science and Engineering, pp. 61-75, 
   https://doi.org/10.12783/dtcse/optim2018/27922
5. Koliechkina, L.N., Dvirna, O.A., Nagornaya, A.N., 2014. “Modified Coordinate Method to Solve Multicriteria Optimization Problems on Combinatorial Configurations”. Cybernetics and Systems Analysis, 59 (4), pp. 620-626.
   https://doi.org/10.1007/s10559-014-9650-4
6. Korte, B., Vygen, J., 2018. Combinatorial Optimization: theory and algorithms. Heidelberg; New York: Springer, 698 p.
   https://doi.org/10.1007/978-3-662-56039-6
7. Pardalos, P.M., Du, D-Z., Graham, R.L., 2013. Handbook of combinatorial optimization. New York: Springer, 3409 p.
   https://doi.org/10.1007/978-1-4419-7997-1
8. Papadimitriou, C.H., Steiglitz, K., 2013. Combinatorial optimization: algorithms and complexity. Mineola: Dover Publications, 528 p.
9. Sergienko, I.V., Shilo, V.P., 2016. “Modern approaches to solving complex discrete optimization problems”. Journal of Automation and Information Sciences, 48(1), pp.15-24.
   https://doi.org/10.1615/JAutomatInfScien.v48.i1.30
10. Hulianytskyi, L., Riasna, I., 2017. “Formalization and classification of combinatorial optimization problems”. Optimization Methods and Applications, S. Butenko et al.(eds.). Springer, New York, pp. 239-250.
    https://doi.org/10.1007/978-3-319-68640-0_11
11. Farzad, B., Pichugina, O., Koliechkina, L., 2018. “Multi-Layer Community Detection”. International Conference on Control, Artificial Intelligence, Robotics Optimization (ICCAIRO), pp. 133-140.
    https://doi.org/10.1109/ICCAIRO.2018.00030
12. Koliechkina, L., Pichugina, O., 2019. “A Horizontal Method of Localizing Values of a Linear Function in Permutation-Based Optimization”. In: Le Thi, H.A., Le, H.M., and Pham Dinh, T. (eds.) Optimization of Complex Systems: Theory, Models, Algorithms and Applications, Springer, Cham, pp. 355-364. 
    https://doi.org/10.1007/978-3-030-21803-4_36
13. Koliechkina, L., Pichugina, O., Yakovlev, S., 2020. “A Graph-Theoretic Approach to Multiobjective Permutation-Based Optimization”. In: Jacimovic, M., Khachay, M., Malkova, V., and Posypkin, M. (eds.) Optimization and Applications, Springer International Publishing, Cham, pp. 383-400.
    https://doi.org/10.1007/978-3-030-38603-0_28
14. Koliechkina, L., Nahirna, A., Dvirna, O., 2019. “Quadratic Optimization Problemon Permutation Setwith Simulationof Applied Tasks”. Proceedings of the Second International Workshop on Computer Modeling and Intelligent Systems (CMIS-2019), Zaporizhzhia, Ukraine, April 15-19, 2019, Vol. 2353, pp. 651-663. http://ceur-ws.org/Vol-2353/paper52.pdf.
15. Kozin, I.V., Kryvtsun, O.V., Pinchuk, V.P., 2015. “Evolutionary-Fragmentary Model of the Routing Problem”. Cybern. Syst. Anal., 51, pp. 432-437.
    https://doi.org/10.1007/s10559-015-9734-9
16. Kozin, I.V., Maksyshko, N.K., Perepelitsa, V.A., 2017. “Fragmentary Structures in Discrete Optimization Problems”. Cybern. Syst. Anal., 53, pp. 931-936.
    https://doi.org/10.1007/s10559-017-9995-6
17. Yakovlev, S., Pichugina, O., 2019. “On Constrained Optimization of Polynomials on Permutation Set”. In: Proceedings of the Second International Workshop on Computer Modeling and Intelligent Systems (CMIS-2019). CEUR, Vol. 2353, pp. 570–580. http://ceur-ws.org/Vol-2353/paper45.pdf
18. Yakovlev, S., Pichugina, O., Yarovaya, O., 2019. “Polyhedral-spherical configurations in discrete optimization problems”. Journal of Automation and Information Sciences, 51, pp. 26-40. 
    https://doi.org/10.1615/JAutomatInfScien.v51.i1.30
19. Emets, O.A., Nedobachii, S.I., Kolechkina, L.N., 2009. “An irreducible set of combinatorial polyhedron constraints in the linear-fractional optimization problem on permutations”. Discrete Mathematics and Applications. 11, pp. 95-103. 
    https://doi.org/10.1515/dma.2001.11.1.95
20. Chase, P., 1973. “Transposition Graphs”. SIAM J. Comput. 2, pp. 128-133.
    https://doi.org/10.1137/0202011
21. Donets, G., Koliechkina, L., Nahirna, A., 2020. “A Method to Solve Conditional Optimization Problems with Quadratic Objective Functions on the Set of Permutations”. Cybernetics and Systems Analysis, 56 (2), pp. 278-288.
    https://doi.org/10.1007/s10559-020-00243-8

Received 14.04.2020