AN EFFICIENT METHOD FOR SOLVING THE PROBLEM OF CHANNEL POWER DISTRIBUTION TAKING INTO ACCOUNT FUZZY CONSTRAINTS ON CONSUMPTION VOLUMES

Authors

  • E. V. Ivohin Shevchenko National University of Kyiv, Kyiv, Ukraine, Ukraine
  • L. T. Adzhubey Taras Shevchenko National University of Kyiv, Kyiv, Ukraine, Ukraine
  • V. V. Gavrylenko National Transport University, Kyiv, Ukraine, Ukraine
  • N. V. Rudoman National Transport University, Kyiv, Ukraine, Ukraine

DOI:

https://doi.org/10.15588/1607-3274-2022-2-12

Keywords:

data transfer, power distribution, fuzzy constraints, optimal solution, backtracking algorithm

Abstract

Context. An efficient algorithm has been developed for solving the problem of rational distribution of the power of data transmission channels with fuzzy restrictions on consumption volumes. A standard solution method based on a fuzzy optimization problem is considered. A constructive variant of finding a solution based on the backtracking method is proposed.

Objective. The goal of the work is to develop an algorithm for solving the problem of rational distribution of the power of data transmission channels with fuzzy restrictions on consumption volumes based on the backtracking method.

Method. This paper The article proposes a method for solving the problem of rational distribution of the power of data transmission channels, taking into account fuzzy restrictions on consumption volumes. A feature of such tasks is the inability to meet the needs of the end user at the expense of the resources of different suppliers. The method of solution based on fuzzy problems of mathematical programming is considered. A constructive algorithm for solving the problem based on the backtracking method has been developed. Computational experiments have been carried out.

Results. The developed method for solving the problem of rational distribution of data transmission channel capacities, taking into account fuzzy restrictions on consumption volumes, made it possible to solve the problem of constructing an optimal configuration of a three-level information and computer network with a given number of communication servers and taking into account fuzzy consumption volumes.

Conclusions. Methods for solving the problem with fuzzy restrictions on the consumption volumes of end users are investigated. A fuzzy optimization problem is formulated, which allows taking into account the interval specified volumes for the connection values. A variant of solving fuzzy optimization problems in the case of using fuzzy numbers is proposed. A multi-criteria problem of efficient distribution of communication channel powers with fuzzy restrictions is formulated. A variant of the algorithm with a return is proposed, which allows solving the obtained problem. The approach is illustrated by a number of numerical examples for the problem of forming a network structure with a given number of end users and different allowable bandwidths of communication servers.

Author Biographies

E. V. Ivohin, Shevchenko National University of Kyiv, Kyiv, Ukraine

Dr. Sc., Professor, Professor of the Department of System Analysis and Decision Support TheoryTaras 

L. T. Adzhubey, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

PhD, Associate Professor, Associate Professor of the Computational Mathematics Department

V. V. Gavrylenko, National Transport University, Kyiv, Ukraine

Dr. Sc., Professor, Professor of the Department of Information Systems and Technologies

N. V. Rudoman, National Transport University, Kyiv, Ukraine

Senior lecturer of the Department of Information Systems and Technologies

References

Afraimovich L. G., Prilutskii M. Kh. Multiindex Resource Distributions for Hierarchical Systems, Automation and remote control, 2006, Vol. 67, No. 6, pр. 1007–1016.

Prilutskii M.Kh. Many-Criteria Distribution of a Homogeneous Resource in Hierarchical Systems, Automation and Remote Control, 1996, No. 2, С. 24–29.

Afraimovich L.G. Multiindex transportation problems with 2-embedded structure, Automation and remote control,2013, Vol. 74, pp. 90–104. DOI: 10.1134/S0005117913010086

Filgus D.I. Optimisation of the process of managing requests in distributed information systems, International Journal of Applied and Fundamental Research, 2018, Iss.4, pp. 34–42. DOI: 10.17513/mjpfi.12179

Schrijver А., Letchford A. N. Theory of Linear and Integer Programming, The Journal of the Operational Research Society, Vol. 51, Iss. 7, pp. 892–893. DOI: 10.2307/253980

Levner E. Multiprocessor Scheduling, Theory and Applications. London, IntechOpen, 2007. [Online]. Available from: https://www.intechopen.com/books/3596. DOI: 10.5772/52

Pentico D. W. Assignment problems: A golden anniversary survey, European Journal of Operational Research, 2007. Vol. 176, pp. 774–793. DOI: 10.1016/j.ejor.2005.09.014

Ivokhin Е., Makhno M. On an approach to construction of structured fuzzy sets and their application for description of fuzzy time response, Journal of Automation and Information Science, 2017, 49(10), pp. 55–63. DOI: 10.1615/JAutomatInfScien.v49.i10.60

Spieksma F.C.R. P.M. Pardalos, L.S. Pitsoulis (Eds.). Multi index assignment problems: complexity, approximation, applications, Nonlinear Assignment Problems. Algorithms and Applications. Dordrecht, Kluwer Academic Publishers, 2000. – P. 1–11. DOI:10.1007/978-1-4757-3155-2_1

Crama Y., Spieksma F.C.R. Approximation algorithms for three-dimensional assignment problems with triangle inequalities, European Journal of Operational Research. – 1992, Vol. 60, pp. 273–279. DOI: 10.1016/0377-2217(92)90078-N

Afraimovich L. G., Prilutskii M. K. Multiindex optimal production planning problems, Automation and remote control, 2010, Vol. 71, pp. 2145–2151. DOI: 10.1134/S0005117910100139.

Orlin J.B. A Faster strongly polynomial minimum cost flow algorithm, Operations research, 1993, Vol. 41, Issue 2, pp. 338–350. DOI: 10.1145/62212.62249

Lukac Z., Hunjet D., Neralic L. Solving the productiontransportation problem in the Petroleum Industry, Revista Investigacion Operacional, 2008, Vol. 29, Issue 1, pp. 63–70.

Ivokhin Е., Аpanasenko D., Navrodskiy V. About production-transport problem reduction to the two-level problem of discrete optimization and its application, Вulletin of Taras Shevchenko Nathional University of Kiev: Еkonomics, 2018, No. 3(198), pp. 48–53. DOI:10.17721/1728-2667.2018/198-3/6

Zadeh L. A. Fuzzy sets, Information and Control, 1965, Vol. 8, pp. 338–353. DOI: 10.1016/S0019-9958(65)90241-X

Bellman R. E., Zadeh L. A. Local and fuzzy logics, Modern Uses of Multiple-Valued Logics, edited by J. M. Dunn and G. Epstein, D. Reidel. Dordrecht-Holland, 1977, pp. 103 – 165. DOI: 10.1007/978-94-010-1161-7_6

Dubois D., Prade H. Systems of linear fuzzy constraints, Fuzzy Sets and Systems, 1980, Vol. 3, Issue 1, pp. 37–48. DOI: 10.1016/0165-0114(80)90004-4

Bablu Jana, Tapan Kumar Roy Multi-Objective Fuzzy Linear Programming and Its Application in Transportation Model, Tamsui Oxford Journal of Mathematical Sciences, 2005, 21(2), pp. 243–268.

Zimmermann H. J. Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and System, 1978, No. 1, pp. 45–55. DOI:10.1016/0165-0114(78)90031-3

Vajda S. Linear programming, Linear Programming. Dordrecht, Springer, 1981, 15 p. DOI: 10.1007/978-94-011-6924-0_1

Bellman R. E., Zadeh L. A. Decision making in a fuzzy environment, Management Science, 1970, No. 17, pp.141–164. DOI: 10.1287/mnsc.17.4.B141

Pavlov Yu. P., Andreev R. D. Decision Support Fundamentals, In Decision Control, Management, and Support in Adaptive and Complex Systems: Quantitative Models. Hershey, PA, IGI Global, 2013. DOI: 10.4018/978-1-4666-2967-7.ch001

Watson Des. A Practical Approach to Compiler Construction. Springer, 2017, 254 р. DOI: 10.1007/978-3-319-52789-5

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Published

2022-06-21

How to Cite

Ivohin, E. V., Adzhubey, L. T., Gavrylenko, V. V., & Rudoman, N. V. (2022). AN EFFICIENT METHOD FOR SOLVING THE PROBLEM OF CHANNEL POWER DISTRIBUTION TAKING INTO ACCOUNT FUZZY CONSTRAINTS ON CONSUMPTION VOLUMES. Radio Electronics, Computer Science, Control, (2), 122. https://doi.org/10.15588/1607-3274-2022-2-12

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Section

Progressive information technologies