Published February 28, 2023 | Version v1
Journal article Open

Features in solving individual tasks to develop service-oriented networks using dynamic programming

Creators

  • 1. Institute of Telecommunications and Global Information Space of National Academy of Sciences of Ukraine; Ternopil Ivan Puluj National Technical University, Ukraine
  • 2. Institute of Telecommunications and Global Information Space of National Academy of Sciences of Ukraine; Kyiv City State Administration , Ukraine
  • 3. Institute of Telecommunications and Global Information Space of National Academy of Sciences of Ukraine, Ukraine

Description

The object of this study is an approach to solving the problems of designing service-oriented networks that warn about emergencies using dynamic programming. The main issue is the complexity of algorithmization of processes that describe the achievement of an optimal solution in multi-stage nonlinear problems. The possibilities of applying the Bellman optimality principle for solving the set tasks for the purpose of their application in the field of engineering and technology are determined. Based on the Bellman functional equation, a model of the optimal number of sensors in the monitoring system for warning of emergencies was built.

A feature of the design is that using the classical Bellman equation, it is proposed to solve problems of various technical directions, provided that the resource determines what exactly makes it possible to optimize work in any way. Important with this approach is the planning of the action as an element of some problem with the augmented state. After that, the proposed structure in formal form extends to other objects.

A problem was proposed and considered, which confirmed the mathematical calculations, as a result of which an optimal plan for replacing the sensors of the system was obtained; and the possibilities of significant cost reduction were identified. In the considered example, an optimal plan for replacing the system sensors was compiled and the possibility of reducing costs by 31.9 % was proved.

The proposed option was used in the development of information technology for modeling a service-oriented network based on energy-efficient long-range protocols; some of the identified features were further developed in the design of a recommendation system for issuing loans and developing an interactive personnel training system

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References

  • Minu, M. (1990). Matematicheskoe programmirovanie. Teoriia i algoritmy. Moscow: Nauka. Gl. red. fiz.mat. lit., 488.
  • Dreyfus, S. (2002). Richard Bellman on the Birth of Dynamic Programming. Operations Research, 50 (1), 48–51. doi: https://doi.org/10.1287/opre.50.1.48.17791
  • Bellman, R. E, Kalaba, R. E. (1959). Dynamic Programming and Feedback Control. RAND Corporation, 1778.
  • Dreyfus, S. (2003). Richard Ernest Bellman. International Transactions in Operational Research, 10 (5), 543–545. doi: https://doi.org/10.1111/1475-3995.00426
  • Kamien, M. I., Schwartz, N. L. (1991). Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management. Amsterdam: Elsevier, 259–263.
  • Cormen, T. H., Leiserson, C. E., Rivest, R. L., Stein, C. (2001). Introduction to Algorithms. MIT Press & McGraw-Hill, 1184.
  • Giegerich, R., Meyer, C., Steffen, P. (2004). A discipline of dynamic programming over sequence data. Science of Computer Programming, 51 (3), 215–263. doi: https://doi.org/10.1016/j.scico.2003.12.005
  • Meyn, S. (2007). Control Techniques for Complex Networks. Cambridge University Press. doi: https://doi.org/10.1017/cbo9780511804410
  • Boyd, S. P., Vandenberghe, L (2004). Convex Optimization. Cambridge University Press, 727. doi: https://doi.org/10.1017/cbo9780511804441
  • Sniedovich, M. (2006), Dijkstra's algorithm revisited: the dynamic programming connexion. Journal of Control and Cybernetics, 35 (3), 599–620.
  • Vasilev, O. M. (2022). Programuvannia movoiu Python. Ternopіl: Navchalna kniga – Bogdan, 504.
  • Dreyfus, S. (2002). Richard Bellman on the Birth of Dynamic Programming. Operations Research, 50 (1), 48–51. doi: https://doi.org/10.1287/opre.50.1.48.17791
  • Bellman, R. (2003). Dynamic programming (Dover ed). Mineola: Dover Publications, 384.
  • Jones, M., Peet, M. M. (2021). A generalization of Bellman's equation with application to path planning, obstacle avoidance and invariant set estimation. Automatica, 127, 109510. doi: https://doi.org/10.1016/j.automatica.2021.109510
  • Jones, M., Peet, M. M. (2021). Extensions of the Dynamic Programming Framework: Battery Scheduling, Demand Charges, and Renewable Integration. IEEE Transactions on Automatic Control, 66 (4), 1602–1617. doi: https://doi.org/10.1109/tac.2020.3002235
  • Dixit, A. K. (1990). Optimization in economic theory. Oxford: Oxford University Press, 164.
  • Miao, J. (2014). Economic Dynamics in Discrete Time. MIT Press, 134.
  • Kriazhych, O. O., Itskovych, V. Ye. (2022). Internet rechei v upravlinni skladnymy systemamy. Naukovi pidsumky 2022 roku. Kharkiv: PC TECHNOLOGY CENTER, 19.
  • Kuprin, O. M. (2022). Algorithmization of processes in recommendation systems. Mathematical Machines and Systems, 1, 71–80. doi: https://doi.org/10.34121/1028-9763-2022-1-71-80
  • Yushchenko, K. S. (2022). Approach to automating the recruitment process using 3D resumes. Mathematical Machines and Systems, 2, 29–39. doi: https://doi.org/10.34121/1028-9763-2022-2-29-39
  • Kryazhych, O., Kovalenko, O. (2019). Examining a mathematical apparatus of Z-approximation of functions for the construction of an adaptive algorithm. Eastern-European Journal of Enterprise Technologies, 3 (4 (99)), 6–13. doi: https://doi.org/10.15587/1729-4061.2019.170824
  • Trofymchuk, O., Adamenko, O., Trysniuk, V. (2021). Heoinformatsiini tekhnolohii zakhystu dovkillia pryrodno-zapovidnoho fondu. Instytut telekomunikatsii ta hlobalnoho informatsiinoho prostoru, Ivano-Frankivskyi natsionalnyi tekhnichnyi universytet nafty ta hazu. Ivano-Frankivsk: Suprun V. P., 343.