Mathematical Models for the Design of GRID Systems to Solve Resource-Intensive Problems

Tynchenko, Valeriya V.; Tynchenko, Vadim S.; Nelyub, Vladimir A.; Bukhtoyarov, Vladimir V.; Borodulin, Aleksey S.; Kurashkin, Sergei O.; Gantimurov, Andrei P.; Kukartsev, Vladislav V.

doi:10.3390/math12020276

Open AccessArticle

Mathematical Models for the Design of GRID Systems to Solve Resource-Intensive Problems

by

Valeriya V. Tynchenko

^1,2,

Vadim S. Tynchenko

^3,4,5,*

,

Vladimir A. Nelyub

³,

Vladimir V. Bukhtoyarov

^3,5

,

Aleksey S. Borodulin

³,

Sergei O. Kurashkin

^3,4,6

,

Andrei P. Gantimurov

³ and

Vladislav V. Kukartsev

^1,3,7

¹

Department of Computer Science, Institute of Space and Information Technologies, Siberian Federal University, 660041 Krasnoyarsk, Russia

²

Department of Computer Science and Computer Engineering, Institute of Computer Science and Telecommunications, Reshetnev Siberian State University of Science and Technology, 660037 Krasnoyarsk, Russia

³

Scientific and Educational Center “Artificial Intelligence Technologies”, Bauman Moscow State Technical University, 105005 Moscow, Russia

⁴

Information-Control Systems Department, Institute of Computer Science and Telecommunications, Reshetnev Siberian State University of Science and Technology, 660037 Krasnoyarsk, Russia

⁵

Department of Technological Machines and Equipment of Oil and Gas Complex, School of Petroleum and Natural Gas Engineering, Siberian Federal University, 660041 Krasnoyarsk, Russia

⁶

Laboratory of Biofuel Compositions, Siberian Federal University, 660041 Krasnoyarsk, Russia

⁷

Department of Information Economic Systems, Institute of Engineering and Economics, Reshetnev Siberian State University of Science and Technology, 660037 Krasnoyarsk, Russia

^*

Author to whom correspondence should be addressed.

Mathematics 2024, 12(2), 276; https://doi.org/10.3390/math12020276

Submission received: 21 December 2023 / Revised: 11 January 2024 / Accepted: 13 January 2024 / Published: 15 January 2024

(This article belongs to the Special Issue Advances in Analysis and Application of Mathematical Optimization Algorithms)

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Abstract

Artificial neural networks are successfully used to solve a wide variety of scientific and technical problems. The purpose of the study is to increase the efficiency of distributed solutions for problems involving structural-parametric synthesis of neural network models of complex systems based on GRID (geographically disperse computing resources) technology through the integrated application of the apparatus of evolutionary optimization and queuing theory. During the course of the research, the following was obtained: (i) New mathematical models for assessing the performance and reliability of GRID systems; (ii) A new multi-criteria optimization model for designing GRID systems to solve high-resource computing problems; and (iii) A new decision support system for the design of GRID systems using a multi-criteria genetic algorithm. Fonseca and Fleming’s genetic algorithm with a dynamic penalty function was used as a method for solving the stated multi-constrained optimization problem. The developed program system was used to solve the problem of choosing an effective structure of a centralized GRID system that was configured to solve the problem of structural-parametric synthesis of neural network models. To test the proposed approach, a Pareto-optimal configuration of the GRID system was built with the following characteristics: average performance–103.483 GFLOPS, cost–500 rubles per day, availability rate–99.92%, and minimum performance–51 GFLOPS.

Keywords: performance model; reliability model; GRID system; genetic algorithm; multi-criteria optimization; optimization problem; Pareto-optimization; neural network models

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MDPI and ACS Style

Tynchenko, V.V.; Tynchenko, V.S.; Nelyub, V.A.; Bukhtoyarov, V.V.; Borodulin, A.S.; Kurashkin, S.O.; Gantimurov, A.P.; Kukartsev, V.V. Mathematical Models for the Design of GRID Systems to Solve Resource-Intensive Problems. Mathematics 2024, 12, 276. https://doi.org/10.3390/math12020276

AMA Style

Tynchenko VV, Tynchenko VS, Nelyub VA, Bukhtoyarov VV, Borodulin AS, Kurashkin SO, Gantimurov AP, Kukartsev VV. Mathematical Models for the Design of GRID Systems to Solve Resource-Intensive Problems. Mathematics. 2024; 12(2):276. https://doi.org/10.3390/math12020276

Chicago/Turabian Style

Tynchenko, Valeriya V., Vadim S. Tynchenko, Vladimir A. Nelyub, Vladimir V. Bukhtoyarov, Aleksey S. Borodulin, Sergei O. Kurashkin, Andrei P. Gantimurov, and Vladislav V. Kukartsev. 2024. "Mathematical Models for the Design of GRID Systems to Solve Resource-Intensive Problems" Mathematics 12, no. 2: 276. https://doi.org/10.3390/math12020276

APA Style

Tynchenko, V. V., Tynchenko, V. S., Nelyub, V. A., Bukhtoyarov, V. V., Borodulin, A. S., Kurashkin, S. O., Gantimurov, A. P., & Kukartsev, V. V. (2024). Mathematical Models for the Design of GRID Systems to Solve Resource-Intensive Problems. Mathematics, 12(2), 276. https://doi.org/10.3390/math12020276

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