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

Valeriya V. Tynchenko, Vadim S. Tynchenko (), Vladimir A. Nelyub, Vladimir V. Bukhtoyarov, Aleksey S. Borodulin, Sergei O. Kurashkin, Andrei P. Gantimurov and Vladislav V. Kukartsev
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Valeriya V. Tynchenko: Department of Computer Science, Institute of Space and Information Technologies, Siberian Federal University, 660041 Krasnoyarsk, Russia
Vadim S. Tynchenko: Scientific and Educational Center “Artificial Intelligence Technologies”, Bauman Moscow State Technical University, 105005 Moscow, Russia
Vladimir A. Nelyub: Scientific and Educational Center “Artificial Intelligence Technologies”, Bauman Moscow State Technical University, 105005 Moscow, Russia
Vladimir V. Bukhtoyarov: Scientific and Educational Center “Artificial Intelligence Technologies”, Bauman Moscow State Technical University, 105005 Moscow, Russia
Aleksey S. Borodulin: Scientific and Educational Center “Artificial Intelligence Technologies”, Bauman Moscow State Technical University, 105005 Moscow, Russia
Sergei O. Kurashkin: Scientific and Educational Center “Artificial Intelligence Technologies”, Bauman Moscow State Technical University, 105005 Moscow, Russia
Andrei P. Gantimurov: Scientific and Educational Center “Artificial Intelligence Technologies”, Bauman Moscow State Technical University, 105005 Moscow, Russia
Vladislav V. Kukartsev: Department of Computer Science, Institute of Space and Information Technologies, Siberian Federal University, 660041 Krasnoyarsk, Russia

Mathematics, 2024, vol. 12, issue 2, 1-33

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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