Modeling the parallelism of empirical models of optimal complexity using a Petri net

Authors

DOI:

https://doi.org/10.15587/1729-4061.2019.171632

Keywords:

empirical model, genetic algorithm, parallelism, Petri net, the number of operations

Abstract

Many physical processes and phenomena in view of their complexity cannot be described analytically. In these cases, empirical modeling is applied. In this research, the method based on the genetic approach is used to construct empirical models of optimal complexity that have the form of a polynomial of assigned power. Implementation of the developed method requires a multiple solution of the system of linear algebraic equations. Solution of the system of linear algebraic equations is found by reducing the corresponding matrix to the upper diagonal form with unities on the main diagonal. Analysis of the algorithm showed that the procedure of reducing the matrix to the upper diagonal form has internal parallelism. Based on the created model of the computational process in the form of a Petri net, the strategy of construction of the parallel algorithm for solving the system of linear algebraic equations was developed. The essence of the strategy is that computations are performed on some parallel processors. One of them was assigned coordinating functions, and it was named master. Other processors – slaves are subordinated to the master. Division of computation volume is such that the number of rows of the matrix, which master operates is at least by unity more than the corresponding number of rows allocated to the servant. The effectiveness of the parallel algorithm for the proposed strategy was evaluated based of the criterion of the total number of arithmetic operations. The proposed strategy is an integral part of the process of synthesis of the empirical model of optimal complexity based on the genetic algorithms. Distribution of computational load between processors working in parallel (master and slaves) ensures the acceleration of the computational process by five times or more.

Author Biographies

Mikhail Gorbiychuk, Ivano-Frankivsk National Technical University of Oil and Gas Karpatska str., 15, Ivano-Frankivsk, Ukraine, 76019

Doctor of Technical Sciences, Professor

Department of Computer Systems and Networks

Olga Bila, Ivano-Frankivsk National Technical University of Oil and Gas Karpatska str., 15, Ivano-Frankivsk, Ukraine, 76019

Postgraduate student

Department of Computer Systems and Networks

Taras Humeniuk, Ivano-Frankivsk National Technical University of Oil and Gas Karpatska str., 15, Ivano-Frankivsk, Ukraine, 76019

PhD

Department of Computer Systems and Networks

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Published

2019-06-26

How to Cite

Gorbiychuk, M., Bila, O., & Humeniuk, T. (2019). Modeling the parallelism of empirical models of optimal complexity using a Petri net. Eastern-European Journal of Enterprise Technologies, 3(4 (99), 56–68. https://doi.org/10.15587/1729-4061.2019.171632

Issue

Vol. 3 No. 4 (99) (2019): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2019 Mikhail Gorbiychuk, Olga Bila, Taras Humeniuk

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