Optimization algorithm based on the Euler method for solving fuzzy nonlinear equations

Authors

DOI:

https://doi.org/10.15587/1729-4061.2022.252014

Keywords:

algorithms, approach, fuzzy, global, Euler method, intelligent techniques, nonlinear equations, numerical optimization, swarms

Abstract

In a variety of engineering, scientific challenges, mathematics, chemistry, physics, biology, machine learning, deep learning, regression classification, computer science, programming, artificial intelligence, in the military, medical and engineering industries, robotics and smart cars, fuzzy nonlinear equations play a critical role. As a result, in this paper, an Optimization Algorithm based on the Euler Method approach for solving fuzzy nonlinear equations is proposed. In mathematics and computer science, the Euler approach (sometimes called the forward Euler method) is a first-order numerical strategy for solving ordinary differential equations (ODEs) with a specified initial value. The local error is proportional to the square of the step size, while the general error is proportional to the step size, according to the Euler technique. The Euler method is frequently used to create more complicated algorithms. The Optimization Algorithm Based on the Euler Method (OBE) uses the logic of slope differences, which is computed by the Euler approach for global optimizations as a search mechanism for promising logic. Furthermore, the mechanism of the proposed work takes advantage of two active phases: exploration and exploitation to find the most important promising areas within the distinct space and the best solutions globally based on a positive movement towards it. In order to avoid the solution of local optimal and increase the rate of convergence, we use the ESQ mechanism. The optimization algorithm based on the Euler method (OBE) is very efficient in solving fuzzy nonlinear equations and approaches the global minimum and avoids the local minimum. In comparison with the GWO algorithm, we notice a clear superiority of the OBE algorithm in reaching the solution with higher accuracy. We note from the numerical results that the new algorithm is 50 % superior to the GWO algorithm in Example 1, 51 % in Example 2 and 55 % in Example 3.

Supporting Agency

  • The authors are very grateful to the University of Mosul./.Collage of Education for Pure Science for their provided facilities, which helped to improve the quality of this work.

Author Biographies

Kais I. Ibraheem, University of Mosul

Assistant Professor, Dean of College

Department of Computer Science

College of Education for Pure Science

Hisham M. Khudhur, University of Mosul

Lecturer

Department of Mathematics

College of Computer Science and Mathematics

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Published

2022-02-25

How to Cite

Ibraheem, K. I., & Khudhur, H. M. (2022). Optimization algorithm based on the Euler method for solving fuzzy nonlinear equations. Eastern-European Journal of Enterprise Technologies, 1(4 (115), 13–19. https://doi.org/10.15587/1729-4061.2022.252014

Issue

Vol. 1 No. 4 (115) (2022): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2022 Kais I. Ibraheem, Hisham M. Khudhur

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