Title: An improved flower pollination algorithm for solving nonlinear system of equations

Authors: Mohamed Abdel-Basset; Yongquan Zhou; Shereen Zaki; Abd El-Nasser H. Zaied

Addresses: Department of Operations Research, Faculty of Computers and Informatics, Zagazig University, Egypt ' College of Information Science and Engineering, Guangxi University for Nationalities, Nanning 530006, China ' Department of Operations Research, Faculty of Computers and Informatics, Zagazig University, El-Zera Square, Zagazig, Sharqiyah 44519, Egypt ' Department of Operations Research, Faculty of Computers and Informatics, Zagazig University, El-Zera Square, Zagazig, Sharqiyah 44519, Egypt

Abstract: It is difficult to solve a system of nonlinear equations, especially for higher-order nonlinear equations when we do not have an efficient and reliable algorithm, even though much work has been done in this area. Newton's method and its improved form are widely used at present, but their convergence and performance characteristics can be highly sensitive to the initial guess of the solution, and the methods fail if the initial guess of the solution is inopportune. It is difficult to select a good initial guess for most systems of nonlinear equations. For this reason, it is necessary to find an efficient algorithm for systems of nonlinear equations. Metaheuristic optimisation algorithms have been proposed by many researchers to solve systems of nonlinear equations. The flower pollination algorithm (FPA) is a novel metaheuristic optimisation algorithm with quick convergence, but its population diversity and convergence precision can be limited in some applications. To enhance its exploitation and exploration abilities, in this paper, an elite opposition-based flower pollination algorithm (EFPA) has been applied for solving systems of nonlinear equations. The results show that the proposed algorithm is robust, has high convergence rate and precision, and can give satisfactory solutions of nonlinear equations.

Keywords: flower pollination algorithm; FPA; meta-heuristics; elite opposition; optimisation; nonlinear equations.

DOI: 10.1504/IJCSM.2021.10039881

International Journal of Computing Science and Mathematics, 2021 Vol.13 No.3, pp.207 - 227

Received: 08 Feb 2018
Accepted: 20 Mar 2018

Published online: 02 Aug 2021 *

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