TY - JOUR
T1 - An improved flower pollination algorithm for solving nonlinear system of equations
AU - Abdel-Basset, Mohamed
AU - Zhou, Yongquan
AU - Zaki, Shereen
AU - Zaied, Abd El Nasser H.
N1 - Publisher Copyright:
Copyright © 2021 Inderscience Enterprises Ltd.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Elite opposition
KW - Flower pollination algorithm
KW - FPA
KW - Meta-heuristics
KW - Nonlinear equations
KW - Optimisation
UR - http://www.scopus.com/inward/record.url?scp=85112028818&partnerID=8YFLogxK
U2 - 10.1504/ijcsm.2021.10039881
DO - 10.1504/ijcsm.2021.10039881
M3 - Article
AN - SCOPUS:85112028818
SN - 1752-5055
VL - 13
SP - 207
EP - 227
JO - International Journal of Computing Science and Mathematics
JF - International Journal of Computing Science and Mathematics
IS - 3
ER -