The Iterative Method for Solving Non-Linear Equations

Document Type: Research Articles

Author

Department of Computer Science, Arak Brancg, Islamic Azad Univeristy, Arak, Iran branch

Abstract

In this paper, we have combined the ideas of the False Position (FP) and Artificial Bee Colony (ABC) algorithms to find a fast and novel method for solving nonlinear equations. Additionally, to illustrate the efficiency of the proposed method, several benchmark functions are solved and compared with other methods such as ABC, PSO and GA.

Keywords


[1] N. Ahmad and V. P. Singh. A New Iterative Method for Solving Non Linear Equations Using Simpson Method, International Journal of Mathematics And Its Applications. Vol. 5, Issue 4-B, pp. 189-193, 2017.

[2] D. T. Pham and D. Karaboga. Intelligent Optimisation Techniques.
Springer, London, 2000.

[3] Xin-She Yang. Nature-Inspired Metaheuristic Algorithms, Luniver Press, 2008

[4] J. Dreo and P. Siarry. Alain Petrowski and Eric Taillard, Metaheuristics for Hard Optimization, Springer Berlin Heidelberg, pp. 1-19, 2006.

[5] D. Karaboga. An Idea Based On Honey Bee Swarm for Numerical Optimization. Technical Report-TR06, Erciyes University, Engineering Faculty, Computer Engineering Department, 2005.

[6] D. Karaboga and B. Basturk. A powerful and ecient algorithm for numerical function optimization: Arti cial Bee Colony (ABC) algorithm. Journal of Global Optimization,Vol. 39 , pp.459-471, 2007.

[7] D. Karaboga and B. Basturk. On the performance of Arti cial Bee Colony (ABC) algorithm. Applied Soft Computing. Vol.8, pp. 687-697, 2008.

[8] A. Baykaso. L. zbakr and P.Tapkan. Arti cial Bee Colony Algorithm and Its Application to Generalized Assignment Problem. Swarm Intelligence, Focus on Ant and Particle Swarm Optimization, Book edited by: Felix T. S. Chan and Manoj Kumar Tiwari, ISBN 978-3-902613-09-7, Itech Education and Publishing, Vienna, Austria, pp. 532, December 2007

[9] R. Storn. K. Price. Di erential evolution A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, Vol.23, pp.689-694, 2010.

[10] P. Mansouri. B. Asady and N.Gupta. A Novel Iteration Method for solve Hard Problems( Nonlinear Equations) with Arti cial Bee Colony algorithm. World Academy of Science, Engineering and Technology, Vol. 59, pp. 594-596, 2011.

[11] J.H.Holland. Adaptation in Natural and Arti cial Systems. University of Michigan Press, Ann Arbor, MI,1975.

[12] B. Asady.P.Mansouri and N. Gupta. The modify version of arti cial bee colony algorithm to solve real optimization problems. International Journal of Electrical and Computer Engineering (IJECE) Vol.2, No.4, pp.
473-480, 2012.

[13] N. Stanarevic. M.Tuba and N.Bacanin. Modi ed arti cial bee colony algorithm for constrained problems optimization, International journal of mathematical model and methods in applied sciences, Issue 3, Vol. 5, 2011.

[14] D.Karaboga.B.Akay and C.Ozturk. Arti cial Bee Colony (ABC)Optimization Algorithm for Training Feed-Forward Neural Networks,Modeling Decisions for Arti cial Intelligence, Vol. 4617, No.0302-9743, pp. 318-329, 2007.

[15] G. Roussy, J. A. Pearcy, Foundations and industrial applications of microwaves and radio frequency elds, John Wiley, New York, 1995.

[16] R. A. Van Gorder, K. Vajravelu, A variational formulation of the Nagumo reaction-diffusion equation and the Nagumo telegraph equation, Nonlinear Analysis: Real World Applications 4, pp.2957-2962, 2010.