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Reseach Article

Solving Linear Systems of Equations using a Memetic Algorithm

by Liviu Octavian Mafteiu-Scai, Emanuela Jana Mafteiu-Scai
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 58 - Number 13
Year of Publication: 2012
Authors: Liviu Octavian Mafteiu-Scai, Emanuela Jana Mafteiu-Scai
10.5120/9341-3658

Liviu Octavian Mafteiu-Scai, Emanuela Jana Mafteiu-Scai . Solving Linear Systems of Equations using a Memetic Algorithm. International Journal of Computer Applications. 58, 13 ( November 2012), 16-22. DOI=10.5120/9341-3658

@article{ 10.5120/9341-3658,
author = { Liviu Octavian Mafteiu-Scai, Emanuela Jana Mafteiu-Scai },
title = { Solving Linear Systems of Equations using a Memetic Algorithm },
journal = { International Journal of Computer Applications },
issue_date = { November 2012 },
volume = { 58 },
number = { 13 },
month = { November },
year = { 2012 },
issn = { 0975-8887 },
pages = { 16-22 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume58/number13/9341-3658/ },
doi = { 10.5120/9341-3658 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:02:24.090525+05:30
%A Liviu Octavian Mafteiu-Scai
%A Emanuela Jana Mafteiu-Scai
%T Solving Linear Systems of Equations using a Memetic Algorithm
%J International Journal of Computer Applications
%@ 0975-8887
%V 58
%N 13
%P 16-22
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This paper proposes a memetic algorithm (MA) to solve linear systems of equations, by transforming the linear system of equations into an optimization problem. Such exploitation of knowledge obtained in a local search/optimization allows the evolutionary programming implementation to produce very good results at a relatively low computational cost. The proposed MA is able to determine solutions of a given linear system of equations, even in cases where traditional methods fail (determinant null, ill-conditioned systems, subdeterminate systems, supradeterminate systems, system doesn't satisfy the convergence conditions etc). In situations when a linear system of equations has multiple solutions, in proposed approach, the task is to find as many solutions as possible,inside of a given interval. In cases where no accurate solution for a linear system of equations exists, an approximate solution can be acceptable and it can be obtained by the proposed method.

References
  1. Al Dahoud Ali , Ibrahiem M. M. El Emary, and Mona M. Abd El-Kareem, Application of Genetic Algorithm in Solving Linear Equation Systems, MASAUM Journal of Basic and Applied Science, Vol. 1, No. 2 Sept. 2009
  2. Ikotun Abiodun M. , Lawal Olawale N. ,Adelokun Adebowale P. The Effectiveness of Genetic Algorithm in Solving Simultaneous Equations, International Journal of Computer Applications (0975 – 8887) Volume 14– No. 8, February 2011
  3. Crina Grosan, Ajith Abraham, Multiple Solutions for a System of Nonlinear Equations, International Journal of Innovative Computing, Information and Control ICIC International , 2008 ISSN 1349-4198
  4. Ibrahiem M. M. El-Emary,Mona M. Abd El-Kareem, Towards Using Genetic Algorithm for Solving Nonlinear Equation Systems, World Applied Sciences Journal 5 (3): pp. 282-289, 2008, ISSN 1818-4952
  5. Crina Grosan, Ajith Abraham, A New Approach for Solving Nonlinear Equations Systems, IEEE Transaction on Systems, Man and Cybernetics-part A: Systems and Humans, vol. 38, no. 3, May 2008
  6. Yong Zhou, Huajuan Huang, Junli Zhang, Hybrid Artificial Fish Swarm algorithm for Solving Ill-Conditioned Linear Systems of Equations, ICICIS 2011 Proceedings, Part 1, Springer 2011, pp. 656-662
  7. Nikos E. Mastorakis, Solving Non-linear Equations via Genetic Algorithms, Proceedings of the 6th WSEAS Int. Conf. on Evolutionary Computing, Lisbon, Portugal, June 16-18, 2005 pp24-28
  8. Ferrante Neri, Carlos Cotta, and Pablo Moscato (Eds. ), Handbook of Memetic Algorithms, Studies in Computational Intelligence, 2012 Springer-Verlag Berlin Heidelberg, ISBN 978-3-642-23246-6
  9. Jason Brownlee, Clever Algorithms: Nature-Inspired Programming Recipes, 2011, ISBN:978-1-4467-8506-5
  10. Michel Gendreanu, J. Y. Potvin, Handbook of Metaheuristics, Springer 2010, ISBN 978-1-4419-1663-1
  11. Teofilo F. Gonzales, Handbook of Approximation Algorithms and Metaheuristics, Chapman&Hall/CRC 2007
  12. N. Krasnogor, Studies in the Theory and Design Space of Memetic Algorithms, PhD thesis, University of the West of England, 2002
Index Terms

Computer Science
Information Sciences

Keywords

linear systems of equations memetic algorithms