(Publisher of Peer Reviewed Open Access Journals)

International Journal of Advanced Technology and Engineering Exploration (IJATEE)

ISSN (Print):2394-5443    ISSN (Online):2394-7454
Volume-5 Issue-44 July-2018
Full-Text PDF
DOI:10.19101/IJATEE.2018.543009
Paper Title : Genetic algorithm based optimization for system of nonlinear equations
Author Name : Chhavi Mangla, Musher Ahmad and Moin Uddin
Abstract :

This work explores a perspective for solving system of nonlinear equations which is an eminent problem in all scientific disciplines. An evolutionary computational technique is used to handle the nonlinear system of equations by converting it into a multi-objective optimization problem. A new fitness function has been proposed, the parameters have been chosen by prior empirical analysis. To validate the performance of the proposed methodology, sensitivity analysis has been carried out by varying the parameters of Genetic algorithm. The results obtained by new approach are quite encouraging and are also compared with other existing work.

Keywords : Evolutionary technique, Genetic algorithm, Nonlinear equations, Optimization.
Cite this article : Chhavi Mangla, Musher Ahmad and Moin Uddin, " Genetic algorithm based optimization for system of nonlinear equations " , International Journal of Advanced Technology and Engineering Exploration (IJATEE), Volume-5, Issue-44, July-2018 ,pp.187-194.DOI:10.19101/IJATEE.2018.543009
References :
[1]David E. Genetic algorithms in search, optimization, and machine learning. Addison-Wesley Longman, USA; 1989.
[2]Abd-El-Wahed WF, Mousa AA, El-Shorbagy MA. Integrating particle swarm optimization with genetic algorithms for solving nonlinear optimization problems. Journal of Computational and Applied Mathematics. 2011; 235(5):1446-53.
[Crossref] [Google Scholar]
[3]Grosan C, Abraham A. A new approach for solving nonlinear equations systems. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans. 2008; 38(3):698-714.
[Crossref] [Google Scholar]
[4]Pourrajabian A, Ebrahimi R, Mirzaei M, Shams M. Applying genetic algorithms for solving nonlinear algebraic equations. Applied Mathematics and Computation. 2013; 219(24):11483-94.
[Crossref] [Google Scholar]
[5]Fogel DB. Evolutionary computation: the fossil record. Wiley-IEEE Press; 1998.
[Crossref] [Google Scholar]
[6]Bianchini M, Fanelli S, Gori M. Optimal algorithms for well-conditioned nonlinear systems of equations. IEEE Transactions on Computers. 2001; 50(7):689-98.
[Crossref] [Google Scholar]
[7]Rovira A, Valdes M, Casanova J. A new methodology to solve nonā€linear equation systems using genetic algorithms. Application to combined cyclegas turbine simulation. International Journal for Numerical Methods in Engineering. 2005; 63(10):1424-35.
[Crossref] [Google Scholar]
[8]Chang WD. An improved real-coded genetic algorithm for parameters estimation of nonlinear systems. Mechanical Systems and Signal Processing. 2006; 20(1):236-46.
[Crossref] [Google Scholar]
[9]Nie PY. An SQP approach with line search for a system of nonlinear equations. Mathematical and Computer Modelling. 2006; 43(3-4):368-73.
[Crossref] [Google Scholar]
[10]N Guessan A. Analytical existence of solutions to a system of nonlinear equations with application. Journal of Computational and Applied Mathematics. 2010; 234(1):297-304.
[Crossref] [Google Scholar]
[11]Ren H, Wu L, Bi W, Argyros IK. Solving nonlinear equations system via an efficient genetic algorithm with symmetric and harmonious individuals. Applied Mathematics and Computation. 2013; 219(23):10967-73.
[Crossref] [Google Scholar]
[12]Raja MA, Sabir Z, Mehmood N, Al-Aidarous ES, Khan JA. Design of stochastic solvers based on genetic algorithms for solving nonlinear equations. Neural Computing and Applications. 2015; 26(1):1-23.
[Crossref] [Google Scholar]
[13]Gong D, Wang G, Sun X, Han Y. A set-based genetic algorithm for solving the many-objective optimization problem. Soft Computing. 2015; 19(6):1477-95.
[Crossref] [Google Scholar]
[14]Mangla C, Bhasin H, Ahmad M, Uddin M. Novel solution of nonlinear equations using genetic algorithm. In industrial mathematics and complex systems 2017 (pp. 249-57). Springer, Singapore.
[Crossref] [Google Scholar]