Sage Journals: Discover world-class research

Abstract

The problem of solving linear and nonlinear system of equations is a largely useful issue of significant importance such as that it is presented on real-time applications. Different numerical methods such as fixed-point, Newton Raphson, bisection and secant methods, and or others, namely; evolutionary and computational methods are used to solve nonlinear system under optimizing the space and time complexity. Genetic Algorithm (GA) proved to be an efficient soft computing approach to solve many linear/non-linear system of equations. In this article, a comparison between different GAs and numerical methods for solving a system of equations are introduced. From the results, a novel approach is introduced which is inspired by using a modified GA to get the optimistic solution for the system which has no numerical solution and verified with the highest performance measures in solving complicated problems.

Keywords

Linear system equations non-linear system equations genetic algorithms numerical optimization and Newton-Raphson

Get full access to this article

View all access options for this article.

References

Madalina

M.D.

, Multi-objective optimization perspectives on reinforcement learning algorithms using reward vectors, European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning Bruges (Belgium), 22–24 April 2015, publ., ISBN 978-287587014-8.

Michael

J.H.

, grasp-based heuristics for continuous global optimization problems, Ph.D. Thesis, University of Florida, 2006.

Abubakar

M.Y.

, Jung

L.T

, Zakaria

, Younes

and Abdel-Aty

, Reversible circuit synthesis by genetic programming using dynamic gate libraries, Quantum Information Processing 16 (2017), 160.

Abubakar

M.Y.

, Jung

L.T.

, Zakaria

M.N.

, Younes

, Abdel-Aty

, New universal gate library for synthesizing reversible logic circuit using genetic programming 2016 3rd International Conference on Computer and Information Sciences (ICCOINS), Kuala Lumpur, 2016, pp. 316–321. doi: 10.1109/ICCOINS.2016.7783234.

Haldurai

, Madhubala

and Rajalakshmi

, A study on genetic algorithm and its applications, International Journal of Computer Sciences and Engineering 4 (2016), 1–14.

Golchha

and Qureshi

S.G.

, Non-dominated sorting genetic algorithm-II – A Succinct Survey, (IJCSIT), International Journal of Computer Science and Information Technologies 6 (2015), 252–255.

Amjad

, Butt

, Kousar

, Ahmad

, Agha

, Faping

, Anjum

and Asgher

, Recent research trends in genetic algorithm based flexible job shop scheduling problems, Hindawi Mathematical Problems in Engineering 2018 (2018), 1–32.

Abdel-Khalek

, Ishak

A.B.

, Omer

O.A.

and Obada

A.-S.F.

, A two-dimensional image segmentation method based on genetic algorithm and entropy, Optik 131 (2017), 414–422.

Malhotra

, Singh

and Singh

, Genetic algorithms: Concepts, design for optimization of process controllers, Computer and Information Science 4 (2011), 39–54.

10.

Shenava

S.J.

, Noruzi

and Mousazadeh

, Solving EED problem by fuzzified multi objective simulated annealing, Applied mathematics in Engineering, Management and Technology 3 (2015), 52–66.

11.

Effati

and Nazemi

A.R.

, A new method for solving a system of the nonlinear equations, Applied Mathematics and Computation 168 (2005), 877–894.

12.

Sivaram

, Batri

, Mohammed

and Porkodi

, Exploiting the Local Optima in Genetic Algorithm using Tabu Search, Indian Journal of Science and Technology 12 (2019), 139–143.

13.

Babajee

D.K.R.

, Madhu

and Jayaraman

, On some improved harmonic mean Newton-like methods for solving systems of nonlinear equations, Algorithms 8 (2015), 895–909.

14.

Soleymani

, Salmani

and Rasouli

, Finding the Moore-Penrose inverse by a new matrix iteration, J. Appl. Math. Comput. 47 (2015), 33–48.

15.

Sharma

J.R.

, Guha

R.K.

and Sharma

, An efficient fourth order weighted-Newton method for systems of nonlinear equations, Numer. Algor. 62 (2013), 307–323.

16.

Grosan

and Abraham

, A new approach for solving nonlinear equations systems, IEEE Transactions on Systems, Manm and Cybernetics-Part A: Systems and Humans 38 (2008), 698–714.

Genetic algorithm and numerical methods for solving linear and nonlinear system of equations: a comparative study

Abstract

Keywords

Get full access to this article

References