Gravitational search algorithm based solution for a class of ternary diophantine equations

Article type: Research Article

Authors: Raja Balachandar, S.^* | Kannan, K. | Srikanth, R. | Balachandran, S. | Venkatesh, S.G. | Balasubramanian, K.

Affiliations: Department of Mathematics, School of Humanities and Sciences, Sastra University, Thanjavur, India

Correspondence: [*] Corresponding author: S. Raja Balachandar, Department of Mathematics, School of Humanities and Sciences, Sastra University, Thanjavur, India. E-mail:srbala09@gmail.com

Abstract: This paper introduces Gravitational Search Algorithm (GSA) to find numerical solutions of Diophantine equations, for which there exists no general method of finding solutions. This algorithm finds upon introducing randomization concept along with the two of the four primary parameters `velocity' and `gravity' in physics. The performance of this algorithm has been evaluated on a set of random values. Computed result shows that the gravitational search algorithm - based heuristic is capable of producing high quality solutions, can offer many solutions of such equations.

Keywords: Gravitational search algorithm, gravity, Newton's law, diophantine equation, genetic algorithm, particle swarm optimization

DOI: 10.3233/JCM-160700

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 16, no. 4, pp. 899-911, 2016