Title: Particle swarm optimisation based Diophantine equation solver

Authors: Siby Abraham, Sugata Sanyal, Mukund Sanglikar

Addresses: Department of Mathematics & Statistics, G.N. Khalsa College, University of Mumbai, Mumbai-400019, India. ' School of Technology & Computer Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400005, India. ' Department of Mathematics, Mithibai College, Vile Parle (W), University of Mumbai, Mumbai-400056, India

Abstract: The paper introduces particle swarm optimisation as a viable strategy to find numerical solution of Diophantine equation, for which there exists no general method of finding solutions. The proposed methodology uses a population of integer particles. The candidate solutions in the feasible space are optimised to have better positions through particle best and global best positions. The methodology, which follows fully connected neighbourhood topology, can offer many solutions of such equations.

Keywords: Diophantine equation; particle swarm optimisation; PSO; fitness function; position; velocity; learning factors; socio-cognitive coefficients; Fermat|s equation; elliptic curves; bio-inspired computation.

DOI: 10.1504/IJBIC.2010.032126

International Journal of Bio-Inspired Computation, 2010 Vol.2 No.2, pp.100 - 114

Available online: 10 Mar 2010 *

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