On the convergence analysis of gravitational search algorithm.

Gravitational search algorithm (GSA) is one of the newest swarm based optimization algorithms, which has been inspired by the Newtonian laws of gravity and motion. GSA has empirically shown to be an efficient and robust stochastic search algorithm. Since introducing GSA a convergence analysis of this algorithm has not yet been developed. This paper introduces the first attempt to a formal convergence analysis of the standard gravitational search algorithm which involves with randomness and time varying parameters. In this analysis the behavior of GSA on the facet of mass interaction is considered. The paper provides a formal proof that each object converges to a stable point.