Analysis on stability conditions for the gravitational search algorithm

In the gravitational search algorithm (GSA), there are many random parameters which influence particle´s trajectory. In this paper, the iterative process of particle´s position is modeled as a second order difference equation with variable coefficients. Then, we study the stability analysis of the difference equation by using Lyapunov stability theory. Based on the results obtained from the analysis, the conditions about random parameters selection are obtained. According to these conditions, numerical experiments are carried out. Simulation results show that the particle´s trajectory can stable convergence.