Stability analysis of particle dynamics in gravitational search optimization algorithm

Abstract

In this paper, particle dynamics and stability analysis of gravitational search algorithm (GSA) are investigated. The GSA is a swarm optimization algorithm which is inspired by the Newtonian laws of gravity and motion. Previously, the convergence analysis of the GSA and improved GSA algorithms were presented to demonstrate each particle converges. In this study, the stability of the particle dynamics using Lyapunov stability theorem and the system dynamics concept is analyzed. Sufficient conditions of stability analysis are investigated and utilized for adapting parameters of the GSA. The modified algorithm based on stability analysis is compared with the standard GSA, PSO, RGA, and two methods of improved GSA in terms of average, median, and standard deviation of best-so-far solutions. Simulation results demonstrate the validity and feasibility of the proposed modified GSA. In solving the optimization problem of various nonlinear functions, the high performance is achieved.