| The optimization problems are closely related to the real life. The optimization algorithm is the most important method to solve these problems. With the development of science and technology, the traditional optimization algorithms have not been adapted to the optimization problems with growing complexity. Therefore, the researches have proposed some heuristic algorithms to solve the complicated optimization problems that we meet in the real word.In 2009, the gravitational search algorithm(GSA) as a new method for solving the optimization problems was proposed by Esmat Rashedi. There are two aspects of the research on GSA. The one is the development of this algorithm, the other one is the application of this algorithm. However, at present, there is little research on the convergence analysis of the GSA. In this paper, two methods of the stability analysis on the algorithm are proposed. We obtain the parameter area. The main work is as follows:1ã€The Lyapunov stability analysis of GSA. At first, the iterative process of particle’s position is modeled as a second order difference equation with variable coefficients. Then, we study the stability of the difference equation by using Lyapunov stability theory and obtain stable area. Based on the results obtained from the analysis, we obtain the parameters setting area. According to the area, numerical experiments are carried out. The experimental results prove the conditions.2ã€The second order discrete linear time-varying system stability analysis of GSA. At first, the iterative process of particle’s position is modeled as a second order discrete linear time-varying system. Then, we study the stability of the second order discrete linear time-varying system by the stable condition and obtain stable area. Based on the results obtained from the analysis, we obtain the parameters setting area. According to the area, numerical experiments are carried out. The experimental results prove the conditions.3ã€Compare with two stability analysis of the GSA... |
