Gravitational search algorithm (GSA) has been shown to yield good performance for solving various optimization problems. However, it tends to suffer from premature convergence and loses the abilities of exploration and exploitation when solving complex problems. This paper presents an improved gravitational search algorithm (IGSA) that first employs chaotic perturbation operator and then considers memory strategy to overcome the aforementioned problems. The chaotic operator can enhance its global convergence to escape from local optima, and the memory strategy provides a faster convergence and shares individual's best fitness history to improve the exploitation ability. After that, convergence analysis of the proposed IGSA is presented based on discrete-time linear system theory and results show that IGSA is not only guaranteed to converge under the conditions, but can converge to the global optima with the probability 1. Finally, choice of reasonable parameters for IGSA is discussed on four typical benchmark test functions based on sensitivity analysis. Moreover, IGSA is tested against a suite of benchmark functions with excellent results and is compared to GA, PSO, HS, WDO, CFO, APO and other well-known GSA variants presented in the literatures. The results obtained show that IGSA converges faster than GSA and other heuristic algorithms investigated in this paper with higher global optimization performance. 
Convergence analysis and performance of an improved gravitational search algorithm