Optimization is the task of minimizing or maximizing an objective function f(x) parameterized by x. A series of effective numerical optimization methods have become popular for improving the performance and efficiency of other methods characterized by high-quality solutions and high convergence speed. In recent years, there are a lot of interest in hybrid metaheuristics, where more than one method is ideally combined into one new method that has the ability to solve many problems rapidly and efficiently. The basic concept of the proposed method is based on the addition of the acceleration part of the Gravity Search Algorithm (GSA) model in the Firefly Algorithm (FA) model and creating new individuals. Some standard objective functions are used to compare the hybrid (FAGSA) method with FA and the traditional GSA to find the optimal solution. Simulation results obtained by MATLAB R2015a indicate that the hybrid algorithm has the ability to cross the local optimum limits with a faster convergence than the luminous Fireflies algorithm and the ordinary gravity search algorithm. Therefore, this paper proposes a new numerical optimization method based on integrating the properties of the two methods (luminous fireflies and gravity research). In most cases, the proposed method usually gives better results than the original methods individually.
