In recent years, metaheuristic algorithms are widely employed to provide optimal solutions for engineering optimization problems. In this work, a recent metaheuristic Firefly Algorithm (FA) is adopted to find optimal solution for a class of global benchmark problems and a PID controller design problem. Until now, few research works have been commenced with FA. The updated position in a firefly algorithm mainly depends on parameters such as attraction between fireflies due to luminance and randomization operator. In this paper, FA is analyzed with various randomization search strategies such as Lévy Flight (LF) and Brownian Distribution (BD). The proposed method is also compared with the other randomization operator existing in the literature. The performance assessment between LF and BD based FA are carried using prevailing parameters such as search time and accuracy in optimal parameters. The result evident that BD based FA provides better optimization accuracy, whereas LF based FA provides faster convergence.