Optimization means to find the best solution for any situation under given constraints. In today’s era, the problems are huge and complex. Nature always finds a way to deal with such problems efficiently in an optimized way. The computational algorithms which are inspired by nature to find solutions for such problems are called Nature inspired optimization algorithms. There are various nature-inspired algorithms and Firefly Algorithm (FA) is one among them. FA is a bio-inspired population-based stochastic algorithm which imitates the behavior of fireflies shown when they attract other fireflies. FA is an algorithm with many parameters that affect the accuracy and the convergence speed. A number of variants and parameter tuning related papers are available in the literature. In this paper first an introduction of Optimization, specifically Nature inspired optimization has been provided. Then, a detailed discussion about FA has been given. It is followed by a brief literature survey in which the work has been compared in tabular form to provide the readers with a better understanding. Further, we intend to improve the accuracy of Firefly algorithm by tuning the parameters namely α and βmin. A range of values of the above parameters is tested by forming their combinations to find out the mutual effect of both these parameters. These values are tested on a test bed of nine benchmark functions. The result is a combination of optimized values of both the parameters. The results are quite clear and provide a pair of optimized values of both the parameters.