As a nature-inspired search algorithm, the Firefly algorithm (being a naturally outstanding search algorithm with few control parameters) may have a considerable influential performance. In this paper, we present a new firefly algorithm to address the parameter selection and adaptation strategy in the standard firefly algorithm. The proposed firefly algorithm introduces a modified exploration and exploitation mechanism, with adaptive randomness and absorption coefficients. The proposed method employs the adaptation of the randomness and absorption coefficients to be a function of time/iterations. Moreover, gray relational analysis advancing fireflies is used to allocate different information from appealing ones effectively. Standard benchmark functions are applied to verify the effects of these improvements and it is illustrated that, in most situations, the performance of the proposed firefly algorithm is superior to (or at least highly competitive with) the standard firefly algorithm, and state-of-the-art approaches in terms of performance.