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Nature Inspired meta-heuristic algorithms are one of the most efficient solution to many engineering optimization problems. The Firefly algorithm is one of the nature inspired solution. The objective of the proposed work is of two folds. In the first fold the firefly algorithm is applied to the back-propagation training phase to optimize the overall training process. One of the problem in this type of implementation is the adjustment of algorithmic parameters and number of firefly population, and for a dynamic system the manual modification of parameter is a troublesome matter. In the second fold, the proposed work is implemented a statistical hypothesis based agent which is adaptively control the various parameters and number of firefly populations in firefly algorithm based back-propagation method and this makes it more convenient for dynamic systems. The effectiveness of automatic parameter adjustment over the performance of algorithm is analyzed through correct classification rate and sum of squared error. The proposed method is tested over five bench mark non-linear standard data set and it is compared with genetic algorithm based back-propagation method. It is observed from the experiment that the agent automatically adjust the parameters and number of firefly populations in each iteration of the back-propagation optimization phase and it is finally converged within a minimum number of iteration.