Classification is one of the important tasks in data mining. The probabilistic neural network (PNN) is a well-known and efficient approach for classification. The objective of the work presented in this paper is to build on this approach to develop an effective method for classification problems that can find high-quality solutions (with respect to classification accuracy) at a high convergence speed. To achieve this objective, we propose a method that hybridizes the firefly algorithm with simulated annealing (denoted as SFA), where simulated annealing is applied to control the randomness step inside the firefly algorithm while optimizing the weights of the standard PNN model. We also extend our work by investigating the effectiveness of using Lévy flight within the firefly algorithm (denoted as LFA) to better explore the search space and by integrating SFA with Lévy flight (denoted as LSFA) in order to improve the performance of the PNN. The algorithms were tested on 11 standard benchmark datasets. Experimental results indicate that the LSFA shows better performance than the SFA and LFA. Moreover, when compared with other algorithms in the literature, the LSFA is able to obtain better results in terms of classification accuracy. 
Hybridizing firefly algorithms with a probabilistic neural network for solving classification problems