Science and technology are growing rapidly and complex networks have become a substantial necessity to our daily life in a way that the separation of people from complex networks built on fundamental needs of human life is almost impossible. In this research, we presented a model for multi-layer dynamic social networks to discover influential groups based on a combination of developing frog-leaping algorithm and C-means clustering. We collected the data in the first step. Then, we conducted data cleansing and normalization in order to identify influential individuals and groups using the optimal data by forming a decision matrix. Hence, using the matrix, we conducted identification and clustering (based on phase clustering) and also determined the importance of each group. In order to discover influential individuals and groups in social networks, frog-leaping algorithm was used to improve identification of influence parameters, which lead to improvement in nodes importance. In measurement and simulation of clustering section, the proposed method was contrasted against K-means method and its equilibrium value in cluster selection resulted 5. The proposed method presented a more genuine improvement in comparison to the other compared methods. However, measuring precision indicator for the proposed method had 3.3 improvement in comparison to similar methods and recorded 3.8 improvement in comparison to M-ALCD basic method.