DNA Sequence mining helps in discovering the patterns which can occur frequently, structures of DNA in DNA data sets. Frequent pattern mining is a central strategy for affiliation guideline discovery, but existing calculations experience the ill effects of low effectiveness or poor error rate on the grounds that natural groupings vary from general successions with more attributes. In our last work, we proposed Prefix Span with Group Search Optimization (PSGSO) to optimize the mined results from the Prefix Span method. We propose a new method called Frequent DNA Sequence Mining using Optimization (FDSMO) which combines Frequent Biological Sequence based on Bitmap (FBSB) and Hybrid of Firefly and Group Search Optimization (HFGSO) in this paper. The FDSMO process includes three stages: (i) applying the Frequent Biological Sequence based on Bitmap (ii) calculate length, width and regular expression (iii) optimization using HFGSO. The exploratory results demonstrate that FDSMO performs better than the existing methods, both in terms of running time and scalability.