In conclusion, the results of our study demonstrate the effectiveness of fragment-based genetic algorithms (FBGAs) and, especially, graph-based genetic algorithms (GBGAs) in the search for novel ligands for catalysts in the Suzuki reaction. The FBGA successfully evolved a population of molecules over 10 generations, yielding 134 unique catalysts with E values within the target range. Our study demonstrates that GAs, requiring on the order of 500 evaluations or less, are effective in directly identifying competitive catalysts using DFT without the need for constructing a Machine Learning (ML) model.