Molecular drug design and development are often hindered by high costs, prolonged development cycles, and significant failure rates, which greatly reduce the efficiency of discovering novel functional molecules. To address these challenges, we present a generalized framework for automatic molecular generation that integrates Gene Expression Programming (GEP) with graph-based modeling, called GEP-Graph4MD. GEP-Graph4MD leverages the strong optimization capabilities of GEP and the accurate representation of molecular topology provided by graph models to explore chemical space and generate novel candidate molecules. Through genetic operations such as recombination and mutation, the method iteratively refines molecular structures to optimize multiple objectives, including the octanol-water partition coefficient, synthetic accessibility, and ring penalty score. We conducted experiments to demonstrate the effectiveness of GEP-Graph4MD against existing molecular generation models, using a case study of generating molecules with specific target attributes. The experimental results show that GEP-Graph4MD can efficiently produce molecules that meet desired criteria, validating its potential for automated molecular generation with specific attributes.