To cover this gap, this work introduces a screening-guided warm start into a genetic algorithm for CAMD. The proposed method is built on the COSMO-CAMD framework, where the candidate population consists of molecules assembled from molecular fragments. Given a design task, we first conduct a large-scale molecular screening. The top-ranked candidate molecules from the screening are then automatically split into molecular fragments. The output of the fragmentation procedure is integrated into a genetic algorithm for molecular design, wherein the initialization is fine-tuned in two key aspects: the molecular fragment library and the initial population. We apply the warm-started COSMO-CAMD framework to two case studies from the literature. By comparing our results with existing bench-90 marks, our method demonstrates a significant improvement in the performance of genetic algorithms for CAMD.