Synthesizability is a quantity that can be calculated following the method as mentioned by Etrl et al. . In this empirical technique the synthetic accessibility is estimated by coupling molecular complexity and molecular fragment effects as analyzed by processing a large collection of chemical structures that have already been synthesized before. This technique therefore contains at some level historical data on the synthesizability of a large collection of molecules. The method is then tested and validated by comparing with 'ease of synthesis' ranks. These values were gathered by domain expert chemists. The agreement between score and the ranks are generally reasonable, where a score close to 0 indicates low synthesizability and one close to 1 high synthesizability. This technique provides a good way to estimate the synthesizability for large molecules that have never been synthesized before. indicates that, in contrast to the molecules in the original data set, the newly generated ones have much higher synthesizability scores, as both low HOMO-LUMO gap and high synthesizability was the criterion to select new molecules creating the new molecule population. This illustrates that a multiobjective search can be performed that will result in a Pareto-optimal set of molecules, combining a number of design targets such as low HOMO-LUMO gaps paired with high values of synthesizability. ing an excellent performance of the HydraGNN surrogate for this task, and the homogeneity of the data set. Such good agreement between surrogate-and DFTB-predicted HOMO-LUMO gaps is lost when considering the situation of the newly generated molecules, shown in Fig. . The MAE is increased to 0.45 eV as the now larger molecules, not contained in the original data set, lead to poorer performance of the HydraGNN surrogate which was only trained on the QM9 database containing molecules with up to 9 heavy chemical elements. This fact indicates the usefulness to perform adaptive surrogate training in iterative molecular design approaches, as indicated in Fig. by the dashed arrow labeled "iteration". Nevertheless, it should be noted that the GCNN surrogate model, even without iterative improvements, was able to provide sufficiently reliable guidance to the MLM for generating new molecular structures with reduced HOMO-LUMO gap.