As with the QED optimization, we compared the molecules generated by optimizing penalized logP using VGAE-MCTS with the molecules in the ZINC dataset and molecules generated using JT-VAE and MolDQN (Figure (A), (B), and (C)). The penalized logP of the molecules generated by VGAE-MCTS (mean: 0.536, median: 0.606) was higher than those in the ZINC dataset (mean: 0.572, median: 0.610) (Mann-Whitney U test: P=6.08×10 -1 ). We found that the molecules generated by VGAE-MCTS had a smaller percentage of low penalized logP values than the molecules in the ZINC dataset and the molecules generated by the previous models. In other words, this suggests that VGAE-MCTS avoids expanding molecules toward the lower penalized logP in the molecular generation using MCTS. VGAE-MCTS was also able to generate molecules with higher penalized logP compared to previous methods, JT-VAE (mean: 0.392, median: 0.309) and MolDQN (mean: 0.472, median: 0.442) (Mann-Whitney U test: P=4.26×10 -14 , P=1.90×10 -3 ).