where s i represents the MTS between the designed molecule and the training data for each prediction model, ρ is a reliability level, v is the desirability of the predicted property, w is the weight, and n is the number of properties to be optimized. As a molecular descriptor for computing Tanimoto similarity, Morgan fingerprint , whose radius and dimension were 2 and 2048, respectively, was applied. To calculate the desirability of the predicted properties, Gaussian scaling functions were defined for each property according to Brown et al. (Fig. ). Weight w is allocated to each property for prioritization during optimization. When calculating the reward function, the evaluation of the generated molecules was changed depending on whether the designed molecule was within the ADs of the property prediction models. If the MTS between the designed molecule and training data exceeds the reliability level defined for all target properties, the designed molecule is judged to be within the ADs. In this case, as a reward, the Dscore , which is the weighted geometric mean of the desirability of each property and is often used in the multi-objective optimization of molecular properties , is calculated. If the MTS is below the reliability level for any objective, it is judged to be outside the ADs, and the reward value is set to 0. By designing the reward function in this manner, we aim to achieve multi-objective optimization of the molecular properties within the ADs of multiple prediction models. The construction and evaluation methods of the prediction models used to evaluate the designed molecules are described below. In this study, we tried two patterns for several target properties: 3 properties and 13 properties. When the 3 properties pattern, as target properties, the following three properties were selected: inhibitory activity against EGFR, metabolic stability, and membrane permeability. When 13 properties pattern, an additional ten properties were incorporated, including inhibitory activity against eight off-target proteins from tyrosine kinases and two other properties. Eight tyrosine kinase proteins were selected as described by Yoshizawa et al. : receptor protein-tyrosine kinase erbB-2, Abelson tyrosine-protein kinase, proto-oncogene tyrosine-protein kinase, lymphocyte-specific tyrosine-protein kinase, platelet-derived growth factor receptor beta, vascular endothelial growth factor receptor 2, fibroblast growth factor receptor 1, and ephrin type-B receptor 4. For the other two properties, inhibitory activity against the human ether-a-go-go-related gene channel (hERG) and solubility were selected. The training data for these models were obtained from ChEMBL28 for inhibitory activity against tyrosine kinases, metabolic stability, and membrane permeability; from Sato et al. for hERG inhibition; and from Tayyebi et al. for solubility. To prepare the input features for the prediction models, Morgan fingerprints with radii and dimensions of 2 and 2048, respectively, were calculated using RDKit software . As a prediction algorithm, light gradient boosting machine was applied, and the hyperparameters were optimized using Optuna software . The prediction performance of each model was evaluated using 5-fold cross-validation (Fig. ). Finally, for each property, prediction models were developed using the entire dataset for the molecular design.