Optimization algorithm for improving the prediction accuracy of API solubility in green solvent

Supercritical carbon dioxide (SC-CO₂) is widely used as an environmentally friendly solvent in pharmaceutical processing, where accurate prediction of drug solubility is essential for efficient formulation design, extraction processes, and process optimization. However, predicting solubility behavior in supercritical systems remains challenging due to the nonlinear interactions between thermodynamic conditions and molecular properties. In this study, a hybrid artificial intelligence framework is developed to predict the solubility of active pharmaceutical ingredients (APIs) in SC-CO₂ using a curated dataset of more than 350 experimentally reported measurements. The proposed framework integrates interpretable deep learning (TabNet) and histogram-based gradient boosting (HGB) with three metaheuristic optimization algorithms, namely the Attack-Leave Optimizer (ALO), Energy Valley Optimizer (EVO), and Botox Optimization Algorithm (BOA), to improve hyperparameter tuning and predictive performance. Model evaluation was conducted using multiple statistical indicators, five-fold cross-validation, prediction interval bootstrapping, and multi-objective Pareto front analysis to assess accuracy and robustness. Among the evaluated configurations, the EVO-tuned TabNet model demonstrated the best predictive performance, achieving a coefficient of determination of \(\:{R}^{2}=0.982\)along with narrow prediction intervals, indicating strong generalization capability within the studied thermodynamic domain. Statistical analysis using the Kruskal–Wallis test confirmed significant differences between optimizer performances (\(\:p<0.05\)). These findings demonstrate that the proposed hybrid pipeline enhances predictive accuracy and interpretability within the thermodynamic domain represented by the compiled dataset. The framework therefore provides a statistically supported computational tool for assisting solvent selection and formulation analysis in supercritical systems, while broader generalization would benefit from future expansion of experimental solubility datasets.