Optimization of ultrasound-assisted extraction of bioactive compounds from Carthamus caeruleus L. rhizome: Integrating central composite design, Gaussian process regression, and multi-objective Grey Wolf optimization approaches

The prediction of ultrasound-assisted extraction (UAE) for total phenolic content (TPC) and total flavonoid content (TFC) from Carthamus caeruleus L. rhizomes was conducted using a Gaussian process regression model (GPR) with a multi-objective Grey Wolf optimization approach (MOGWO). A central composite design (CCD) was employed first, examining ethanol concentration, temperature, time, and solvent-to-solid ratio as independent variables. TPC and TFC responses were analyzed under various conditions, revealing significant quadratic and interaction effects (p < 0.05). The GPR was then utilized to predict TPC and TFC, showing high accuracy with correlation coefficients near 1 and minimal root mean square error (RMSE) values. To simultaneously maximize TPC and TFC, the MOGWO was used in a multi-objective framework. Validation through CCD and GPR highlighted GPR's superior predictive accuracy. Optimal conditions (10 % ethanol, 40°C, 20 minutes sonication, and 50 mL g⁻¹ solvent to solid ratio) showed significant discrepancies in CCD predictions but high accuracy in GPR predictions. An interactive tool predicts TPC and TFC using CCD and GPR models. Users input extraction parameters and receive predictions, with a GWO-based optimization module for optimal conditions. The interface enables model comparison, improves process understanding, and optimizes bioactive compound extraction.