Novel QIMARA-Bayesian hybrid framework for optimizing microwave-assisted nitrate extraction: A sustainable analytical approach

In this paper, a two-strategy hybrid method is proposed to combine predictive modeling and optimization using the Quantum-Inspired Multi-Objective Adaptive Resonance Algorithm (QIMARA) and Bayesian optimization to optimize microwave-assisted extraction (MAE) techniques to increase nitrate extraction from turnip samples ( Brassica rapa L.). Nitrate estimation in vegetables is critical due to nutritional values and health hazards caused by excessive nitrate in food. Conventional methods often experience challenges in optimizing complex parameter interactions and handling uncertainty. This two-strategy method succeeds in creating mathematical models to predict nitrate extraction in turnip samples using MAE methods while establishing optimal methods to consider four major MAE parameters. The model shows excellent predictability with RMSE = 2.99 mg/kg, MAE = 2.87 mg/kg, SMAPE = 0.95%, NSE = 0.98, KGE = 0.93, and R² = 0.98. The model is further validated to show excellent generalized capability of models to training, validation, and testing periods in cross-validation to show values of R² > 84% in each period. The model shows excellent optimization to increase nitrate to a higher level above 80 °C in 30 to 35 min to generate values of 277.6 to 334.1 mg/kg nitrate, while in four of five experiments, values exceeded 300 mg/kg. In summary, the QIMARA and Bayesian model is an effective method to be used in a wide variety of MAE methods to follow analytical chemistry practices effectively. • Hybrid QIMARA-Bayesian model optimizes microwave nitrate extraction efficiency • Predictive modeling achieved high accuracy: RMSE 2.99, R² 0.98, SMAPE 0.95% • Optimal conditions (80°C, 30–35 min) yielded up to 334.1 mg/kg nitrates • Sustainable approach reduces energy and solvent use, improving precision • Dual-strategy framework sets new standard in sustainable analytical chemistry