Tree-Based Machine Learning and Nelder–Mead Optimization for Optimized Cr(VI) Removal with Indian Gooseberry Seed Powder

Wastewater containing a mixture of heavy metals, a byproduct of chemical, petrochemical, and refinery activities driven by urbanization and industrial expansion, poses significant environmental threats. Analyzing such wastewater through adsorbate-adsorbent experiments yields extensive datasets. However, traditional methodologies like the Box–Behnken design (BBD) within the response surface methodology (RSM) struggle with managing large datasets and capturing the complex, nonlinear relationships inherent in such experimental data. To address these challenges, ML techniques have emerged as promising tools for accurately predicting the removal percentage of heavy metals from wastewater. In this study, we utilized tree-based regression models—specifically decision tree regression (DTR), random forest regression (RFR), and extra tree regression (ETR)—to forecast the efficiency of gooseberry seed powder in removing chromium (Cr(VI)) from wastewater. Additionally, we employed an ML-based Nelder–Mead optimization approach to identify the optimal values for key features (initial Cr(VI) concentration, pH, and Indian gooseberry powder dosage) which maximized the Cr(VI) removal percentage. Our experimental results reveal that the ETR model achieved an impressive <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>R</mi><mn>2</mn></msup></semantics></math></inline-formula> score of 0.99, demonstrating a low error rate in predicting the Cr(VI) removal percentage. Furthermore, we used DTR-Nelder–Mead, RFR-Nelder–Mead, and ETR-Nelder–Mead optimization approaches on a synthesized dataset of 2000 instances while varying the initial Cr(VI) concentration, pH, and Indian gooseberry powder dosage. The analysis determined that the DTR-Nelder–Mead and RFR-Nelder–Mead approaches yielded the highest Cr(VI) removal percentages of 78.21% and 78.107% at an initial concentration of 95.55 mg/L, respectively, a pH level of four, and an adsorbent dosage of 8 g/L of gooseberry seed powder. Furthermore, the ETR-Nelder–Mead approach obtained the maximum Cr(VI) removal percentage of 85.11% at an initial concentration of 99.25 mg/L, a pH level of 4.97, and an adsorbent dosage of 9.62 g/L of gooseberry seed powder. These results reported an increase in the Cr(VI) removal percentage ranging from 4.66% to 11.56% more than the Cr(VI) removal percentage obtained by experimentation. These findings underscore the efficacy of tree-based regression models and ML-based Nelder–Mead optimization in elucidating chromium removal processes from wastewater, offering valuable insights into effective treatment strategies.