Modeling and multi-objective optimization of microalgae biomass production and CO₂ biofixation using hybrid intelligence approaches

This study investigates the impacts of temperature, light-dark cycles (LD), and nitrogen-phosphorus ratios (NP) on Chlorella vulgaris microalgae biomass productivity (BP) and CO₂ biofixation (R_CO2). Three artificial intelligence (AI) modeling approaches - boosted regression tree (BRT), artificial neural networks (ANN), and support vector regression (SVR) were applied. Bayesian optimization algorithm (BOA) was combined with each AI approach to predict BP and R_CO2. Real-life experimental data, according to Box-Behnken design (BBD) were employed to assess the models using relative error (RE), coefficient of determination (R²), mean absolute error (MAE), mean absolute relative error (MARE), root mean square error (RMSE), and fractional bias (FB). The performance of the ANN and SVR models are comparable. However, the SVR model performs much better than the BRT and ANN models. Regarding R_CO2, the SVR model yields low errors (MAE of 0.0128, MARE of 0.4131, RMSE of 0.0189) with a high R² of 0.911. The value of FB is close to zero (0.0088), suggesting the model is reliable. The SVR model shows a better prediction capability of R_CO2 compared to BBD with a performance improvement of 17.16%. MARE of BBD for R_CO2 is 0.7409, which is higher than that of SVR model. Finally, the crow search algorithm was combined with the SVR for multi-objective optimization to determine the global optimal conditions for maximizing BP and R_CO2, respectively. The optimum conditions were calculated to be 40 °C, 1:1 of N/P, and 12/12 h/h of LD with BP and R_CO2 of 0.0979 g L⁻¹d⁻¹ and 0.1408 g L⁻¹d⁻¹, respectively.