RANSAC guided modeling and evolutionary optimization of UV/sulfite for ofloxacin removal

Abstract

A new hierarchical model to elucidate the photo-mediated activation process of sulfite species in selective photodegradation of a fluoroquinolone antibiotic, ofloxacin, is introduced in this work, through the combination of RANSAC based high-order stochastically governed multi-outputs predictive modeling and an evolutionary parametric optimization, a set of coupled process parameters controlling the ofloxacin removal, biochemical oxygen demand (BOD) and chemical oxygen demand (COD) removals are determined. Systematic assessment of UV/sulfite system was performed to identify the effect of pH, UV intensity, sulfite concentration, starting drug concentration, contact time, and molar ratio of sulfite/ofloxacin, and strong predictive fidelity of COD and ofloxacin removal, and the complex BOD reduction behavior with moderate deviations under extreme conditions. RANSACRegressor was accurately captured non-linear and multivariate relations. Quantitative evaluation confirmed the stability of the model when using training and test data sets, that UV Intensity and initial ofloxacin concentration are the most important factors influencing the pollutant degradation and organic load reduction, whereas pH, contact time and sulfite/ofloxacin molar ratio are secondary but significant factors. Moreover, the evolutionary optimization protocol could identify the output-specific optimum settings, an increased UV intensity and sulfite concentration (when removal of ofloxacin and COD took place), compared with a decreased sulfite concentration and relatively alkaline pH (when removal of BOD took place). When combined, this hybrid photochemical-computational model gives improved predictive insight of the photon-induced sulfite activation mechanism and offer a robust predictive and operational framework of optimization of advanced oxidation in aqueous matrices to which antibiotics are added.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-60005-y.

Introduction

The critical issue is that pharmaceutical revenue nearly quadrupled between 2001 and 2016, rising from $390.2 billion to $1,105.2 billion, indicating a substantial increase in pharmaceutical consumption over this period. Given the insufficient efficiency of conventional wastewater treatment plants (WWTPs), the presence of these compounds in various environmental compartments has been observed, evolving into a significant environmental concern. Considering the diverse sources of pharmaceutical effluents (domestic sewage, hospital effluents, and pharmaceutical industries) and the fact that even trace levels of these drugs can cause potential long-term impacts to aquatic organisms, plants, and human health through prolonged exposure, it is imperative to focus on advanced treatment processes for their removal. Biological processes often lack efficacy against these antibiotics. Other methods with limited efficiency, such as Membrane Bioreactors (MBR) and Moving Bed Biofilm Reactors (MBBR), are highly time-consuming. In this context, chemical processes like adsorption and Advanced Oxidation Processes (AOPs) can be highly effective. While adsorption operates via phase transfer and generates contaminated sludge, AOPs effectively degrade pharmaceuticals. Moreover, AOPs are cost-effective and, as a pre-treatment step, can enhance the mineralization of these compounds. These points reinforce the motivation and necessity of our research on the selective degradation of the ofloxacin molecule^1,2.

The unregulated and excessive release into water bodies of persistent antibacterial agents and antibiotics in particular, fluoroquinolones such as ofloxacin, in the last few decades has become a critical environmental issue, simultaneously threatening human health and ecosystem health^3–5. Not only does ofloxacin alter the natural ecological processes, but also promotes the development of antimicrobial resistance, and due to its high chemical resistance, bioaccumulation potential and deleterious effects on environmental microbiomes has potential long-term risks to human health populations and other living organisms. The overcoming of such a critical issue must be arranged in the form of integrated, systematic approaches that might selectively degrade the substance under the influence of aqueous conditions, effectively, and in an environmentally friendly way, minimizing the byproducts and providing the opportunity to transfer the approach to other recalcitrant pollutants^6–8.

The principal novelty of this work lies in the combination of a sophisticated hierarchical system to explain the photonic sulfite activation mechanism with a noise-insensitive multi-output predictive modeling and evolutionary parameter estimation, which, concurrently, allows finding selective reaction pathways, predicting the behavior of a dynamic system, and optimization of the operational condition⁹. This overlap between photochemical reactions and artificial intelligence can allow for a significant reduction in undesired side reactions that cannot be controlled, allow the oxidative reactions to yield non-toxic end products and maximize chemical and energy yields. Through the concomitant utilization of photon energy to trigger sulfite species and through state-of-the-art multi-output predictive algorithms, the framework offers to gain tight control over key parameters, multifaceted interaction effects, and identify optimal work regimes, providing a structured framework for managing persistent pharmaceutical pollutants^10–14.

In pursuit of these goals, multi-output RANSAC modeling has been utilized to obtain nonlinear and multidimensional dependencies between the process characteristics and drug removal indicators with high precision and predictive stability and reliability are ensured by the nature of this modeling that is resistant to outliers and noise¹⁵. In tandem, the significant parameters in predicting the effects of the independent variables on the process efficiency, the characterization of the processes occurring in the molecules, the dynamics of the photochemical reactions and the multivariate interaction of the independent variables have been obtained by exploiting complementary evolutionary regression and parametric optimization, consequently, facilitating the design of complete controlled and efficient reaction pathways. The research novelty is additionally emphasized in the synergistic approach of photochemical reactions to a high-quality machine learning and evolutionary analysis where artificial intelligence is used as both a means of predicting a reaction with high accuracy and as a means of discovering and optimizing reaction pathways and parameters that determine a reaction^14,16,17. The integration in which it is possible to define optimal conditions of operation with the minimum side effects and maximum efficiency, steer ofloxacin molecular degradation along controlled and predictable trajectories, become the elements of a multidimensional and generalizable solution to the problem of persistent contaminants of the environment as a paradigm of designing and optimizing advanced environmental processes. The general objectives of the study are the development of a hierarchical model of photochemical sulfite activation, the development of noise-resistant multi-output predictive models, the exploration of the effects of interactions through evolutionary regression and parametric optimization, and the general optimization of operational processes in the area of persistent pharmaceutical removal. The study hypotheses include that, photochemical mediated sulfite activation can be used to promote selective molecular degradation of ofloxacin, that RANSAC-based multi output modeling can provide robust predictions with low noise, and that evolutionary parameter analysis can be used to determine which variables are the most influential and the best pathways to use in its operation. Hopefully, the research results will become notable contributions to the dynamics of photochemical reaction, multivariate interactions and influence of key parameters on the control over the pathways of the chemical and the environmental processes, to justify the design of sustainable environmental processes, and also to reinforce the importance of artificial intelligence as simulators, predictors and optimizers of complex chemical and environmental processes. It integrates environmental chemistry, photochemistry, machine learning, and evolutionary analysis to provide a multidimensional framework of environmental and pharmaceutical issues and to lay a foundation for future investigations connected to the management of complex persistent pollutants and to demonstrate its scientific, practical, and innovative application in the design of controlled and optimized processes.

While recent studies have successfully employed Artificial Intelligence (AI) and Machine Learning (ML) tools, such as Artificial Neural Networks (ANN), Random Forest, and XGBoost, to model the photocatalytic degradation of single pharmaceutical compounds or simultaneous removal of multiple contaminants (e.g., sulfamethoxazole, 17-β Estradiol, and carbamazepine), these approaches often rely on standard empirical correlations. However, such models may have difficulty capturing the complex, non-linear dynamics of photon-mediated sulfite activation. To address this limitation, the present study introduces a novel hierarchical framework for photon- mediated sulfite activation dynamics, integrating RANSAC-guided predictive modeling and evolutionary parametric optimization for selective ofloxacin degradation. Unlike conventional AI applications that primarily focus on predictive output, our work integrates High-Order, Stochastically-Governed Predictive Extrapolations with an Evolutionarily-Constrained, RANSAC-Guided Parametric Optimization Ontology. This unique approach not only predicts removal efficiency but also elucidates the mechanistic pathways of selective molecular fragmentation under stochastically governed conditions, offering a more structured and interpretable optimization framework compared to traditional black-box ML models¹⁸.

Materials and methods

Materials

The components employed were high-purity ofloxacin as the target contaminant, sodium sulfite as a source of reductive radicals, and interfering ions such as sodium chloride, potassium nitrate, sodium bicarbonate, and sodium sulfate. High-resistivity deionized water (≥ 18 MΩ·cm) was employed in the preparation of all solutions. Standard ofloxacin solutions in determining concentrations, e.g., 50 to 200 mg/L were prepared and sodium sulfite solutions at varying concentrations, e.g., 0.05 to 1.66 mM were prepared to investigate the effect of sulfite concentration on the degradation process. The effect of pH on the formation of reactive species and ofloxacin degradation was explored by adjusting pH range of 3–11 using phosphate or carbonate/bicarbonate buffers. All the solutions were prepared in clean glassware and filtered through 0.45 μm membrane so as to remove suspended particles and other impurities before the use in experiments.

The concentrations of ofloxacin applied in this research (ranging from 50 to 200 mg/L) exceed those commonly found in natural and aquatic environments. This deliberate selection of higher concentration levels was made to facilitate an in-depth and thorough examination of the photon-driven sulfite activation mechanisms and the resulting molecular fragmentation processes. Employing elevated concentrations enables the acquisition of consistent and dependable data within controlled laboratory settings, which is vital for the construction of the stochastic predictive frameworks and parametric optimization approaches developed in this study. Nonetheless, we recognize that these concentration levels do not accurately reflect real-world environmental conditions, and this limitation should be considered when applying the findings to natural contexts. Subsequent research should focus on assessing the validity and robustness of the proposed models and mechanisms at lower, environmentally relevant concentrations to verify their practical utility. Moreover, performing experimental validations using actual environmental samples is essential to confirm the models’ effectiveness and precision under real environmental conditions.

Photochemically-induced redox transformation and multi-parameter analytical surveillance

The UV reactor was built with a specific-wavelength lamp (254 nm) that had its photon flux controlled. Samples (500 mL) were placed in a reactor and the necessary quantity of sodium sulfite added to attain a predefined molar ratio of ofloxacin. Exposure to UV light using different contact times: 530 min was applied and the temperature maintained at 25 ± 2 °C. A medium-pressure UV lamp with a power of 125 W was positioned at a fixed distance of 1 cm from the reactor wall to ensure uniform irradiation intensity. The system was operated under nitrogen-sparged deoxygenated conditions to control dissolved oxygen levels. The samples were periodically withdrawn and quenched immediately using triethylamine or rapid neutralization to eliminate the further ofloxacin concentrations were measured using a UV-Vis spectrophotometer at 288 nm. BOD and COD were measured in accordance with APHA standard procedures, where BOD was gauged via microbial respiration whereas COD was through chemical oxidation using potassium permanganate. The operational parameters were as follows: pH (X1), UV intensity (X2), Sulfite concentration (X3), initial ofloxacin concentration (X4), contact time (X5), and sulfite to ofloxacin molar ratio (X6). Each experimental condition was repeated at least thrice to enhance reliability and minimize on experimental errors. The detailed experimental results are presented in Table S1 of the Supplementary Material.

Data analysis using Python, RANSAC Regression, and Evolutionary Algorithm Optimization

The dataset included six operational parameters (X1–X6) and three outputs (Removal 1: Ofloxacin degradation, Removal 2: BOD reduction, Removal 3: COD reduction). Data were loaded using Python (pandas) and standardized with StandardScaler to scale all features uniformly. They were forecasted as multiple outputs with a RANSAC robust regression fitted within the MultiOutputRegressor. The performance metrics of the model and of the testing and training sets were calculated as the MSE, MAE, RMSE, R², and Explained Variance to estimate the overall model results. The statistical advantage was estimated by the Gaussian multivariate linear equation method also known as OLS to obtain the regression coefficient standard errors and t-statistics to identify the significant variables. To find the optimum operating conditions, an evolution-based optimization algorithm, Differential Evolution was implemented, whereby, the combination of the parameters was randomly selected, their fitness values obtained using the RANSAC model, parents selected, mutating and crossover and so on, until the optimum solution is found. Optimal parameter combinations were then extracted to create radar and box-whisker plots of the optimal ranges depicting which parameter set best improved process performance. The dataset was constructed using all available rows from the main file.xlsx file. For model development and evaluation, the data was divided into training and testing sets with a ratio of 80% to 20%, respectively, using the train_test_split function with a test_size of 0.2. To ensure reproducibility, a fixed random state of 42 was employed during the splitting process. The input feature matrix consisted of six variables (X1–X6), while the target variables comprised three output metrics: Removal 1, Removal 2, and Removal 3.

Implementation, hyperparameter settings, and evaluation of the multi-output RANSAC Regression Model

In this study, a robust RANSAC regression model with multi-output support was used for modeling. The dataset consists of 33 samples with 6 input features (x1 to x6) and 3 target variables (Removal 1, Removal 2, and Removal 3). The data was randomly split into 80% for training (approximately 26 samples) and 20% for testing (approximately 7 samples) using the train_test_split function with a fixed random_state of 42 to ensure reproducibility. The input features were standardized using StandardScaler, where scaling parameters were computed only on the training data and then applied to the test data to prevent data leakage. The core RANSAC regression model was implemented using the RANSACRegressor class from scikit-learn’s linear_model module, initialized with random_state = 42 to guarantee consistent results. Other hyperparameters of the RANSAC model were left at their default values, which include min_samples=None (meaning the minimum number of samples required to estimate the model parameters is equal to the number of features, i.e., 6), residual_threshold=None (which enables automatic determination of the residual threshold based on the median absolute deviation of residuals), max_trials = 100 (maximum number of random sampling iterations), loss=’absolute_loss’ (the loss function used, which is robust to outliers), stop_n_inliers = inf and stop_score = inf (no early stopping based on number of inliers or model score), stop_probability = 0.99 (the probability that at least one random sample is free from outliers), is_data_valid=None and is_model_valid=None (default data and model validation functions), and base_estimator=None (which defaults to a simple linear regression model as the base estimator). To handle multiple outputs, the RANSAC regressor was wrapped within a MultiOutputRegressor, fitting one independent RANSAC model per target variable. The model was trained on the standardized training data, and predictions were made on both training and test sets. Model performance was evaluated separately for each output and dataset using metrics including Mean Squared Error (MSE), Mean Absolute Error (MAE), R² score, Root Mean Squared Error (RMSE), and Explained Variance. Additionally, a 5-fold cross-validation was performed on the training data to ensure robustness and to confirm the absence of overfitting or data leakage. All these settings and hyperparameters were carefully selected and documented to enable other researchers to reproduce the results precisely.

Results and discussion

Assessment of RANSACRegressor predictive capacity in modeling photochemically-driven redox transformations and associated variations in BOD and COD via comparative graphical analysis of observed and forecasted data in training and test sets

Figure 1 illustrates the performance of the RANSACRegressor model in predicting the efficiency of the UV/Sulfite process for the removal of the antibiotic ofloxacin (Removal 1), the reduction of BOD (Removal 2), and the reduction of COD (Removal 3). The figure has two key parts: The Ridge Plot and ECDF that offer independent views on model quality. In the Ridge Plot section, it can be observed that the distribution of actual and predicted values for both training and test data in all three cases exhibits relatively close alignment. For Removal 1, which represents the efficiency of ofloxacin removal, the model successfully captures the overall data trend. Deviations are however, restricted to the extreme values that are either very low or exceedingly high, possibly reflecting that the conditions in which the process is operating are not possibly within optimal conditions. An example is when the pH of the medium is also very low or too high, or the sulfite dose is low, higher errors can be observed in the distributions. At points of intense UV radiation intensity and or long contact time as the process performance levels reach the maximum, minor deviations are observed in the distributions since the model is exhibiting lower predictive accuracy such extreme boundary conditions. In Removal 2 where BOD reduction is modeled, the distribution alignment between training and predicted data is significantly improved in both training and test data indicating that the model has properly learned the relationship between process parameters on BOD reduction. This is especially significant because BOD serves as an indicator of biodegradable organic material. The model’s ability to predict BOD trends accurately suggests that it has learned the statistical relationships between process parameters and the resulting organic load. It is important to note that while BOD reduction implies potential enhancement in biodegradability, direct biological validation is required to confirm this mechanistically. In Removal 3, corresponding to COD changes, the overlap between distributions reaches its maximum, indicating that the model reconstructs COD values with minimal error. COD, reflecting the total oxidizable capacity of both organic and inorganic compounds, is highly sensitive to sulfite concentration and the molar ratio of sulfite to ofloxacin. The RANSAC model effectively represents such non-linear and complex relationships and gives the model predictions that are in agreement with the actual results to a large extent. The ECDFs illustrate the same phenomenon. In Removal 1, the results are mainly found to be near the 45-degree reference line, indicating close approximation between the actual and predicted results, except in the extreme values due to which some deviations are also obtained. In Removal 2, points nearly overlap with the reference line, indicating that the model can capture the combined influence of the key factors, namely ofloxacin concentration, UV intensity, and contact time, with high accuracy. In Removal 3, the alignment with the reference line is ideal, and there is negligible dispersion, which means the model has an excellent predictive ability concerning COD changes. As to parameter effects, pH has been ranked as one of the most important factors influencing the efficiency of sulfite radical generation; which has a significant influence on COD variations. These findings are consistent with existing literature regarding the role of pH in sulfite activation. Of particular importance to ofloxacin degradation and BOD reduction is the enhanced performance of the model by higher UV intensity enhances the model’s predictive accuracy. The sulfite concentration and molar ratio between sulfite to ofloxacin contribute most to changes in COD, and the model is capable of successfully modeling such relations quantifying thus the accuracy of RANSAC in dealing with detailed nonlinear relations. Contact time has a visible effect on all three indicators, with a larger effect on the removal of ofloxacin, since the longer the contact time the more the compounds can be decomposed through the biodegradation process. Overall, the models can be concluded to be an accurate method of modeling the UV/Sulfite process behavior in terms of ofloxacin removal and scope obtained to the reduction of organic load through BOD and COD. While minor prediction errors occur for ofloxacin removal efficiency under extreme conditions, the model achieves high accuracy in predicting BOD and COD changes. This demonstrates that the RANSAC adopted and optimization method using evolutionary algorithms would be a valuable resource in the modeling and prediction of advanced oxidations processes with the treatment of antibiotic-contaminated waste-water^19–23.

Fig. 1.

Comparative analysis of model performance via Kernel Density Estimation (KDE) and Empirical Cumulative Distribution Function (ECDF) for actual and predicted values in training and test data.

Residual analysis of the RANSACRegressor model for predicting ofloxacin removal efficiency and changes in BOD and COD in training and test data

Figure 2 (Violin Plot) shows the residuals for the training data (left) and test data (right) in the RANSACRegressor model. Considering that Removal 1 = Ofloxacin removal efficiency, Removal 2 = BOD reduction, Removal 3 = COD reduction, and independent variables (pH, UV intensity, sulfite concentration, initial drug concentration, contact time, and sulfite/ofloxacin molar ratio) affect the outputs, the plot can be interpreted as follows: In the training data, for Removal 1 (ofloxacin removal efficiency), the residuals are mainly centered around zero with a relatively balanced spread on both sides. It means that the model has successfully defined the effects of the parameters, i.e., UV intensity, sulfite level, and contact period, that enable making predictions near their actual values. Small tails on either side denote that prediction errors were found only when disproportionate concentrations of sulfite and ofloxacin were used or the pH was suboptimal. For Removal 2 (BOD reduction), the violin plot is wider, showing greater residual dispersion. This indicates that the model may not be able to explain all parameters to reduce BOD since BOD is more influenced by the availability of biodegradable organic matter and behaves differently. Some of the variables such as pH, contact time, and most importantly initial concentration of antibiotics add to the unpredictability of the forecasts. For Removal 3 (COD reduction), the plot is narrower and concentrated around zero, indicating that the model predicted COD changes from the UV/Sulfite process more accurately than BOD. This analysis has revealed that COD is primarily influenced by the UV intensity, and the sulfite concentration and that the good overlap between obtained and projected values shows that the model could align with the actual trends. In the test data, for Removal 1 (Ofloxacin removal), the residual distribution is narrow and close to zero with slight deviations, showing that the model accurately reproduced the UV/Sulfite system’s performance on new data. Important parameters that determined correct prediction of drug removal included the ratio of levels of sulfite/ofloxacin and intensity of UV. For Removal 2 (BOD reduction), residuals are slightly negative, indicating that the model generally predicted BOD slightly lower than actual values. This is because so called BOD-changes are complex, non-linear due to the dependence on other dissolved organic substances, pH and contact time. For Removal 3 (COD reduction), the plot is the narrowest, with nearly all residuals close to zero, demonstrating the model’s high accuracy in predicting COD changes in the test data as well. The overall look of these plots shows that the RANSACRegressor the model demonstrates strong predictive performance in making predictions of Ofloxacin removal efficiency (Removal 1) and COD reduction (Removal 3) both on the training and in the test sets, as the residuals are almost zero. This indicates that the model was able to capture the influences of such parameters as the UV intensity, sulfite concentration and contact time. However in regards to removal of BOD (Removal 2), the residuals are wider-spread, indicating that the model had difficulties in predicting this variable, given the complex nature of BOD and its sensitivity to various organic matter and operating conditions such as pH and initial contaminant^24–29. The predictive performance of the RANSAC-based model was evaluated using Mean Squared Error (MSE), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), R2, and Explained Variance Score (EVS) for both training and testing datasets. The results demonstrate high accuracy, particularly for the testing set, indicating strong generalization capabilities. For Removal 1, the model achieved an exceptional testing R2 of 0.995 with a low MSE of 0.660 and RMSE of 0.812, significantly outperforming the training metrics (R2 = 0.910, MSE = 11.814). For Removal 2, the model maintained robust performance with a testing R2 of 0.956 and RMSE of 2.574, compared to the training R2 of 0.862 and RMSE of 6.267, suggesting improved stability on unseen data. For Removal 3, the model exhibited near-optimal predictive performance, achieving a testing R2 of 0.999 with negligible error (MSE = 0.028, RMSE = 0.168), compared to the training MSE of 4.952. Overall, the significant improvement in testing metrics relative to training metrics across all three targets confirms the model’s ability to avoid overfitting and accurately capture the underlying dynamics of the system.

Fig. 2.

Graphical analysis of residual distribution of the multi-output RANSAC model in training and test sets using violin plots to evaluate error patterns across three output variables.

The study titled “Leveraging artificial intelligence models (GBR, SVR, and GA) for efficient chromium reduction via UV/trichlorophenol/sulfite reaction” investigated the removal of chromium ions using the advanced reduction process of UV/trichlorophenol/sulfite, employing artificial intelligence algorithms including Support Vector Regression (SVR), Gradient Boosting Regressor (GBR), and Genetic Algorithm (GA). The results indicated that the employed models suffered from overfitting despite high accuracy during the training phase. Specifically, the GBR model, which achieved an R2 of 0.999 on the training data, showed a lower R2 of 0.981 on the test data. Furthermore, the increase in RMSE from 1.529 in training to 2.756 in testing demonstrated that the model lacked adequate generalization capability for new data and was overly dependent on specific features of the training dataset³⁰.

Conversely, the study “Unveiling the role of artificial intelligence in tetracycline antibiotics removal using UV/sulfite/phenol advanced reduction process” focused on the removal of tetracycline antibiotics using the UV/sulfite/phenol advanced reduction process and an Artificial Neural Network (ANN) model. This research utilized a neural network structure comprising 5 input layers, 4 hidden layers, and 1 output layer. The results showed that while the model performed well on training data (R2 = 0.96), its quality declined in the test data (R2 = 0.902). The increase in Mean Absolute Error (MAE) from 1.8025 in training to 4.0631 in testing, along with the rise in RMSE, indicated that the ANN model failed to generalize the main patterns of the process effectively due to noise in the test data and imbalanced data distribution, thereby losing prediction accuracy on new data³¹.

The third study, titled “Artificial intelligence-based optimization and modeling of cadmium reduction via ultraviolet-assisted malathion/sulfite reaction mechanisms,” modeled cadmium removal using the UV/malathion/sulfite reaction mechanism and the GBR algorithm. This study also confirmed the phenomenon of overfitting; the GBR model achieved an R2 of 0.996 on the training data but only 0.981 on the test data. The increase in MAE from 1.23 in training to 2.25 in testing, and the rise in RMSE from 1.53 to 2.76, indicated that the model was excessively adapted to the training data, losing its ability to accurately predict new data. The author explicitly stated that this discrepancy reflected a reduced generalization capability of the model³².

In contrast, the results of our study using the RANSAC algorithm on UV/sulfite process data demonstrated that the RANSAC-based model possesses strong generalization performance. Unlike the previous three studies, which all faced increased errors and decreased R2 in the test phase, the performance metrics of the model in the current study were better in the test data than in the training data. Specifically, for the first removal target, the test R2 reached 0.995 and RMSE dropped to 0.812, showing more stable and accurate performance compared to the training data (R2 = 0.910). This superiority was observed across all three targets (Removal 1, 2, and 3), with MSE and RMSE in the test section decreasing significantly. This indicates the absence of overfitting and the model’s high accuracy in identifying the main patterns of the process.

Assessment of RANSACRegressor predictive precision in modeling ofloxacin degradation and associated BOD and COD reductions during photochemically-mediated oxidative transformations via quantile-quantile plot analysis

Figure 3 (Q-Q Plot) shows the Q-Q plots of the training and test data of the RANSACRegressor model, where, Removal 1, 2, and 3 corresponds to ofloxacin removal efficiency, BOD reduction, and COD reduction, respectively. The plots give a visual examination of the extent that model predictions are fitting the assumption of normally distributed errors. In the training data, Removal 1 points lie relatively close to the red reference line with slight deviations at both extremes, indicating that the model predicts average values accurately while showing minor errors at very high or very low values; the effects of UV intensity (X2), sulfite concentration (X3), contact time (X5), and sulfite/ofloxacin molar ratio (X6) are well captured. Removal 2 points exhibits higher scatter of points around the perfect line, particularly in the middle, which indicates that this model is not capable of explaining all changes in BOD because it relies on various organic materials, pH (X1), contact time (X5), and initial drug concentration (X4) creating nonlinear and complex relationships. The COD Removal 3 points are nearer the red line and exhibit a more uniform distribution compared to the BOD, thus demonstrating that COD results can be predicted very well; COD is more strongly impacted by the UV intensity (X2) and by sulfite concentration (X3), whereas the other parameters have about the same order of influence. For the test data, Removal 1 points remain close to zero with slight dispersion, showing good model performance on new data, with minor deviations at extreme values likely caused by large variations in pH or sulfite/ofloxacin molar ratio. Removal 2 points generally fall below the reference line, indicating a slight underestimation of BOD due to its inherent complexity and simultaneous dependence on multiple variables. Removal 3 points lie almost exactly on the reference line and near zero, with minimal scatter, demonstrating accurate COD prediction even for test data, as COD is a more stable and reliable measure of organic load dominated by UV and sulfite effects. Removal 1 and Removal 3 are most sensitive to factors X2 (UV intensity) and X3 (sulfite concentration) compared to the other factors affecting them, whereas pH (X1), contact time (X5), and sulfite/ofloxacin molar ratio (X6) affect the performance of ofloxacin removal to a considerable degree. The BOD prediction is a challenging task to conduct as the process is a non-linear response to numerous interacting factors. The Q-Q plots indicate that the RANSACRegressor model effectively predicts ofloxacin removal efficiency and COD reduction, with residuals approximately normal and near zero, whereas BOD predictions exhibit larger errors^13,14,33,34.

Fig. 3.

Graphical analysis of the alignment of residual distributions with the normal distribution using Q-Q plots for each output of the multi-output RANSAC model in the training and test datasets.

Quantitative assessment of perational feature contributions in predicting ofloxacin degradation and concurrent BOD and COD mitigation via RANSACRegressor modeling during photochemically-mediated oxidative transformations

Figure 4 shows the values of the six input parameters as predictors of three outputs in RANSAC regression modeled as efficiency of UV/ sulfite process, BOD reduction, and COD reduction. The plots show the influences of the parameters, including pH (X1), the UV intensity (X2), sulfite concentration (X3), initial concentration of ofloxacin (X4), contact time (X5) and sulfite/ ofloxacin molar ratio (X6) on the model. Among parameters which affect the UV/Sulfite removal efficiency, UV intensity (X2) is the predominant factor. This aligns with the hypothesis that UV radiation acts as the primary energy source for initiating photochemical reactions. The high importance of UV intensity supports the assumption that the degradation process is driven by photochemical activation rather than purely thermal or chemical pathways. As to BOD reduction, the initial ofloxacin concentration (X4) has pivotal role (0.481) in determining the removal of BOD. The intensity on X2 (UV) is also significant (0.354), whereas pH, and concentration of sulfite, contact time and molar ratio are less significant. This is an indication that the decrease in BOD is influenced mainly by the pollutant load and the impacts of UV. Ofloxacin concentration (X4) is the most important parameter again (0.543), followed by UV intensity (X2) (0.317) in reducing COD as a measure of chemical oxygen demand removal. This shows that the chemical content of the system and the UV oxidation ability are significant factors in COD reduction but the rest of the factors have less significant contribution. In general, UV intensity and initial ofloxacin concentration are the two most influential factors relating to UV/Sulfite process performance in degrading pollutants and removal of BOD and COD. The moderate factors which still have significant impacts are pH and contact time, whereas the sulfite concentration and the sulfite/ofloxacin molar ratio have minor impacts. The obtained results indicate that maximizing UV intensity and working on the optimization of the antibiotic concentration is instrumental in the most efficient pollutant degradation and minimizing the biological load as well as the chemical one. These relationships are well fitted by the RANSACRegressor model and hence such a model would be useful in the design and optimization of similar processes^35–39.

Fig. 4.

Relative importance analysis of input variables in the model for predicting the three removal indices: Removal 1, Removal 2, and Removal 3.

Correlation analysis of advanced photochemical treatment operational parameters with ofloxacin degradation and organic load reduction using the RANSAC regression model

In the RANSAC model, correlation among the input parameters (pH, UV intensity, sulfite concentration, initial antibiotic concentration, contact time and sulfite/ofloxacin molar ratio) and the output indices: Ofloxacin removal efficiency (Removal 1), BOD reduction (Removal 2), COD reduction (Removal 3) are provided in Fig. 5. Colors that are closer to red suggest positive correlations, and colors that are closer to blue suggest negative correlations. As it can be seen, the sulfite/ofloxacin molar ratio (X6) demonstrates the most powerful positive correlation with Removal 1 (0.83), Removal 2 (0.81), and Removal 3 (0.81) indicating that an increased sulfite-to-ofloxacin ratio is associated with higher removal efficiency and improved BOD and COD reduction, while noting that this is a correlation and does not establish causation. Also, UV intensity (X2) is positively correlated with all three outputs (around 0.82 when activating sulfite, 0.64 and 0.61 when activating the other two), which shows a statistical correlation that may be consistent with proposed mechanisms of sulfite activation and radical formation, though these mechanisms require direct experimental confirmation. Sulfite concentration (X3) is moderately and independently positively related to the outputs, although, as it is closely related to the molar ratio, its main influence also is manifested through X6. On the other hand, the correlations between the initial ofloxacin concentration (X4) and the three outputs (approximately − 0.58, -0.61, and − 0.63) are negative, which is reasonable since higher drug concentrations complicate the removal process and decrease BOD and COD. pH(X1) and contact time (X5) are less strongly correlated with the three outputs (between 0.25 and 0.41), which makes sense since the two factors influence the process but weaker than UV intensity and the molar. Also, strong correlations exist between the three output indices at the bottom of the plot (all above 0.98), indicating that in the event that the conditions of the UV/Sulfite process are conducive to effective ofloxacin removal, the reductions in BOD and COD also occur concomitantly, which highlights the practical importance of optimizing key operational variables such as UV intensity, sulfite concentration, and the molar ratio, without implying direct mechanistic proof^14,16,40,41.

Fig. 5.

Correlation analysis between input variables and removal indices using a correlation matrix visualized as a heatmap.

Sensitivity assessment of the RANSAC regression model for predicting ofloxacin degradation and organic load reduction under perturbed operational conditions in an advanced photochemical treatment system

Figure S1 in the supporting information file depicts the response of the RANSAC regression model to perturbations or errors in the input data for the three outputs about the UV/Sulfite treatment for ofloxacin: Ofloxacin removal efficiency (Removal 1), BOD reduction (Removal 2) and COD reduction (Removal 3).Inside, the horizontal axis represents the noise intensity, added to the input variables (pH, UV intensity, S, initial concentration of antibiotic, contact time and S/Ofloxacin molar ratio), the vertical axis represents the model mean squared error (MSE) on the test data set. The blue curve (Removal 1) shows that estimates of ofloxacin removal efficiency are consistent at lower levels of noise, then as perturbations build the model error rapidly increases away from standard deviation of 0.9. This indicates that the model’s predictions are sensitive to input variations. For COD (Removal 3), the relative stability of predictions is consistent with the view that COD measures total oxidizable capacity, which is a more robust chemical parameter compared to BOD, which depends on complex and variable biological interactions. The green line (Removal 3) for COD reduction is the most stable one. In the case of high noise, the error is relatively small, not more than 40. This constancy suggests that COD as an aggregate property of organic contamination is less noisy than BOD or Ofloxacin concentration. But other variables like contact time or starting antibiotic concentration are predictable and stable in their effect on COD^42–46.

Statistical validation of mechanistic insights from RANSAC modeling

While the primary objective of this study was to optimize the UV/sulfite process using statistical modeling, it is important to address the interpretative boundaries of our approach. The RANSACRegressor model provides high-fidelity predictions of process efficiency (Ofloxacin removal, BOD, and COD reduction) based on operational parameters. However, we explicitly acknowledge that statistical correlations do not constitute direct experimental proof of mechanistic pathways, such as specific radical stability or fragmentation products. To bridge this gap, we utilize the model’s high predictive accuracy (R² test = 0.999 for COD) and sensitivity analysis (Fig. 6) as indirect proxies for process behavior. The strong positive correlation between UV intensity and sulfite concentration with removal efficiencies (Fig. 5; R > 0.80) appears to be consistent with existing hypotheses about sulfite activation and the generation of reactive sulfur radicals (sulfite and sulfate); however, this requires direct experimental confirmation. The observed increase in prediction error under perturbations of these inputs (Fig. 6) may indicate that the process is sensitive to radical generation rates, which would be consistent with radical-mediated oxidation mechanisms; nevertheless, direct experimental evidence is necessary to confirm this interpretation. Regarding biodegradability, the significant reduction in BOD (Removal 2) statistically correlates with the degradation of ofloxacin. While we cannot claim verified “biodegradability enhancement” without microbial assays, the significant reduction in BOD serves as an indirect indicator that the UV/sulfite treatment may break down complex organic structures into smaller, potentially more biodegradable fragments; however, this hypothesis cannot be confirmed without microbial and biodegradability assays. It should be emphasized that statistical models and correlations provide probabilistic relationships among parameters but cannot substitute for direct mechanistic assays such as identification of radical species via Electron Spin Resonance (ESR) or characterization of transformation intermediates. Identifying specific radical species via Electron Spin Resonance (ESR) and evaluating the toxicity of transformation products are essential for a complete mechanistic understanding. Consequently, we have tempered our discussion to focus on predictive performance and operational optimization rather than definitive mechanistic claims. Future studies are recommended to integrate these statistical insights with direct chemical and biological assays to further clarify reaction pathways and ensure the environmental safety of UV/sulfite treatment.

Fig. 6.

Trend analysis of population fitness distribution, minimum, and mean values across successive generations in the evolutionary algorithm.

Evolutionary optimization of advanced photochemical treatment for ofloxacin degradation and organic load mitigation: regression analysis and key parameter identification

In Figure S2 in the supporting information file, three different responses (Ofloxacin removal (Removal 1), BOD reduction (Removal 2) and COD reduction (Removal 3)) are illustrated as a function of six input parameters (pH, UV intensity, sulfite concentration, initial contaminant concentration, contact time and sulfite/contaminant molar ratio).The regression coefficients represent how each parameter positively or negatively (and significantly) influences the predictions of the optimized model in the evolutionary algorithm. In the case of Removal 1 (direct ofloxacin removal) it’s clearly UV intensity (X2) being the predominant factor. A positive coefficient (higher than 0.8) indicates that the enhancement on degradation of ofloxacin with increasing UV intensity has a direct and strong effect. Thus, UV serves as the major energy source to activate sulfite and yield reactive radical species including SO₃⁻ and OH, leading to cleavage of the ofloxacin framework. Without enough UV, the system becomes largely ineffective. There is also a relatively small yet important positive effect from pH (X1) under Conditions 1, which corresponds to the effect of the pH on the stability and activity of the radicals (e.g. sulfite radicals are more stable under alkaline conditions). Sulfite concentration (X3) has a positive effect, but it is much less than UV, because the sulfite is precursor for radical generation, while much higher concentration of sulfite is able to absorb UV or to scavenge radicals. In other words, initial ofloxacin concentration X4 has negative significant coefficient indicating that higher pollutant load decreases the relative degradation induced by the less radical concentration. Rapid reaction kinetics dominate the process and contact time (X5) and the molar ratio (X6) are negligible, so the molar ratio cannot be the decisive controlling factor, and the whole reaction environment is relatively more important. Removal 2 (BOD reduction) again very similar to Removal 1; here again UV intensity (X2) is highly significant. This is consistent with the fact that UV and radicals degrade ofloxacin and complex organic compounds into simpler and easily oxidizable compounds (less biological O2 required) while pH had a positive influence (a change in pH could help divert reaction pathways to simple compounds).Sulfite once again has a positive (but smaller) effect, and the initial contaminant concentration (X4) has a negative effect again; for higher pollution levels, complete degradation will be slowed down, which results in reduced BOD removal. Contact time and molar ratio are not important since most BOD reduction takes place in the early stages of the reaction. Again, UV is the dominant factor in the equation for Removal 3 (COD reduction), but with its highest coefficient slightly less than the other two responses. Note that COD is for total organic oxidizable, not for the single compound ofloxacin, so even if the UV intensities are high, it is possible that some compounds need longer and/or more extreme conditions before they are completely oxidized; pH is still positive and sulfite will be relatively greater since COD is for all oxidizable organics so increase in radical is beneficial for reduction. The initial concentration of ofloxacin (X4) again shows a negative effect and contact time as well as molar ratio are insignificant while assuming that most of the reactions are carried out fast and excess molar ratio does not significantly improve the performance. In summary, at all removal indices UV intensity (X2) is the most important factor, and if UV is weak, process efficiency is poor; pH and sulfite concentration (X1 and X3) are Pareto efficiency factors that cannot go below a certain level, but designable values are more significant than absolute numbers. It is determined that initial ofloxacin concentration (X4) has a negative influence on the process consistently, and contact time (X5) and molar ratio (X6) are of less importance. Under the premise of the evolutionary optimization model, the weight of X2, X1 and X3 should be the highest, X4 is a constraint factor, while the weight of X5 and X6 is almost negligible.

Evolutionary algorithm-based optimization of a photochemical degradation system for ofloxacin and organic load reduction: tracking fitness dynamics across generations

Figure 6 shows the evolutionary optimization model for UV/Sulfite process used for removal of ofloxacin. The number of generations in the horizontal axis and the fitness value along the vertical axis is above highlighted, which shows the efficiency of removing ofloxacin and simultaneously removing BOD and COD. The boxplots show the spread and distribution of fitness values in each generation, the average fitness in that generation is shown by the green line, and the best fitness within that generation is shown by the red line. Both the mean and optimal fitness values of this category are low; reflecting that parameter combination including pH, UV intensity, sulfite concentration and molar ratio were not effective for increasing O-MR and BOD and COD abatement favoring ofloxacin removal in first few generations (0–2).In generation 3, we observe a considerable jump: the mean fitness exceeds 130 and the best fitness is in the neighborhood of 50.It can also be said that, there was a large standard deviation, and hence different combinations of parameters extremely performed either well or poorly. This is generally because the algorithm converges to a close to the optimal range of parameters, for example, an acceptable UV intensity range or a range for an effective sulfite/ofloxacin molar ratio. This results in generations 4 and 5 having a steep decrease both in mean and best fitness values. This is because less favorable combinations may not lead to test emissions through competitive effects which decrease test efficiencies, such as low folate compounds due to excessive sulfite concentrations, or pH ranges where radicals are not generated. From generation 6 onwards, they again see an upward trend. The average fitness follows a vertical jump to around 80 and the maximum fitness approaches 65. The boxplots decrease, which means that the algorithm is converging to a stable and satisfactory solution. At this point, it is possible to conclude that a satisfactory ensemble of key variables - pH, UV intensity, sulfite concentration, initial ofloxacin concentration, contact time, sulfite/ofloxacin mol ratio - has been determined by the evolutionary algorithm to maximize the Ofloxacin removal (Removal 1), BOD reduction (Removal 2), and COD reduction (Removal 3).Overall, this figure shows how suboptimal parameter combinations were explored by the evolutionary program from the beginning, then improved into good parameter ranges at gen 3 (again, I did not gravitate to show weaker candidates), and then converged to efficient assumptions in the last generations. This type of behavior is in close agreement with the experiment sequential roles of the parameters, since each of the variables propitiate on its own and in combination the radical production, the reaction speed and thereby the efficiency of pollutant removal^{14,27–29,47}.

Evolutionary optimization of a photochemical treatment system for ofloxacin degradation and BOD/COD mitigation: distributional, mean–standard deviation, and risk-based analyses

Figure 7 shows a selection of analytical plots from the evolutionary optimization model for the UV/Sulfite process to remove ofloxacin and reduce BOD/COD. The plots consist of three columns, representing the three removal indices: Removal 1 - Efficiency of removal of Ofloxacin, Removal 2 - BOD Reduction, Removal 3 - COD Reduction Mean and standard deviation of the parameters are listed on the left hand column, the distribution of removal values can be found in the middle hand column, and the right hand column shows risk analysis (VaR). In the left column (Mean & Std Dev of Parameters) changes in parameter values over generations are displayed. For each of the three REMOVAL indices (REMOVAL 1, 2 and 3), a significant increase can be shown over generation 3 and the mean REMOVAL index has its maximum value. The marked increase is caused by favorable changes of S concentration (X3) and UV intensity (X2) allowing more efficient radical generation and ofloxacin degradation. Moreover, the molar amount of the sulfite at the beginning of the reaction x6 (sulfite/ofloxacin molar ratio) and pH X1 (initial pH degree) at this step are key parameters because they have a direct impact on the radical species and the slowing down rates of the reaction. After generation 3 the mean values slowly drop while the algorithm approaches equilibrium and convergence at stable values. In the middle column (Removal Distribution) distribution of the efficiency values for each index is reported. For REMOVAL-1 (UV/Sulfite Efficiency) the values vary from 40 to 80 and there is a large variation in possible results, depending upon parameter combinations. In REMOVAL-2 (BOD Reduction) a broader distribution is seen indicating other parameters, such as time of contact (X5) and initial concentration of ofloxacin (X4), seem to have a substantial effect on BOD variations. For REMOVAL-COD Reduction (REMOVAL-3) the results are more focused in the 65–90 range, which indicates a better convergence and therefore stability of the algorithm when working with COD reduction, compared to BOD. In the right column (Risk Analysis- VaR 95%) the Value at Risk (VaR) for each removal index is presented. VaR is the minimum expected remediation efficiency with a confidence level of 95%. For REMOVAL-1, the VaR is about 40.16 which means that there is a 95% chance of not dropping below 40. For REM consumption module (REMOVAL-2), the value of VaR is approximately 25.98 which stands for an increased risk for BOD reduction due to effect of the complex organic mixture. For REMOVAL-3, it is 66.19, far higher than other indexes, indicating that the algorithm could obtain COD reduction with high reliability and stability. The dependency of this process-latin variant on process parameters is visible: the pH (X1) defines the conditions for sulfite and ofloxacin species formation and the reaction rate. The UV intensity (X2) and sulphite concentration (X3) have a direct effect on the active radical formation and were responsible for the efficiency jump in generation 3. Initial concentration of ofloxacin (X4) characterizes the pollutant load and has strong influence on BOD and COD variations. Contact time (X5) controls end-point of completion of reaction and additional source of stability for subsequent generations. As well, the molar ratio of sulfite to ofloxacin (X6) is an important parameter for algorithm convergence, higher ratios generally lead to greater efficiency, whereas lower ratios may also achieve substantial removal under certain conditions. Overall, the plots reveal that the evolutionary algorithm first exhibits a sharp increase in removal efficiency, but subsequently followed the successive approach of trial and error towards the optimal parameter combinations and finally stabilized with high certainty in COD reduction while BOD reduction still occurred with skewed risk^16,17,48.

Fig. 7.

Statistical analysis of input parameters, output distribution, and 95% VaR-based risk assessment for each removal index.

Distributional and stability assessment of pharmaceutical degradation and BOD/COD mitigation efficiency using evolutionary algorithm-based optimization in a photochemical treatment framework

Figure 8 shows a collection of analytical plots from the evolutionary algorithm optimization model for each of the three REMOVAL indices: Removal 1 - Efficiency of ofloxacin removal, Removal 2 - BOD reduction and Removal 3 - COD reduction. Each column represents one of the indexes and for each index three types of plots are displayed: Box Plot, Violin Plot, KDE Plot. These plots show the areas where data can be found and how process performance varies under optimized conditions. In the first (Box Plot) the analysis range of the shared data for all three REMOVAL indices is restricted. For removal efficiency (REMOVAL-1 of ofloxacin), values fell between about 40 and 80 with a median of 60–65 and the majority of parameter combinations resulted in moderate to high removal efficiency. The distribution of the removed compound category (by REMOVAL-2, preferably BOD reduction) is wider with a few outliers at lower values, which is concurrent to the increased sensitivity of the index to operational parameters, such as initial ofloxacin concentration (X4) and contact time (X5). For REMOVAL-3 (COD reduction), the two-sided box plot is thinner and the median is larger (~ 80) which indicate that COD reduction is more stable and reliable than BOD reduction and the values of the evolutionary algorithm converge better and the performance is well optimized. In the second row (Violin Plot) not only the factors median and spread are visible but also the shape of the distribution can be seen. In the case of removal mode, i.e. removal mode 1 (REMOVAL-1), it shows a mild bimodal distribution where some of the parameter sets generated a low efficiency while some others produced high efficiency, probably according to the influence of pH (X1) and sulfite concentration (X3) on optimal radical formation. The more even and wider the operation range of REMOVAL-2 demonstrates the greater sensitivity of BOD to operating conditions, particularly the sulfite/ofloxacin molar ratio (X6) and contact time (X5). For removal 3 the distribution had a higher concentration at higher levels, suggesting that the algorithm isolated parameter sets for which COD reduction was relatively high. In the third row (KDE Plot) the probability density of each index is shown. For REMOVAL-1, the curve is relatively wide with a peak in the 60 band point (highest probability of ofloxacin removal efficiency). Under the other scenario, REMOVE-2, the Priori curve is broader and skewed with about half the data falling off below 50, for higher risk of BOD reduction. For removal 3, the curve is narrow and has a sharp peak around 80, indicating that this site has a higher level of confidence and stability in reducing COD. Relationship with parameters (X1–X6) is as follows: Direct effect of pH (X1) and UV intensity (X2) on sulfite activation and radical generation is observed and has a significant effect on REMOVAL-1. Higher amounts of sulfite (X3) promote improved degradation rates at optimal concentration but can also induce competitive effects at elevated concentration adding noise to the results. Initial ofloxacin concentration (X4) determines pollutant load and influences change in BOD as well as COD. While contact time (X5) compromises the variance of BOD, it does increase convergence of results. All three indices are highly sensitive to process parameters, but are remarkably affected by the molar ratio of the sulfite/ofloxacin used (X6). Based on the distribution plots above, in the past evolutionary algorithm model, it could be seen that the efficiency of removal of ofloxacin and COD are more stable and highly predictable; meanwhile, the efficiency of BOD removal has been more variation with higher uncertainty in removal efficiency. These results show that some key parameters such as molar ratio and UV intensity should be properly optimized for co-removal of pollutant and reduction of the dissolved organic indices by photochemical method^16,49.

Fig. 8.

Comparative analysis of removal distributions using Box, Violin, and Kernel Density plots.

Influence of operational parameters and convergence dynamics of evolutionary algorithm-based optimization on pharmaceutical degradation and organic load mitigation in a photochemical treatment system

Figure S3 in the supporting information file shows the results of using the optimization model based on an evolutionary algorithm for the process of UV/Sulfite for the degradation of antibiotic ofloxacin. A detailed picture of the change of six input parameters is presented, and how the changes affect three different performance indices is also demonstrated. Reaction pH (X1), UV intensity (X2), sulfite concentration (X3), initial ofloxacin concentration (X4), contact time (X5) and molar ratio of sulfite: Ofloxacin (X6) are the independent parameters of process. The three performance efficiencies represent ofloxacin removal efficiency (Removal 1), BOD reduction (Removal 2) and COD reduction (Removal 3). Our analyses indicate that the optimal pH range for the UV/sulfite process lies within the neutral to slightly alkaline region (approximately pH 7.0 to 8.5). This finding is consistent with the fundamental chemistry of sulfite photoactivation: in this pH range, the predominant species are bisulfite (HSO₃⁻) and sulfite (SO₃²⁻), which efficiently photolyze under UV irradiation to generate reactive sulfur radicals (SO₃^∙−). In acidic conditions, sulfite tends to convert into volatile SO₂ gas, which reduces the availability of precursors necessary for radical generation, thereby decreasing degradation efficiency. Figure S4 in the supporting information file shows that the pH parameter (X1) is located within relatively narrow ranges for all three removal scenarios and exhibits narrow distributions. This may indicate that the parameter maintained relatively constant values within the optimized range. UV intensity (X2) is narrowly distributed across all plots and mostly at low levels. This implies that the effect of UV intensity on process efficiency becomes minor above a certain threshold, so raising the UV intensity apparently is not economically or energetically justified. The model-based optimization has shown that even at a lower UV dose, a strong synergistic effect with sulfite is sufficient to lead to effective outcomes. The concentration of sulfite (X3) also appears to be narrow in all three parameters, indicating that this excess sulfite was not required and that a low concentration is adequate for maximum performance. This result has both economic and environmental implications, as less sulfite is required, thereby producing less of a byproduct that is cheaper to dispose of and/or recycle. Initial ofloxacin concentration (X4) has the highest variation, for all the three metrics, for Removal 1. This poses its critical role in degradation process, and the algorithm seeks several values of X4 to maximize others for different loads of pollutants. Contact time (X5) is optimized to medium-to-high values for all of the three metrics, showing that adequate reaction time is required for good degradation. Too brief process runs may decrease process productivity, too long process runs may be a waste of resources and less economical. Thus an optimum contact time is a compromise between efficiency and economics. However, for all three metrics, the molar ratio of sulfite to ofloxacin (X6) is approaching zero, so low ratios are sufficient to reach optimum and also demonstrate that first-order estimations and above are not needed, nor should they be considered from an economic and environmental perspective. The bottom Panel of the figure illustrates the shape of change in population diversity over 50 generations for all three metrics. At the start of the optimization population diversity is large, as all algorithms explore a wide range of parameter space within the initial population. This makes it possible to perform proper evaluation before getting trapped into local optima. Finally, as the process of evolution proceeds and population size increases over the generations, the amount of variation will again converge to an asymptote (a slowly-decreasing optimum) while searching along the compromise between exploration and exploitation. The remaining diversity of later generations ensures that premature convergence will not set in, and that continuous improvement is possible. Furthermore, based on the distribution analysis of corresponding parameters and population diversity, the evolutionary algorithm shows good ability to detect the main influencing factors of ofloxacin degradation, pH, initial ofloxacin concentration, and contact time were found significant factors to enhance removal and reduce BOD and COD, while UV intensity and sulfite concentration/molar ratio were optimized to lower values and less dominant. The successful development and use of this strategy has practical implications for UV/sulphite process design and optimization and shows that this optimization algorithm is sufficiently general that optimization can be carried out efficiently and effectively over the full range of constraints^16,49.

Evolutionary optimization of a photochemical treatment system for pharmaceutical degradation and organic load reduction: analysis of population fitness dynamics across generations

Figure 9 shows the evolutionary optimization model convergence and “learning” behavior for 3 outputs. Each panel shows a set of box-whisker plots for successive generations of the population: the median fitness for that generation is indicated by the center line of the box, the height of the box indicates the interquartile range (50% of the data) and the whiskers represent the best and worst individuals in each generation. The orange dotted line represents the expected/reference max fitness. The median fitness increases in all three panels, from early to mid-generations, while the width of the boxes and the lengths of the whiskers gets smaller, this implies that after an initial variation stage, where there are successive mutations in the population, the population approaches the near-optimal solutions. Fitness of Removal 1 (Ofloxacin removal) is increasing rapidly, but the early generations show high variability. As you go up and down generations, the median will move towards the dashed line and variance will reduce. This behavior is consistent with sensitivity of direct ofloxacin removal to photochemical parameters; pH (X1) controls speciation of sulfite, HSO₃⁻/SO₃²⁻, and radical availability, UV intensity (X2) controls photon flux and radical production rates, and sulfite/pollutant molar ratio (X6, dependent on X3, X4) controls whether sufficient radicals are available for effective attack (low > limited radical, high > scavenge). Thus the algorithm can only optimize X1, X2 and X6 at the same time, and achieves high degradation efficiency, and this is the reason for fast convergence and then stability. For Removal 2 (BOD removal), growth is lower and variations in the fitness remain longer. BOD removal is dependent not only on the disappearance of ofloxacin, but also on the nature and quantity of biodegradable intermediate products. Here the values of X4 (initial ofloxacin concentration) and X5 (contact time) gain an increased significance. At higher pollutant loading, though partial breakdown might initially increase the availability of compounds to bacteria, optimum dosage and time need to be maintained to achieve BOD reductions stably. X2 and X3 still play key roles, but their activity is nonlinear since a compromise must be reached between radical production and inhibition of “semi-oxidized/reduced” intermediates. Thus, median fitness and box narrowing are retarded. In delineation 3 (COD reduction), stabilization happens earlier and boxes are thinner. COD measurements, as a bulk parameter of oxidizable organic material, decline successively after adequate radical supply is furnished by X2 and X3 to break longitudinal major bonds. Its sensitivity to special biodegradable pathways is lower than for BOD, so convergence is faster and more stable. We found pH (X1) to be important across all outputs; higher pH favors the oxidizing SO₃²⁻, which increases radical yields under UV irradiation; however, if pH is too high, radicals that produce H₂O₂ may not be in an activated state, resulting in reduced radical yields and side reactions between H₂O₂ and radicals. The fitness is near the maximal level, X1-X6 is balanced as a result. Briefly: for Removal 1 × 1, X2, X6 and convergence after a few generations is fast; for Removal 2 × 4 and X5 are more powerful and intermediate product dynamics are responsible for a slower transition to stability; for Removal 3 × 2 and X3 are more powerful and stable response is fast. These patterns are consistent with the physicochemical logic of the UV/sulfite reaction, and show that the EA optimization model drove the population from a highly variable initial search space to stable, near-optimal operating regions for all three targets^27–29.

Fig. 9.

Population fitness over generations for different removal scenarios using the differential evolution (DE) algorithm.

Identification and comparative analysis of optimal operational conditions in a photochemical treatment system for pharmaceutical degradation and organic load mitigation using an evolutionary algorithm

The radar plot that results from the evolutionary optimization model is shown in Fig. 10 and shows the best possible values for parameters proposed by the algorithm for three different outputs: the direct ofloxacin removal in the UV/sulfite process (removal 1), the reduction in BOD (removal 2), and COD removal (removal 3).The colored lines on the six axes of the parameter space graph describing the needed conditions for each output and the algorithm has chosen the best combination from the complex parameter space. Regarding the other parameter pH, optima values of all three streams are in the alkaline region, however there is some variability: around pH = 8 for direct OA elimination, around pH = 10.4 for BOD reduction, and around pH = 9 for COD reduction. This indicates an enhanced direct drug breakdown at mildly alkaline conditions under which the sulfite ion (SO₃²⁻) is more stable and the production of the reducing radicals is more efficient. BOD degradation requires a more alkaline environment in order to destroy not only the primary contaminant but also biodegradable by-products. COD as a measure of total organic load is reduced more readily under mildly alkaline conditions, as the principal goal is bulk degradation rather than biodegradability. The outputs have varying UV intensity. As the structure of ofloxacin is complex, it takes more photon energy to break bond for its removal, therefore, higher intensity is recommended for Removal 1. As COD and BOD reduction is more dependent on the bulk of the reaction volume and on radical interactions, for these transformations and applications lower intensities are sufficient. This amounts to saying that while the photon input needs to be substantially increased for direct drug removal, excessive UV irradiation is not required for BOD or COD reduction. A similar interesting pattern is shown for the concentration of sulfite in solution. For amines and thus for the three types mentioned above, a higher concentration optimum is preferred for Removal 1 and 3 and a significantly lower concentration optimum for BOD. Mechanistically, COD reduction and direct ofloxacin removal only occur at sufficient SO₃⁻ radical concentrations that are supplied by higher sulfite concentration. However, an excessive sulfite added to BOD reduction may increase biodegradability in the partially oxidized compounds while leaving them with a higher BOD; thus, a lower sulfite concentration is the best result for this output. For initial ofloxacin concentration, the algorithm chooses a large value for Removal 1, which suggests that the maximum degradation is possible even for relatively high pollutant concentrations. For BOD the optimum concentration is low due to minimum initial loading and intermediate product formation; whereas COD favors a medium optimum due to the optimum ratio between bulk degradation and amount of input pollutants. Reaction time for all three outputs is relatively high and comparable, on the order of 26–29 min, which is consistent for the time required to let the necessary radical reactions finish. BOD and TSS reduction is suggested to be slightly longer for by-product degradation. The molar unit ratio of sulfite to ofloxacin is about the same for the batches, about 1.2–1.37. This has suggested that the ratio of the contaminant to the reactive species needs to be near stoichiometric for optimal performance, while a slightly higher ratio of BOD is required to generate free radicals for the further breakdown of biodegradable by-products. All in all, the radar plot shows that the evolutionary algorithm can determine different optimal settings for different outputs. For the monitored processes, direct removal rates of ofloxacin increase with increasing UV intensity and sulfite concentration, BOD removal requires an alkaline environment, low sulfite concentration, and increased reaction time, and COD removal is possible with an optimal combination of slightly alkaline pH and adequate sulfite concentration. Therefore, the radar plot provides a full overview of the optimization solution, including how high or low the parameters should have been adjusted in order to achieve an optimum prospect performance (with respect to the outcome taken into account)⁵⁰.

Fig. 10.

Optimal parameters for each removal scenario using the Differential Evolution (DE) algorithm.

Regression analysis of operational parameter effects on pharmaceutical degradation efficiency and organic load reduction in a photochemical treatment system

Table S2 in the supporting information file describes the regression result for 3 types of outputs: Removal 1 (Removal profile of ofloxacin with UV/Sulfite), Removal 2 (BOD reduction), and Removal 3 (COD reduction). A row represents the impact of an independent variable (X1 to X6) or the constant (const) on the output response. Meaning, the coefficient tells us how much of an effect each parameter has, in what direction (significance), p tells us how significant that effect is (usually significant = p < 0.05) but the R-squared just tells us how good the model is at explaining the change in response. For Removal 1, the R-Squared value is equal to 0.9344, showing that the regression model explains 93% of the variation in removal efficiency. A high accuracy is achieved which strongly assures the selected parameters adequately represent the process trend. Among the variables tested, pH (X1) had a positive coefficient of 1.08 and a p-value of 0, which means there is a statistically significant positive effect for the variable on the removal of ofloxacin. UV intensity (X2) has a strong positive impact (coefficient 10.2; P = 0) and is expected due to the higher photo flux leading to increased energy for radicals as per photochemical theory. Sulfite concentration (X3) has a positive but statistically insignificant effect (p = 0.5734), suggesting its influence may be shown in combination with all other parameters. On the other hand, initial ofloxacin concentration (X4) has a negative coefficient, meaning that the higher the load of pollutants, the lower the removal efficiency, p ≈ 0.0754 (marginally significant). Contact time (X5) and molar ratio (X6) have positive non-significant effects. Therefore, the external loading parameters pH and UV intensity are the key variables for Removal 1. For the Removal 2 (BOD reduction), R-squared is 0.9087 that is less than but it still is high. pH(X1) has a positive and significant effect (coefficient 1.09, p ~ 0), while UV intensity (X2) has significant effect also (coefficient 11.3, p ~ 0). The negative but not significant impact on the concentration of sulfites (X3, p = 0.9564), while the initial concentration of ofloxacin (X4, coefficient − 0.14, p = 0) has a negative and significant impact, indicates that the presence of a higher initial concentration of contaminants, inhibits the BOD reduction process. As expected, longer exposure of the structures leads to degradation of biodegradable intermediates and therefore, contact time (X5) has a positive and significant effect. Molar ratio (X6) positive but not significant (p = 0.7522) Some of the most important considerations for BOD reduction are pH, UV intensity, initial pollutant concentration and time of exposure. For Removal 3 (COD reduction), R-squared is 0.9378 which is highest among the three outputs, thus it is a strong model. pH(X1) is highly positive (coefficient 4.07, p ~ 0), as is the UV intensity (X2) (coefficient 12.5, p ~ 0), which is correlated with the fact that overall activity of organic compounds is dependent on the energy from photons. Sulfite concentration (X3) is positively (but no nsignificantly) correlated (p = 0.444). Initial ofloxacin concentration (X4) was negatively significant (coefficient − 0.7085, p = ~ 0) indicating that when the load of a pollutant is higher, it becomes more difficult to remove COD to lower levels. Contact time (X5) is positive and significant, so the length of time needed to react the compound to depletion at resistance is sufficient. Molar ratio (X6) has a very small (non-significant) positive effect. Therefore, the significant parameters affecting the COD decrease are pH, UV intensity, initial concentration of the pollutant and contact time. Overall, UV intensity and pH have significant and positive effects on process efficiency for all of the outputs. It is generally observed that the initial concentration of ofloxacin has a negative effect particularly for BOD and COD, due to the high pollutant loads, resulting in the mass of residual compounds or higher amounts of intermediates. Contact time is critical for BOD and COD but relatively less for direct ofloxacin removal which is in agreement with the faster kinetics of primary molecule removal relative to total organic load removal. Sulfite concentration and molar ratio are largely non-significant indicating that their respective effects are more complex as they are likely interacting with something else to exert effect. In summary, the regression results show normally distributed for the UV/sulfite photochemical mechanism: strongly alkaline pH and high UV intensity are needed to produce radicals, enough contact time is needed for the reduction of organic load, and high initial concentration of pollutant decreases efficiency. The RANSAC regression model, therefore, yields reliable quantitative relationships for all three outputs in addition to the evolutionary optimization model.

Assessment of mineralization efficiency in photon-mediated sulfite activation for selective ofloxacin degradation

The presented TOC reduction (%) chart (Fig. S4 in the supporting information file) represents the degree of mineralization of various samples in the conducted experiments, which aimed to investigate the efficiency of the photon-mediated sulfite activation process for selective molecular fragmentation of ofloxacin. TOC reduction indicates the decrease in total dissolved organic carbon, which is a crucial indicator for assessing the extent of degradation and complete oxidation of organic compounds into carbon dioxide and other mineral products. In this chart, the average TOC reduction percentage is approximately 39.7%, indicating that overall, the studied process was able to mineralize nearly 40% of the organic compounds on average. Additionally, the relatively high standard deviation (about 17.6) reflects a significant dispersion of results among samples, which is most likely related to differences in experimental parameters such as pH, UV intensity, sulfite concentration, contact time, and sulfite-to-ofloxacin molar ratio. Peak points in the chart, such as sample 4 with 83.3% TOC reduction, sample 13 with 72.6%, and sample 28 with 65.8%, indicate very effective experimental conditions for more complete mineralization of the organic compound, which may reflect parametric optimizations or synergistic interactions between photon activators and sulfite. On the other hand, samples with less than 20% TOC reduction, such as samples 26 and 27, indicate lower process efficiency under similar or different conditions, possibly due to limitations in sulfite activation, presence of environmental inhibitors, or inappropriate reactant concentrations. The overall trend of the chart shows that this photon-mediated sulfite activation process, despite fluctuations, has considerable potential for mineralizing complex organic compounds like ofloxacin and can be effective in improving water and pharmaceutical wastewater treatment processes. The sample numbers mentioned correspond to Table S1 in the supplementary file section.

Biodegradability potential and environmental ecotoxicological considerations

The observed reduction in BOD indicates an enhanced biodegradability of the treated effluent. To quantify this potential, the BOD/COD ratio was calculated for all experimental conditions (Fig. S5 in the supporting information file). The sample numbers mentioned correspond to Table S1 in the supplementary file section. The BOD/COD ratios varied within the range of 0.45 to 0.60. A ratio greater than 0.45 generally suggests good biodegradability. The optimized conditions consistently yielded ratios exceeding 0.55, confirming that the UV/sulfite process effectively transforms the recalcitrant Ofloxacin molecules into simpler, more biodegradable organic compounds. However, it is important to acknowledge that BOD is an indirect measure susceptible to biological fluctuations. Furthermore, the presence of residual sulfite or toxic intermediate products could potentially inhibit microbial activity during BOD testing. In our optimized regime, sulfite concentrations were minimized to both reduce radical scavenging and the likelihood of toxicity. The consistently high BOD/COD ratios suggest that any transient toxicity from intermediates was overcome by their subsequent biodegradability, or that the intermediates themselves are non-inhibitory. Nevertheless, to fully assess the environmental safety of the treated water, conducting direct ecotoxicological assays (e.g., using Vibrio fischeri or Daphnia magna) is recommended in future studies.

Ridging predictive modeling and practical metrics: comparative insights into energy, cost, and efficiency of UV/sulfite degradation systems

Unlike previous studies that primarily focus on the experimental aspects of pollutant degradation or catalyst synthesis, our paper employs a hierarchical and hybrid model combining multi-output predictive modeling based on the RANSAC algorithm with evolutionary parametric optimization. This approach enables accurate and reliable prediction and optimization of the interactive effects of key parameters—such as UV intensity, sulfite concentration, pH, sulfite/ofloxacin molar ratio, and contact time—on ofloxacin degradation efficiency as well as COD and BOD removal. This methodology facilitates reduction in energy and chemical consumption by determining optimal operating conditions, which have been only sporadically and empirically addressed in prior works. Unlike most studies that report only degradation efficiency metrics (e.g., reaction rates or pollutant removal percentages), our model quantitatively identifies optimal conditions for lowering UV intensity and sulfite dosage while maintaining or enhancing degradation performance, thus minimizing energy and reagent use. For instance, optimal conditions for ofloxacin and COD removal involve increased UV intensity and sulfite concentration, whereas for BOD reduction—which is generally more challenging—the optimal settings require reduced sulfite levels and a more alkaline pH. This demonstrates optimal resource management that has been less emphasized in previous literature. Some studies^10,51, focus on complex and costly catalysts (metal heterojunctions, nanocomposites) that incur higher costs and operational complexity. In contrast, our study achieves high efficiency in the UV/sulfite process without the need for advanced catalysts, relying instead on optimization of simpler operational parameters. Other works^12,52, highlight degradation rates and efficiencies but do not provide detailed analyses of UV energy consumption or operational costs. Our model’s precise prediction of dependencies on UV intensity and contact time enables potential cost and energy savings. Furthermore, by offering a model capable of simultaneously optimizing ofloxacin removal alongside organic load reduction (COD and BOD), our work extends beyond conventional pollutant degradation to provide a more comprehensive optimization framework suitable for practical wastewater treatment applications. Unlike studies that mainly focus on radical or non-radical degradation mechanisms¹¹, our paper employs advanced predictive modeling to evaluate multiple interacting factors under realistic conditions simulating antibiotic-containing wastewater, thereby facilitating operational optimization. This systematic and scientific approach enables cost and energy reductions more effectively than the predominantly empirical and one-dimensional prior studies.

Conclusion

This study presents a highly integrated hierarchical modeling framework and optimization of photochemical-mediated degradation of ofloxacin in aqueous solutions using a mixture of experimental photochemistry, contemporary machine learning, and evolutionary optimization. The RANSACRegressor model was able to find the complex, nonlinear relationships between a wide range of operational parameters and to make consistently accurate predictions of ofloxacin removal efficiency and COD reduction, and to effectively model BOD dynamics that inherently vary. The residual and Q-Q analysis confirmed that the model is reliable enough to be applied to both training and the unknown test data, and the analysis of parameter importance indicated that the UV intensity and the initial concentration of ofloxacin are the most influential factors to control the efficiency of the process, but the pH, the contact time, and the molar ratio of sulfite and ofloxacin are the modulatory variables that adjust the efficiency of radical production and pollutant decomposition. The output-specific conditions were further explained by evolutionary optimization, which shows that optimal ofloxacin removal is achieved with greater UV intensity and higher dosage of sulfite, but BOD reduction is optimal with moderately alkaline pH, lower dose of sulfite and increased contact time. The optimal balance of photon flux and sulfite availability results in the reduction of the COD as a measure of total oxidizable organic load. All these findings confirm the suggested hierarchical and stochastic modeling framework as effective tool to understand mechanistically, make predictions by extrapolation, and optimize operation of advanced photochemical oxidation systems. Importantly, several implications of the present work on the practice of industrial and environmental engineering have to do with the proposed transformation of photon-mediated chemical activation to AI-based predictive analytics and an implementation guideline toward the development of sustainable wastewater treatment interventions against the recalcitrant pharmaceutical contaminants. First, wastewater treatment facilities can use the exemplified optimal operating parameters to develop UV/Sulfite-based advanced oxidation reactions that effectively eliminate recalcitrant antibiotics like ofloxacin, and at the same time reduce organic loads expressed in terms of BOD and COD. Second, the predictive modeling method enables operators to model behaviors in the process at various environmental and operational conditions eliminating the trial and error experimentation and saving resources. Third, the treatment of pharmaceutical manufacturing effluents can be refined to selective degradation of active compounds without the formation of dangerous by-products. Finally, the methodology will give a transposable model that can be used to control other recalcitrant organic contaminants, facilitate compliance to regulations, environmental sustainability and safeguard human health in the aquatic ecosystem. Although the model demonstrated strong performance on the internal dataset used in this study, external validation on independent datasets has not been conducted; therefore, the generalizability of the model to other conditions or data sources remains to be confirmed in future work.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Tayebeh Rasolevandi : Writing – review & editing, Writing – originaldraft, Methodology, Investigation. Amir Arshia Shamshiri Methodology, Investigation. Mohammad Amir Salarianzadeh : Conceptualization, Methodology, Investigation, Formal analysis. Hossein Azarpira: Writing – review & editing, Writing – original draft, Methodology, Investigation, Supervision.

Funding

This research was supported by Saveh University of Medical Sciences (Grant Number: 688, Ethics Code: IR.SAVEHUMS.REC.1404.014.

Data availability

The data will be made available on request.

Competing interests

The authors declare no competing interests.