Gradient Boosting Regression Tree Optimized with Slime Mould Algorithm to Predict the Higher Heating Value of Municipal Solid Waste
Abstract
:1. Introduction
2. Research Significance
3. Materials and Methods
3.1. An Overview of Modeling Methods
3.1.1. Classification and Regression Tree (CART)
3.1.2. Gradient Boosting Regression Tree (GBRT)
- (a)
- Start with weak learners:
- (b)
- Create m weak learners:
- (c)
- Update the weak learner fm(x):
- (d)
- The final gradient lifting regression tree expression is achieved following M rounds of iterations
3.2. Slime Mould Algorithm (SMA)
4. Database Used
5. Model Results
5.1. Cross Validation Results
5.2. Evaluating the Prediction Performance
5.3. SMA-GBRT and Default GBRT Comparison
5.4. Reliability Analysis
5.5. Graphical User Interface
6. Conclusions
- The results of the five-fold cross-validation showed that the SMA-GBRT model successfully optimized the RMSE performance metric, achieving values below two for most folds. This indicates a strong generalization capability of the SMA-GBRT model, effectively minimizing the risks of overfitting and underfitting.
- The performance analysis graphs for the training and testing sets showed nearly perfect matches between the predicted and actual HHVs. Additionally, the RMSE and R2 values, as performance indicators, were exceptionally low and high, respectively, confirming the model’s reliability and precision.
- When compared to the default GBRT model and other previously developed machine learning models (GEP, FFNN, and RBAS-SVM), the SMA-GBRT model outperformed them in all statistical metrics. The SMA-GBRT model exhibited lower RMSE and MAE values, as well as higher R2 values, both in the training and testing phases. This indicates that the SMA optimization significantly enhances the GBRT model’s predictive capabilities.
- The residual distribution histograms further substantiated the SMA-GBRT model’s superiority, showing lower mean residuals and standard deviations compared to other models. This highlights the model’s predictive stability and accuracy.
- To address the practical usability issues of the SMA-GBRT model as a “black box”, a web application was developed. This application allows users to input relevant parameters interactively and obtain immediate HHV predictions, thereby making the model accessible and convenient for real-world applications.
7. Futures and Perspectives
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Statistics | O (%) | S (%) | N (%) | H (%) | C (%) | Experimental HHV |
---|---|---|---|---|---|---|
Min | 0.00 | 0.00 | 0.00 | 2.00 | 9.00 | 3.50 |
Max | 48.62 | 2.64 | 10.00 | 14.50 | 92.00 | 49.30 |
Mean | 31.39 | 0.31 | 1.18 | 6.43 | 49.09 | 21.19 |
Std | 13.98 | 0.47 | 1.50 | 2.27 | 15.57 | 8.47 |
Parameter | Range | Default | Best Value |
---|---|---|---|
max_depth | [3, 10] | 3 | 10.000 |
learning_rate | [0.01, 0.3] | 0.1 | 0.233 |
n_estimators | [50, 500] | 100 | 234.000 |
subsample | [0.1, 1.0] | 1 | 0.675 |
min_samples_split | [2, 20] | 2 | 2.000 |
Phase | Metrics | Default GBRT | SMA GBRT |
---|---|---|---|
Training | RMSE | 0.510 | 0.145 |
MAE | 0.383 | 0.017 | |
R2 | 0.996 | 1.000 | |
Testing | RMSE | 1.462 | 1.175 |
MAE | 1.036 | 0.815 | |
R2 | 0.976 | 0.984 |
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Shehab, E.Q.; Taha, F.F.; Muhodir, S.H.; Imran, H.; Ostrowski, K.A.; Piechaczek, M. Gradient Boosting Regression Tree Optimized with Slime Mould Algorithm to Predict the Higher Heating Value of Municipal Solid Waste. Energies 2024, 17, 4213. https://doi.org/10.3390/en17174213
Shehab EQ, Taha FF, Muhodir SH, Imran H, Ostrowski KA, Piechaczek M. Gradient Boosting Regression Tree Optimized with Slime Mould Algorithm to Predict the Higher Heating Value of Municipal Solid Waste. Energies. 2024; 17(17):4213. https://doi.org/10.3390/en17174213
Chicago/Turabian StyleShehab, Esraa Q., Farah Faaq Taha, Sabih Hashim Muhodir, Hamza Imran, Krzysztof Adam Ostrowski, and Marcin Piechaczek. 2024. "Gradient Boosting Regression Tree Optimized with Slime Mould Algorithm to Predict the Higher Heating Value of Municipal Solid Waste" Energies 17, no. 17: 4213. https://doi.org/10.3390/en17174213
APA StyleShehab, E. Q., Taha, F. F., Muhodir, S. H., Imran, H., Ostrowski, K. A., & Piechaczek, M. (2024). Gradient Boosting Regression Tree Optimized with Slime Mould Algorithm to Predict the Higher Heating Value of Municipal Solid Waste. Energies, 17(17), 4213. https://doi.org/10.3390/en17174213