# A Comparative Study of Random Forest and Genetic Engineering Programming for the Prediction of Compressive Strength of High Strength Concrete (HSC)

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## Abstract

**:**

^{2}= 0.96 with fewer errors. The GEP algorithm depicts a good response in between actual values and prediction values with an empirical relation. An external statistical check is also applied on RF and GEP models to validate the variables with data points. Artificial neural networks (ANNs) and decision tree (DT) are also used on a given data sample and comparison is made with the aforementioned models. Permutation features using python are done on the variables to give an influential parameter. The machine learning algorithm reveals a strong correlation between targets and predicts with less statistical measures showing the accuracy of the entire model.

## 1. Introduction

^{2}= 0.97 with experimental results. Qinghua et al. [26] employed random forest approach to predict the compressive strength of high-performance concrete. Similarly, Sun et al. [39] used evolved random forest algorithm on 138 data samples to predict the compressive strength of rubberized concrete which was collected from published literature. This advanced-based approach gave better performance with a strong coefficient correlation of R

^{2}= 0.96. ANN and other models have been adopted for predicting the mechanical strength parameters of high-performance concrete and recycled aggregate concrete [40,41,42,43,44]. Pala et al. [45] studied the influence of silica and fly ash on the compressive strength of concrete. A comprehensive experimental was carried out to analyze the impact of varying w/c ratios and varying percentages of silica and fly ash on the performance of concrete. In addition, ANN was adopted to depict the effect on the strength parameters of concrete [45]. Azim et al. [44] used a GEP-based machine learning algorithm to predict the compressive arch action of a reinforced concrete structure. The author found that GEP is an effective tool for prediction performance.

## 2. Research Methodology

#### 2.1. Random Forest Regression

- Collection of trained regression trees using training set.
- Calculating average of the individual regression tree output.
- Cross-validation of the predicted data using validation set.

#### 2.2. Gene Expression Programming

## 3. Experimental Database Representation

#### 3.1. Dataset Used in Modeling Aspect

#### 3.2. Programming-Based Presentation of Datasets

## 4. GEP Model Development

_{0}: cement content, d

_{1}: fine to coarse aggregate, d

_{2}: water, d

_{3}: superplasticizer) were used in modeling. These input parameters were utilized for the development of the model based on gene expression programming. In addition, simple mathematical operations (+, −, /, ×) were used which were part of the function set. A simple arithmetic operation was used to build an empirical-based relation which is the function of the following parameters

## 5. Model Performance Analysis

^{2}). The mathematical expressions for these indicators are given below.

^{2}). The model is deemed effective when the value of R

^{2}is greater than 0.8 and is close to 1 [58]. The value obtained through model is the reflection that shows the correlation between the experimental and predicted outcomes. Lower values of the indicator errors like MAE, RRMSE, RMSE, and RSE indicate higher performance. Machine learning is a good approach in the prediction of properties. However, overfitting issues in a dataset have a malignant effect in validation and fore casting of mechanical aspect of HSC. Thus, overcoming this problem of overfitting has become a dire need in supervised machine learning algorithms. Researchers used objective function (OBF) for the accuracy of models. OBF uses overall data samples along with the error and regression coefficient. This then provides a more accurate generalized model with adamant higher accuracy and is represented in Equation (8) [59].

## 6. Results and Discussion

#### 6.1. Random Forest Model Analysis

^{2}= 0.96 between experimental and predicted values and gives good validation results as illustrated in Figure 2b,c. In addition, the model performance shows less error as illustrated in Figure 2d. All the predicted data points lie in the same range of experimental values with an error less than 10MPa. This shows that the random forest ensemble algorithm gives adamant good results.

#### 6.2. Empirical Relation of HSC Using the GEP Model

#### 6.3. GEP Model Evaluation

^{2}. This value is greater than 0.8 which depicts the accuracy of the model as 0.91 and 0.90 for the testing (see Figure 4a) and validation (see Figure 4b) sets, respectively. Normalization of gathered data from published literature was also done within the range of zero and one to show the accurateness of data as illustrated in Figure 4c.

^{2}value greater than 0.8. Thus, it depicts the accuracy of the finalized model. Further analysis is also performed to evaluate the performance of the model by determining the standard deviation (SD) and covariance (COV). The values of SD and COV are determined to be 0.16 and 0.059, respectively.

## 7. Statistical Analysis Checks on RF and GEP Model

## 8. Comparison of Models with ANN and Decision Tree

^{2}= 0.96 and its error distribution as shown in Figure 6a,b. Whereas individual models ANN, DT, and GEP show good response with R

^{2}= 0.89, 0.90, and 0.90, respectively. Figure 6d represents the error distribution of decision tree with maximum error below 10 MPa. However, 18.19 MPa is reported as the maximum error. A similar trend has also been observed for ANN and GEP models with maximum error values of 11.80 MPa and 7.48 MPa, respectively as shown in Figure 6f,h. Moreover, researchers used different algorithm-based machine learning techniques for the prediction of mechanical properties of high strength concrete. Ahmed et al. [63] used an ANN algorithm and forecasted the mechanical properties (slump and compressive strength) of HSC. The author evaluated its model with ANN and revealed strong correlation for slump and compressive of about 0.99. Singh et al. [64] forecasted the mechanical properties of HSC by using RF and M5P algorithms and reported strong correlation for the testing set of 0.876 and 0.814, respectively.

## 9. Permutation Feature Analysis (PFA)

## 10. Conclusions

- Random forest is an ensemble approach which gives adamant performance between observed and predicted value. It is due to incorporation of a weak learner as base learner (decision tree) and gives determination of coefficient R
^{2}= 0.96. - GEP is an individual model rather than an ensemble algorithm. It gives a good relation with the empirical relation. This relation can be used to predict the mechanical aspect of high strength concrete via hand calculation.
- Comparison of the RF and GEP models is made with ANN and DT. However, RF outbursts and gives an obstinate relation of R
^{2}= 0.96. GEP model gives R^{2}= 0.90. ANN and DT models give 0.89 and 0.90, respectively. Moreover, RF gives less errors as compared to others individual algorithms. This is due to the bagging mechanism of RF. - Permutation features give an influential parameter in HSC. This help us to check and know the most dominant variables in using experimental work; thus, all the variables have an effect on compressive strength.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Zhang, X.; Han, J. The effect of ultra-fine admixture on the rheological property of cement paste. Cem. Concr. Res.
**2000**, 30, 827–830. [Google Scholar] [CrossRef] - Khaloo, A.; Mobini, M.H.; Hosseini, P. Influence of different types of nano-SiO2 particles on properties of high-performance concrete. Constr. Build. Mater.
**2016**, 113, 188–201. [Google Scholar] [CrossRef] - Hooton, R.D.; Bickley, J.A. Design for durability: The key to improving concrete sustainability. Constr. Build. Mater.
**2014**, 67, 422–430. [Google Scholar] [CrossRef] - Farooq, F.; Akbar, A.; Khushnood, R.A.; Muhammad, W.L.B.; Rehman, S.K.U.; Javed, M.F. Experimental investigation of hybrid carbon nanotubes and graphite nanoplatelets on rheology, shrinkage, mechanical, and microstructure of SCCM. Materials
**2020**, 13, 230. [Google Scholar] [CrossRef][Green Version] - Carrasquillo, R.; Nilson, A.; Slate, F.S. Properties of High Strength Concrete Subjectto Short-Term Loads. 1981. Available online: https://www.concrete.org/publications/internationalconcreteabstractsportal.aspx?m=details&ID=6914 (accessed on 27 September 2020).
- Mbessa, M.; Péra, J. Durability of high-strength concrete in ammonium sulfate solution. Cem. Concr. Res.
**2001**, 31, 1227–1231. [Google Scholar] [CrossRef] - Baykasoǧlu, A.; Öztaş, A.; Özbay, E. Prediction and multi-objective optimization of high-strength concrete parameters via soft computing approaches. Expert Syst. Appl.
**2009**, 36, 6145–6155. [Google Scholar] [CrossRef] - Demir, F. Prediction of elastic modulus of normal and high strength concrete by artificial neural networks. Constr. Build. Mater.
**2008**, 22, 1428–1435. [Google Scholar] [CrossRef] - Demir, F. A new way of prediction elastic modulus of normal and high strength concrete-fuzzy logic. Cem. Concr. Res.
**2005**, 35, 1531–1538. [Google Scholar] [CrossRef] - Yan, K.; Shi, C. Prediction of elastic modulus of normal and high strength concrete by support vector machine. Constr. Build. Mater.
**2010**, 24, 1479–1485. [Google Scholar] [CrossRef] - Ahmadi-Nedushan, B. Prediction of elastic modulus of normal and high strength concrete using ANFIS and optimal nonlinear regression models. Constr. Build. Mater.
**2012**, 36, 665–673. [Google Scholar] [CrossRef] - Safiuddin, M.; Raman, S.N.; Salam, M.A.; Jumaat, M.Z. Modeling of compressive strength for self-consolidating high-strength concrete incorporating palm oil fuel ash. Materials
**2016**, 9, 396. [Google Scholar] [CrossRef] [PubMed] - Al-Shamiri, A.K.; Kim, J.H.; Yuan, T.F.; Yoon, Y.S. Modeling the compressive strength of high-strength concrete: An extreme learning approach. Constr. Build. Mater.
**2019**, 208, 204–219. [Google Scholar] [CrossRef] - Aslam, F.; Farooq, F.; Amin, M.N.; Khan, K.; Waheed, A.; Akbar, A.; Javed, M.F.; Alyousef, R.; Alabdulijabbar, H. Applications of Gene Expression Programming for Estimating Compressive Strength of High-Strength Concrete. Adv. Civ. Eng.
**2020**, 2020, 1–23. [Google Scholar] [CrossRef] - Samui, P. Multivariate adaptive regression spline (MARS) for prediction of elastic modulus of jointed rock mass. Geotech. Geol. Eng.
**2013**, 31, 249–253. [Google Scholar] [CrossRef] - Gholampour, A.; Mansouri, I.; Kisi, O.; Ozbakkaloglu, T. Evaluation of mechanical properties of concretes containing coarse recycled concrete aggregates using multivariate adaptive regression splines (MARS), M5 model tree (M5Tree), and least squares support vector regression (LSSVR) models. Neural Comput. Appl.
**2020**, 32, 295–308. [Google Scholar] [CrossRef] - Shahmansouri, A.A.; Bengar, H.A.; Ghanbari, S. Compressive strength prediction of eco-efficient GGBS-based geopolymer concrete using GEP method. J. Build. Eng.
**2020**, 31, 101326. [Google Scholar] [CrossRef] - Javed, M.F.; Farooq, F.; Memon, S.A.; Akbar, A.; Khan, M.A.; Aslam, F.; Alyousef, R.; Alabduljabbar, H.; Rehman, S.K.U. New prediction model for the ultimate axial capacity of concrete-filled steel tubes: An evolutionary approach. Crystals
**2020**, 10, 741. [Google Scholar] [CrossRef] - Sonebi, M.; Abdulkadir, C. Genetic programming based formulation for fresh and hardened properties of self-compacting concrete containing pulverised fuel ash. Constr. Build. Mater.
**2009**, 23, 2614–2622. [Google Scholar] [CrossRef] - Rinchon, J.P.M. Strength durability-based design mix of self-compacting concrete with cementitious blend using hybrid neural network-genetic algorithm. IPTEK J. Proc. Ser.
**2017**, 3. [Google Scholar] [CrossRef][Green Version] - Kang, F.; Li, J.; Dai, J. Prediction of long-term temperature effect in structural health monitoring of concrete dams using support vector machines with Jaya optimizer and salp swarm algorithms. Adv. Eng. Softw.
**2019**, 131, 60–76. [Google Scholar] [CrossRef] - Ling, H.; Qian, C.; Kang, W.; Liang, C.; Chen, H. Combination of support vector machine and K-fold cross validation to predict compressive strength of concrete in marine environment. Constr. Build. Mater.
**2019**, 206, 355–363. [Google Scholar] [CrossRef] - Ababneh, A.; Alhassan, M.; Abu-Haifa, M. Predicting the contribution of recycled aggregate concrete to the shear capacity of beams without transverse reinforcement using artificial neural networks. Case Stud. Constr. Mater.
**2020**, 13, e00414. [Google Scholar] [CrossRef] - Xu, J.; Chen, Y.; Xie, T.; Zhao, X.; Xiong, B.; Chen, Z. Prediction of triaxial behavior of recycled aggregate concrete using multivariable regression and artificial neural network techniques. Constr. Build. Mater.
**2019**, 226, 534–554. [Google Scholar] [CrossRef] - Van Dao, D.; Ly, H.B.; Vu, H.L.T.; Le, T.T.; Pham, B.T. Investigation and optimization of the C-ANN structure in predicting the compressive strength of foamed concrete. Materials
**2020**, 13, 1072. [Google Scholar] [CrossRef][Green Version] - Han, Q.; Gui, C.; Xu, J.; Lacidogna, G. A generalized method to predict the compressive strength of high-performance concrete by improved random forest algorithm. Constr. Build. Mater.
**2019**, 226, 734–742. [Google Scholar] [CrossRef] - Zounemat-Kermani, M.; Stephan, D.; Barjenbruch, M.; Hinkelmann, R. Ensemble data mining modeling in corrosion of concrete sewer: A comparative study of network-based (MLPNN & RBFNN) and tree-based (RF, CHAID, & CART) models. Adv. Eng. Inform.
**2020**, 43, 101030. [Google Scholar] [CrossRef] - Zhang, J.; Li, D.; Wang, Y. Toward intelligent construction: Prediction of mechanical properties of manufactured-sand concrete using tree-based models. J. Clean. Prod.
**2020**, 258, 120665. [Google Scholar] [CrossRef] - Vakhshouri, B.; Nejadi, S. Predicition of compressive strength in light-weight self-compacting concrete by ANFIS analytical model. Arch. Civ. Eng.
**2015**, 61, 53–72. [Google Scholar] [CrossRef] - Dutta, S.; Murthy, A.R.; Kim, D.; Samui, P. Prediction of Compressive Strength of Self-Compacting Concrete Using Intelligent Computational Modeling Call for Chapter: Risk, Reliability and Sustainable Remediation in the Field OF Civil AND Environmental Engineering (Elsevier) View project Ground Rub. 2017. Available online: https://www.researchgate.net/publication/321700276 (accessed on 27 September 2020).
- Vakhshouri, B.; Nejadi, S. Prediction of compressive strength of self-compacting concrete by ANFIS models. Neurocomputing
**2018**, 280, 13–22. [Google Scholar] [CrossRef] - Info, A. Application of ANN and ANFIS Models Determining Compressive Strength of Concrete. Soft Comput. Civ. Eng.
**2018**, 2, 62–70. Available online: http://www.jsoftcivil.com/article_51114.html (accessed on 27 September 2020). - Iqbal, M.F.; Liu, Q.f.; Azim, I.; Zhu, X.; Yang, J.; Javed, M.F.; Rauf, M. Prediction of mechanical properties of green concrete incorporating waste foundry sand based on gene expression programming. J. Hazard. Mater.
**2020**, 384, 121322. [Google Scholar] [CrossRef] - Trtnik, G.; Kavčič, F.; Turk, G. Prediction of concrete strength using ultrasonic pulse velocity and artificial neural networks. Ultrasonics
**2009**, 49, 53–60. [Google Scholar] [CrossRef] [PubMed][Green Version] - Shahmansouri, A.A.; Yazdani, M.; Ghanbari, S.; Bengar, H.A.; Jafari, A.; Ghatte, H.F. Artificial neural network model to predict the compressive strength of eco-friendly geopolymer concrete incorporating silica fume and natural zeolite. J. Clean. Prod.
**2020**, 279, 123697. [Google Scholar] [CrossRef] - Javed, M.F.; Amin, M.N.; Shah, M.I.; Khan, K.; Iftikhar, B.; Farooq, F.; Aslam, F.; Alyousef, R.; Alabduljabbar, H. Applications of gene expression programming and regression techniques for estimating compressive strength of bagasse Ash based concrete. Crystals
**2020**, 10, 737. [Google Scholar] [CrossRef] - Nour, A.I.; Güneyisi, E.M. Prediction model on compressive strength of recycled aggregate concrete filled steel tube columns. Compos. Part B Eng.
**2019**, 173. [Google Scholar] [CrossRef] - Zhang, J.; Ma, G.; Huang, Y.; Sun, J.; Aslani, F.; Nener, B. Modelling uniaxial compressive strength of lightweight self-compacting concrete using random forest regression. Constr. Build. Mater.
**2019**, 210, 713–719. [Google Scholar] [CrossRef] - Sun, Y.; Li, G.; Zhang, J.; Qian, D. Prediction of the strength of rubberized concrete by an evolved random forest model. Adv. Civ. Eng.
**2019**. [Google Scholar] [CrossRef][Green Version] - Bingöl, A.F.; Tortum, A.; Gül, R. Neural networks analysis of compressive strength of lightweight concrete after high temperatures. Mater. Des.
**2013**, 52, 258–264. [Google Scholar] [CrossRef] - Duan, Z.H.; Kou, S.C.; Poon, C.S. Prediction of compressive strength of recycled aggregate concrete using artificial neural networks. Constr. Build. Mater.
**2013**, 40, 1200–1206. [Google Scholar] [CrossRef] - Chou, J.S.; Pham, A.D. Enhanced artificial intelligence for ensemble approach to predicting high performance concrete compressive strength. Constr. Build. Mater.
**2013**, 49, 554–563. [Google Scholar] [CrossRef] - Chou, J.S.; Tsai, C.F.; Pham, A.D.; Lu, Y.H. Machine learning in concrete strength simulations: Multi-nation data analytics. Constr. Build. Mater.
**2014**, 73, 771–780. [Google Scholar] [CrossRef] - Azim, I.; Yang, J.; Javed, M.F.; Iqbal, M.F.; Mahmood, Z.; Wang, F.; Liu, Q.f. Prediction model for compressive arch action capacity of RC frame structures under column removal scenario using gene expression programming. Structures
**2020**, 25, 212–228. [Google Scholar] [CrossRef] - Pala, M.; Özbay, E.; Öztaş, A.; Yuce, M.I. Appraisal of long-term effects of fly ash and silica fume on compressive strength of concrete by neural networks. Constr. Build. Mater.
**2007**, 21, 384–394. [Google Scholar] [CrossRef] - Anaconda Inc. Anaconda Individual Edition, Anaconda Website. 2020. Available online: https://www.anaconda.com/products/individual (accessed on 27 September 2020).
- Downloads, (n.d.). Available online: https://www.gepsoft.com/downloads.htm (accessed on 27 September 2020).
- Breiman, L. Random forests. Mach. Learn.
**2001**, 45, 5–32. [Google Scholar] [CrossRef][Green Version] - Svetnik, V.; Liaw, A.; Tong, C.; Culberson, J.C.; Sheridan, R.P.; Feuston, B.P. Random forest: A classification and regression tool for compound classification and QSAR modeling. J. Chem. Inf. Comput. Sci.
**2003**, 43, 1947–1958. [Google Scholar] [CrossRef] - Patel, J.; Shah, S.; Thakkar, P.; Kotecha, K. Predicting stock market index using fusion of machine learning techniques. Expert Syst. Appl.
**2015**, 42, 2162–2172. [Google Scholar] [CrossRef] - Jiang, H.; Deng, Y.; Chen, H.S.; Tao, L.; Sha, Q.; Chen, J.; Tsai, C.J.; Zhang, S. Joint analysis of two microarray gene-expression data sets to select lung adenocarcinoma marker genes BMC Bioinform. BMC Bioinform.
**2004**, 5. [Google Scholar] [CrossRef][Green Version] - Prasad, A.M.; Iverson, L.R.; Liaw, A. Newer classification and regression tree techniques: Bagging and random forests for ecological prediction. Ecosystems
**2006**, 9, 181–199. [Google Scholar] [CrossRef] - Ferreira, C. Gene Expression Programming: A New Adaptive Algorithm for Solving Problems. 2001. Available online: http://www.gene-expression-programming.com (accessed on 29 March 2020).
- Behnood, A.; Golafshani, E.M. Predicting the compressive strength of silica fume concrete using hybrid artificial neural network with multi-objective grey wolves. J. Clean. Prod.
**2018**, 202, 54–64. [Google Scholar] [CrossRef] - Getahun, M.A.; Shitote, S.M.; Gariy, Z.C.A. Artificial neural network based modelling approach for strength prediction of concrete incorporating agricultural and construction wastes. Constr. Build. Mater.
**2018**, 190, 517–525. [Google Scholar] [CrossRef] - Project Jupyter, Project Jupyter, Home. 2017. Available online: https://jupyter.org/ (accessed on 27 September 2020).
- Gholampour, A.; Gandomi, A.H.; Ozbakkaloglu, T. New formulations for mechanical properties of recycled aggregate concrete using gene expression programming. Constr. Build. Mater.
**2017**, 130, 122–145. [Google Scholar] [CrossRef] - Gandomi, A.H.; Babanajad, S.K.; Alavi, A.H.; Farnam, Y. Novel approach to strength modeling of concrete under triaxial compression. J. Mater. Civ. Eng.
**2012**, 24, 1132–1143. [Google Scholar] [CrossRef] - Gandomi, A.H.; Roke, D.A. Assessment of artificial neural network and genetic programming as predictive tools. Adv. Eng. Softw.
**2015**, 88, 63–72. [Google Scholar] [CrossRef] - Frank, I.; Todeschini, R. The data analysis handbook. Data Handl. Sci. Technol.
**1994**, 14, 1–352. [Google Scholar] [CrossRef] - Alavi, A.H.; Ameri, M.; Gandomi, A.H.; Mirzahosseini, M.R. Formulation of flow number of asphalt mixes using a hybrid computational method. Constr. Build. Mater.
**2011**, 25, 1338–1355. [Google Scholar] [CrossRef] - Golbraikh, A.; Tropsha, A. Beware of q2! J. Mol. Graph. Model.
**2002**, 20, 269–276. [Google Scholar] [CrossRef] - Öztaş, A.; Pala, M.; Özbay, E.; Kanca, E.; Çaǧlar, N.; Bhatti, M.A. Predicting the compressive strength and slump of high strength concrete using neural network. Constr. Build. Mater.
**2006**, 20, 769–775. [Google Scholar] [CrossRef] - Singh, B.; Singh, B.; Sihag, P.; Tomar, A.; Sehgal, A. Estimation of compressive strength of high-strength concrete by random forest and M5P model tree approaches. J. Mater. Eng. Struct. JMES
**2019**, 6, 583–592. Available online: http://revue.ummto.dz/index.php/JMES/article/view/2020 (accessed on 21 August 2020).

**Figure 1.**Hex contour graph of input parameters; (

**a**) Cement; (

**b**) Coarse aggregate; (

**c**) Fine aggregate; (

**d**) Super plasticizer; (

**e**) Water; (

**f**) Compressive strength.

**Figure 2.**Model evaluation (

**a**) Ensemble model with 20 submodels; (

**b**) validation based on RF; (

**c**) testing based on RF; (

**d**) error distribution of the testing set.

**Figure 4.**Model evaluation (

**a**) Validation results of data based on GEP; (

**b**) testing results of data; (

**c**) normalized range of data.

**Figure 6.**Model evaluation with errors (

**a**) RF regression analysis; (

**b**) error distribution based on the RF model; (

**c**) decision tree (DT) regression analysis; (

**d**) error distribution based on DT; (

**e**) artificial neural network (ANN) regression analysis; (

**f**) error distribution based on ANN; (

**g**) GEP regression analysis; (

**h**) error distribution based on GEP.

**Figure 7.**Permutation analysis of input variables (

**a**) model base (

**b**) contribution of input variables.

Properties | Data Points | Algorithm | References |
---|---|---|---|

Compressive strength, Slump test | 187 | ANN | [7] |

Elastic modulus | 159 | ANN | [8] |

Elastic modulus | 159 | FUZZY | [9] |

Elastic modulus | 159 | SVM | [10] |

Elastic modulus | 159 | ANFIS and nonlinear | [11] |

Compressive strength | 20 | ANN | [12] |

Compressive strength | 324 | ELM | [13] |

Compressive strength | 357 | GEP | [14] |

Parameters | Cement | Fine/Coarse Aggregate | Water | Superplasticizer |
---|---|---|---|---|

Mean | 384.34 | 0.96 | 173.56 | 2.34 |

Standard Error | 4.92 | 0.01 | 0.82 | 0.14 |

Median | 360 | 0.92 | 170 | 1.25 |

Mode | 360 | 1.01 | 170 | 1 |

Standard Deviation | 93.00 | 0.26 | 15.56 | 2.69 |

Sample Variance | 8650.50 | 0.06 | 242.19 | 7.24 |

Kurtosis | 0.36 | 6.45 | 15.59 | 2.88 |

Skewness | 0.14 | 2.12 | 2.45 | 1.79 |

Range | 440 | 1.86 | 170.08 | 12 |

Minimum | 160 | 0.23 | 132 | 0 |

Maximum | 600 | 2.1 | 302.08 | 12 |

Sum | 137,212.84 | 344.07 | 61,963.8 | 837.61 |

Count | 357 | 357 | 357 | 357 |

Parameters | Cement | Fine/Coarse Aggregate | Water | Superplasticizer |
---|---|---|---|---|

Mean | 383.29 | 0.97 | 173.72 | 2.42 |

Standard Error | 6.06 | 0.01 | 1.08 | 0.17 |

Median | 360 | 0.92 | 170 | 1.37 |

Mode | 320 | 1.01 | 170 | 1 |

Standard Deviation | 95.95 | 0.27 | 17.17 | 2.74 |

Sample Variance | 9206.57 | 0.07 | 295.07 | 7.54 |

Kurtosis | 0.60 | 5.82 | 14.42 | 2.96 |

Skewness | 0.19 | 2.08 | 2.48 | 1.82 |

Range | 420 | 1.86 | 170.08 | 12 |

Minimum | 180 | 0.23 | 132 | 0 |

Maximum | 600 | 2.1 | 302.08 | 12 |

Sum | 95,823.1 | 242.79 | 43,431.75 | 606.43 |

Count | 250 | 250 | 250 | 250 |

Parameters | Cement | Fine/Coarse aggregate | Water | Superplasticizer |
---|---|---|---|---|

Mean | 387.04 | 0.92 | 172.18 | 1.98 |

Standard Error | 12.46 | 0.02 | 1.34 | 0.33 |

Median | 400 | 0.90 | 170 | 1 |

Mode | 360 | 0.75 | 170 | 1 |

Standard Deviation | 95.76 | 0.18 | 10.35 | 2.55 |

Sample Variance | 9170.56 | 0.03 | 107.25 | 6.55 |

Kurtosis | 0.22 | 6.82 | 0.18 | 4.75 |

Skewness | 0.17 | 1.66 | 0.33 | 2.19 |

Range | 440 | 1.22 | 45.2 | 12 |

Minimum | 160 | 0.58 | 154.8 | 0 |

Maximum | 600 | 1.80 | 200 | 12 |

Sum | 22,835.54 | 54.38 | 10,159.18 | 117.09 |

Count | 54 | 54 | 54 | 54 |

Parameters | Cement | Fine/Coarse Aggregate | Water | Superplasticizer |
---|---|---|---|---|

Mean | 390.52 | 0.90 | 173.07 | 2.10 |

Standard Error | 12.58 | 0.02 | 1.21 | 0.34 |

Median | 378 | 0.90 | 175 | 1 |

Mode | 360 | 1.04 | 180 | 0.5 |

Standard Deviation | 89.86 | 0.15 | 8.67 | 2.47 |

Sample Variance | 8076.29 | 0.02 | 75.21 | 6.11 |

Kurtosis | 1.08 | 0.52 | −0.18 | 2.17 |

Skewness | 0.17 | 0.61 | −0.62 | 1.65 |

Range | 440 | 0.73 | 38.32 | 10.5 |

Minimum | 160 | 0.66 | 154 | 0 |

Maximum | 600 | 1.39 | 192.32 | 10.5 |

Sum | 19,916.87 | 46.34 | 8826.8 | 107.57 |

Count | 55 | 55 | 55 | 55 |

Parameters | Settings |
---|---|

General | $f{\u2019}_{c}$ |

Genes | 4 |

Chromosomes | 30 |

Linking function | Addition |

Head size | 10 |

Function set | +, −, ×, ÷ |

Numerical constants | |

Constant per gene | 10 |

Lower bound | −10 |

Data type | Floating number |

Upper bound | 10 |

Genetic Operators | |

Two-point recombination rate | 0.00277 |

Gene transposition rate | 0.00277 |

Model | RMSE | MAE | R^{2} | |||
---|---|---|---|---|---|---|

Fc | Validation | Testing | Validation | Testing | Validation | Testing |

1.22 | 1.42 | 0.475 | 0.495 | 0.967 | 0.041 | |

RRMSE | RSE | P(row) | ||||

Validation | Testing | Validation | Testing | Validation | Testing | |

0.0186 | 0.021 | 0.072 | 0.053 | 0.024 | 0.025 |

Model | RMSE | MAE | RSE | |||
---|---|---|---|---|---|---|

Fc | Validation | Testing | Validation | Testing | Validation | Testing |

1.42 | 1.62 | 0.575 | 0.595 | 0.092 | 0.023 | |

RRMSE | R | P(row) | ||||

Validation | Testing | Validation | Testing | Validation | Testing | |

0.0286 | 0.031 | 0.957 | 0.031 | 0.014 | 0.015 |

S.No | Equation | Condition | RF Model | GEP Model |
---|---|---|---|---|

1 | $k=\frac{{{\displaystyle \sum}}_{i=1}^{n}\left({e}_{i}\times {m}_{i}\right)}{{e}_{i}{}^{2}}$ | $0.85<k<1.15$ | 0.99 | 0.98 |

2 | $k\u2019=\frac{{{\displaystyle \sum}}_{i=1}^{n}\left({e}_{i}\times {m}_{i}\right)}{{m}_{i}^{2}}$ | $0.85<k<1.15$ | 1.00 | 1.00 |

3 | ${R}_{o}^{2}-\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left({m}_{i}-{e}_{i}^{o}\right)}^{2}}{{{\displaystyle \sum}}_{i=1}^{n}{\left({m}_{i}-{m}_{i}^{o}\right)}^{2}},{e}_{i}^{o}=k\times {m}_{i}$ | ${R}_{o}^{2}\cong 1$ | 0.99 | 0.97 |

4 | ${R}_{o}^{\u20192}-\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left({e}_{i}-{m}_{i}^{o}\right)}^{2}}{{{\displaystyle \sum}}_{i=1}^{n}{\left({e}_{i}-{e}_{i}^{o}\right)}^{2}},{m}_{i}^{o}=k\u2019\times {e}_{i}$ | ${R}_{o}^{2}\cong 1$ | 0.99 | 0.99 |

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**MDPI and ACS Style**

Farooq, F.; Nasir Amin, M.; Khan, K.; Rehan Sadiq, M.; Faisal Javed, M.; Aslam, F.; Alyousef, R.
A Comparative Study of Random Forest and Genetic Engineering Programming for the Prediction of Compressive Strength of High Strength Concrete (HSC). *Appl. Sci.* **2020**, *10*, 7330.
https://doi.org/10.3390/app10207330

**AMA Style**

Farooq F, Nasir Amin M, Khan K, Rehan Sadiq M, Faisal Javed M, Aslam F, Alyousef R.
A Comparative Study of Random Forest and Genetic Engineering Programming for the Prediction of Compressive Strength of High Strength Concrete (HSC). *Applied Sciences*. 2020; 10(20):7330.
https://doi.org/10.3390/app10207330

**Chicago/Turabian Style**

Farooq, Furqan, Muhammad Nasir Amin, Kaffayatullah Khan, Muhammad Rehan Sadiq, Muhammad Faisal Javed, Fahid Aslam, and Rayed Alyousef.
2020. "A Comparative Study of Random Forest and Genetic Engineering Programming for the Prediction of Compressive Strength of High Strength Concrete (HSC)" *Applied Sciences* 10, no. 20: 7330.
https://doi.org/10.3390/app10207330