Prediction of Compressive Strength of Geopolymer Concrete Landscape Design: Application of the Novel Hybrid RF–GWO–XGBoost Algorithm

Abstract

Landscape geopolymer concrete (GePoCo) with environmentally friendly production methods not only has a stable structure but can also effectively reduce environmental damage. Nevertheless, GePoCo poses challenges with its intricate cementitious matrix and a vague mix design, where the components and their relative amounts can influence the compressive strength. In response to these challenges, the application of accurate and applicable soft computing techniques becomes imperative for predicting the strength of such a composite cementitious matrix. This research aimed to predict the compressive strength of GePoCo using waste resources through a novel ensemble ML algorithm. The dataset comprised 156 statistical samples, and 15 variables were selected for prediction. The model employed a combination of the RF, GWO algorithm, and XGBoost. A stacking strategy was implemented by developing multiple RF models with different hyperparameters, combining their outcome predictions into a new dataset, and subsequently developing the XGBoost model, termed the RF–XGBoost model. To enhance accuracy and reduce errors, the GWO algorithm optimized the hyperparameters of the RF–XGBoost model, resulting in the RF–GWO–XGBoost model. This proposed model was compared with stand-alone RF and XGBoost models, and a hybrid GWO–XGBoost system. The results demonstrated significant performance improvement using the proposed strategies, particularly with the assistance of the GWO algorithm. The RF–GWO–XGBoost model exhibited better performance and effectiveness, with an RMSE of 1.712 and 3.485, and R² of 0.983 and 0.981. In contrast, stand-alone models (RF and XGBoost) and the hybrid model of GWO–XGBoost demonstrated lower performance.

1. Introduction

The release of greenhouse gases into the environment has led to the melting of glacier reservoirs, posing significant threats globally [1]. The concrete sector stands out as a major contributor to greenhouse gas emissions, accounting for up to 50% of global emissions [2,3]. Notably, Portland cement (PC), a key component of concrete, plays a substantial role in GHG emissions [4]. PC production contributes approximately 7% of atmospheric emissions, with the calcination of calcium oxide (CaO) during the manufacturing process accounting for 50% of CO₂ emissions [5]. Current production levels of PC stand at 4000 million tons annually, projected to reach around 6000 million tons by 2060 [6]. These figures underscore the need for alternative measures to satisfy the growing demand for concrete while minimizing resource use and CO₂ emissions [7]. On the other hand, with the development of cementing technology, concrete is no longer only used in the construction of infrastructure. Because of its greater rigidity and stability, it has become an important carrier of artistic creation. Due to the physical characteristics of concrete, art sculptures (as shown in Figure 1) created not only have a stable structure but can also effectively reduce the environmental damage to the sculpture, such as rain erosion and wind damage. However, due to the different shapes of sculptures, their stress structure is changeable and special compared with the fixed structure of a house. The lack of flexibility of traditional concrete may lead to the material being unable to meet the needs of sculptures [8]. Therefore, adding geopolymer to concrete can not only effectively improve the flexibility of concrete, but also effectively reduce the large amount of carbon dioxide generated by cement production, which is in line with the national strategy of green development [9].

The incorporation of recycled and waste materials into concrete emerges as a scientific and pragmatic solution to address its high demand [10]. This approach not only meets the increasing need for concrete but also mitigates environmental risks [11]. In this context, fly ash (FA) and ground granulated blast furnace slag (GGBS), recognized natural pozzolanic materials, offer effective supplementary cementitious options in the construction sector [12,13,14]. Utilizing these materials, along with alkaline solvents such as sodium silicate (Na₂SiO₃) and sodium hydroxide (NaOH), results in the production of environmentally friendly concrete, such as geopolymer concrete [15,16,17,18]. Geopolymer concretes, in their amorphous gel form, exhibit exceptional characteristics, including resistance to sulfate attack, acid resistance, enhanced durability, fire resistance, and significantly greater compressive strength than conventional concrete [19,20,21,22,23]. Their use in construction can substantially reduce CO₂ emissions into the atmosphere [24,25]. A visual representation of the distinction between ordinary Portland cement and geopolymer concretes is provided in Figure 2.

Studies indicate that the chemical and physical properties of the matrix play a crucial role in determining the strength of geopolymer concretes [27,28,29]. Parameters such as fly-ash-to-NaOH ratio, Na₂SiO₃-to-NaOH ratio, workability, fly-ash-to-sand ratio, molarity, and alkaline ratio have notable effects on concrete strength. Observations by Ukritnukun et al. [30] highlight the positive impact of blast furnace slag concentration, curing temperature, and silicate modulus. Gholizadeh-Vayghan et al. [31] identified optimal molar ratios of Ca/Si and (Na + K)/Si, as well as an ideal volume ratio (H₂O/solid)vol, for enhancing the strength properties of geopolymer concretes. Songpiriyakij et al. [32] determined that a Si-to-Al ratio of 15.9 resulted in geopolymer concretes with a high compressive strength of 73 MPa. Puertas et al. [33] examined the strength and growth characteristics of fly-ash/slag-paste-hydration products, reporting mechanical properties exceeding 50 MPa for a mix with a fly-ash/slag ratio of 1.0, cured at 25 °C and stimulated with a 10 M NaOH solution after 28 days.

In the production of geopolymer concretes, pozzolanic materials with binding properties undergo polymerization at elevated temperatures in an alkaline medium, resulting in the formation of a crystalline and amorphous compound that imparts the desired mechanical properties [34]. However, the substantial heat curing required for geopolymerization compound production poses challenges for in-field applications. The elevated heat demand associated with curing may hinder the widespread use of fly ash (FA)-based geopolymer concretes in construction [35,36,37]. Mitigating this heat demand can be achieved by incorporating a slag blend rich in calcium, silica, and alumina. Combining ground granulated blast furnace slag (GGBS) with FA yields a dense microstructure with enhanced hydration and polymerization products, significantly boosting the early-age strength of geopolymer concretes. A study by Yazdi et al. [38] investigated the impact of varying FA dosage with GGBS, demonstrating a substantial increase in compressive and flexural strength by 100 MPa and 10 MPa, respectively, when FA was replaced with GGBS. Additionally, Fang et al. [35] explored the effect of varying slag content on the flexural and split tensile strength of FA-based geopolymer concretes, revealing increased strength due to the formation of C-A-S-H gel and N-A-S-H, expediting the reaction process of geopolymer concretes.

Noteworthy, thermodynamic modeling enables a precise prediction of the potential reaction products in geopolymeric systems, providing valuable insights into the material’s composition and properties. By understanding the thermodynamic landscape, researchers can guide the design of geopolymers by selecting appropriate precursors and controlling the synthesis conditions. Notably, thermodynamic modeling facilitates the optimization of precursor mixtures to achieve the desired properties in the final geopolymeric material.

The assessment of compressive strength in concrete traditionally involves physical tests on cubical and cylindrical specimens, produced with precise mixture ratios and cured in water for approximately 28 days to obtain hydrated products [25,39,40]. The compressive strength is subsequently determined using a compression-testing machine, a method employed both in fieldwork and laboratory settings, albeit known for its inefficiency and time consumption [41,42]. Empirical regression methodologies are emerging as preferable alternatives for estimating concrete strength, deviating from standard experimental procedures. The literature underscores the significant influence of chemical composition and physical proportions on geopolymer concretes [43,44], creating heterogeneity in their production due to various involved parameters [45,46,47,48]. While statistical approaches offer methods for evaluating the compressive nature of geopolymer concretes, the intricate relationship between factors and mechanical strength remains not fully understood [49,50,51,52]. As a response, machine learning (ML) approaches are gaining prominence in predicting compressive strength, leveraging recent advancements in artificial intelligence algorithms [53,54,55]. Advanced prediction algorithms developed through ML techniques serve various purposes, involving regressions, classifications, and data clustering [56,57,58,59,60]. The application of ML regression functions extends to estimating the compressive loading capacity of concretes, demonstrating higher precision compared to traditional regression methods [61,62,63,64]. The advent of artificial intelligence algorithms has empowered researchers to tackle challenging problems [65,66,67,68,69]. Some ML algorithms used to predict various characteristics of concretes are tabulated in Table 1 [70,71,72,73,74].

The application of machine learning algorithms, particularly the novel Ensemble RF–GWO–XGBoost Algorithm proposed in this research, signifies a pioneering effort to improve the performance and productiveness of estimating geopolymer concretes’ compressive strength [3,41,42]. RF was chosen for its ability to handle complex, non-linear relationships in the data and provide a robust performance. Its ensemble nature helps mitigate overfitting and enhances generalization on diverse datasets. Notably, GWO was selected for optimization tasks due to its inspiration from the social behavior of gray wolves, offering a balance between exploration and exploitation. Its adaptability makes it suitable for various optimization problems, including those encountered in our research. Furthermore, XGBoost was included for its strong performance in handling structured/tabular data and its efficiency in boosting weak learners. Its capability to model complex relationships and feature interactions makes it well suited for predictive modeling tasks. Hence, the combination of these algorithms was intended to leverage their individual strengths and address different aspects of the problem at hand. RF provides robustness, GWO aids in optimizing parameters, and XGBoost enhances predictive accuracy. Traditional methods often fail to capture the intricate relationships between various input parameters and the resulting mechanical properties. The Ensemble approach, combining random forest (RF), gray wolf optimizer (GWO), and XGBoost algorithms, offers a sophisticated solution by harnessing the strengths of each constituent algorithm, thereby presenting a robust and innovative predictive model [75]. The predictive accuracy achieved through the Ensemble RF–GWO–XGBoost Algorithm not only contributes to the optimization of geopolymer concrete production but also holds the potential to streamline and advance construction practices. Accurate predictions of compressive strength are crucial for ensuring the structural stability and longevity of geopolymer concrete structures, thereby facilitating their widespread adoption in sustainable construction projects [62,76,77]. Furthermore, this research contributes to the broader scientific community by showcasing the applicability of advanced machine learning techniques in the realm of construction materials. The methodology presented in this study opens avenues for further exploration and adaptation in predicting other material properties, fostering a paradigm shift toward data-driven and precision-based approaches in the construction industry. In conclusion, the significance of this research lies in its pioneering approach to anticipate the CSGePoCo through the innovative Ensemble RF–GWO–XGBoost Algorithm.

Table 1. The used ML techniques in predicting different characteristics of concretes.

Authors	Years	Techniques	Number of Datasets
Huang et al.	2021	Support Vector Machine	114
Sarir et al. [78]	2019	Gene Expression Programming	303
Balf et al. [79]	2021	Data Envelopment Analysis	114
Ahmad et al. [80]	2021	Gene Expression Programming, Artificial Neural Network, Decision Tree	642
Azimi-Pour et al. [81]	2020	Support Vector Machine	-
Saha et al. [82]	2020	Support Vector Machine	115
Hahmansouri et al. [83]	2020	Gene Expression Programming	351
Hahmansouri et al. [84]	2019	Gene Expression Programming	54
Aslam et al. [85]	2020	Gene Expression Programming	357
Farooq et al. [86]	2020	Random Forest and Gene Expression Programming	357
Asteris and Kolovos [87]	2019	Artificial Neural Network	205
Selvaraj and Sivaraman [88]	2019	Support Vector Machine–Random Forest, Response Surface Method	114
Zhang et al. [89]	2019	Random Forest	131
Kaveh et al. [90]	2018	M5, Multivariate Adaptive Regression Splines	114
Sathyan et al. [91]	2018	Random Kitchen Sink Algorithm	40
Vakhshouri and Nejadi [92]	2018	Adaptive Neuro Fuzzy Inference System	55
Belalia Douma et al. [93]	2017	Artificial Neural Network	114
Abu Yaman et al. [94]	2017	Artificial Neural Network	69
Ahmad et al. [95]	2021	Gene Expression Programming, Decision Tree and Bagging	270
Farooq et al. [96]	2021	Artificial Neural Network, bagging and boosting	1030
Javad et al. [51]	2020	Gene Expression Programming	277
Nematzadeh et al. [97]	2020	Response Surface Method, Gene Expression Programming	108
Zhou et al. [60]	2023	Decision Tree, Random Forest, Extreme Gradient Boosting	259

Table 1. The used ML techniques in predicting different characteristics of concretes.

Authors	Years	Techniques	Number of Datasets
Huang et al.	2021	Support Vector Machine	114
Sarir et al. [78]	2019	Gene Expression Programming	303
Balf et al. [79]	2021	Data Envelopment Analysis	114
Ahmad et al. [80]	2021	Gene Expression Programming, Artificial Neural Network, Decision Tree	642
Azimi-Pour et al. [81]	2020	Support Vector Machine	-
Saha et al. [82]	2020	Support Vector Machine	115
Hahmansouri et al. [83]	2020	Gene Expression Programming	351
Hahmansouri et al. [84]	2019	Gene Expression Programming	54
Aslam et al. [85]	2020	Gene Expression Programming	357
Farooq et al. [86]	2020	Random Forest and Gene Expression Programming	357
Asteris and Kolovos [87]	2019	Artificial Neural Network	205
Selvaraj and Sivaraman [88]	2019	Support Vector Machine–Random Forest, Response Surface Method	114
Zhang et al. [89]	2019	Random Forest	131
Kaveh et al. [90]	2018	M5, Multivariate Adaptive Regression Splines	114
Sathyan et al. [91]	2018	Random Kitchen Sink Algorithm	40
Vakhshouri and Nejadi [92]	2018	Adaptive Neuro Fuzzy Inference System	55
Belalia Douma et al. [93]	2017	Artificial Neural Network	114
Abu Yaman et al. [94]	2017	Artificial Neural Network	69
Ahmad et al. [95]	2021	Gene Expression Programming, Decision Tree and Bagging	270
Farooq et al. [96]	2021	Artificial Neural Network, bagging and boosting	1030
Javad et al. [51]	2020	Gene Expression Programming	277
Nematzadeh et al. [97]	2020	Response Surface Method, Gene Expression Programming	108
Zhou et al. [60]	2023	Decision Tree, Random Forest, Extreme Gradient Boosting	259

2. Methodology

2.1. Random Forest (RF)

Machine learning (ML) techniques are employed across various academic areas for accurate prediction. Random forest (RF) is an accurate ensemble machine learning technique that was first presented by Breiman [98] and relies upon the decision trees topology that is included inside the bagged learning architecture. The algorithm builds numerous decision trees by selecting data from data points at random in order to develop its projections, and then it aggregates these projections to produce the final outcome. The decision trees learn based on an individual combination of characteristics and data samples, ultimately resulting in a diversified model ensemble that, when combined, produces accurate forecasts. This ensemble learning strategy reduces the probability of the model being overfitting and improves its capacity to generalize [98].

RF is an excellent method for capturing complicated non-linear interactions between input parameters. Consequently, it is possible for the model to correctly reflect the complex relationships that exist between input parameters. In addition, RF fails to establish any severe assumption on the distribution of the dataset, which allows for more flexibility in the estimation of real-world and actual situations. Additionally, RF is capable of handling a large number of input parameters and is capable of automatically selecting the features that contain the most information. This simplifies the procedure for simulating and improves its interpretability [98]. In RF regression, the approach creates results from a number of different decision trees and then determines the mean of those findings. Figure 3 illustrates the general scheme of the RF algorithm and the whole research process after the RF modeling is given in Figure 4. The following is a condensed version of the regression equation that was used for the examination of the RF method [99]:

$$\overline{M}\left(x\right)=\frac{1}{N}{\displaystyle \sum _{i=1}^n\left(y_i\left(x,{\theta }_n\right)\right)}$$

(1)

2.2. Extreme Gradient Boosting (XGBoost)

Extreme gradient boosting (XGBoost) stands as an algorithm rooted in the principles of a gradient boosting tree [100], wielding significant influence in gradient enhancement. Leveraging the classifications and regressions tree theorem, XGBoost emerges as a potent solution for both regressions and classifications challenges [101,102]. Positioned as a soft computing library, XGBoost seamlessly integrates innovative algorithms with Gradient Boosted Decision Trees (GBDT) methodologies. Following optimization, the objective function of XGBoost encompasses two distinct components: one reflecting the model’s deviation, and the other serving as a regularization term to mitigate overfitting concerns [103].

Represented by D = {(x_i, y_i)}, where x_i and y_i denote features and labels, respectively, the dataset comprises n samples and m features. The predictive variable manifests as an additive model composed of k basic models. The outcomes of sample predictions are expressed as follows [103]:

$${\widehat{y}}_i={\displaystyle \sum _{k=1}^K{f}_k\left(x_i\right)\hspace{0.17em},\hspace{0.17em}}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{f}_k\in \phi$$

(2)

$$\phi =\left\{f\left(x\right)=w_s\left(x\right)\right\}\hspace{0.17em}\hspace{0.17em}\left(s\hspace{0.17em}:\hspace{0.17em}\hspace{0.17em}{R}^m\to T,w_s\in R^T\right)$$

(3)

where ${\widehat{y}}_i$ denotes the predicted label for the sample x_i, f_k(x_i) signifies the score predicted for the given sample, and φ represents the set of regression trees with parameters s, f(x), and w, where w denotes the weight of leaves and s denotes the number of leaves. The objective function of XGBoost integrates both the conventional loss function and model complexity, offering a metric to assess the algorithm’s operational efficiency. Formula (3) encapsulates this objective function, with the initial term denoting the traditional loss function and the subsequent term signifying the model’s complexity [103].

$$O={\displaystyle \sum _{i=1}^{n}l\left(y_i,{\widehat{y}}_i^{\left(t-1\right)}+f_i\left(x_i\right)\right)+\mathsf{\Omega }\left(f_k\right)}$$

(4)

$$\mathsf{\Omega }\left(f_k\right)=\gamma T+\frac{1}{2}\lambda w^2$$

(5)

Here, i signifies the number of samples in the dataset, and m denotes the total data incorporated into the k tree. Parameters gamma and lambda are utilized to fine tune the tree’s complexity, with regularization terms ensuring a smooth learning weight distribution and preventing overfitting.

2.3. Gray Wolf Optimizer Algorithm

The gray wolf optimizer (GWO) was initially presented by Mirjalili et al. [104], drawing inspiration from the natural behaviors of gray wolves. Within the GWO algorithm, there are distinct components such as a social hierarchy and processes related to prey tracking, encircling, and attacking. The gray wolf population is hierarchically structured into four segments: alpha (α), beta (β), delta (δ), and omega (ω). Alpha wolves make critical decisions, including those related to hunting and choosing sleeping locations. Beta wolves assist the alpha group in decision making, while delta wolves, occupying the third rank, submit to more dominant wolves. The remaining gray wolves, with the lowest rank, fall into the omega (ω) group. The mathematical representation of the gray wolf algorithm involves three key steps. Firstly, the encircling behavior is modeled mathematically, where gray wolves encircle prey during hunting. This behavior is expressed as follows [104]:

$$\overrightarrow{D}=\left|\overrightarrow{C}{\overrightarrow{X}}_P\left(t\right)-\overrightarrow{X}\left(t\right)\right|$$

(6)

$$\overrightarrow{X}\left(t+1\right)={\overrightarrow{X}}_P\left(t\right)-\overrightarrow{A}\cdot \overrightarrow{D}$$

(7)

where $\overrightarrow{A}$ and $\overrightarrow{D}$ are coefficient vectors, ${\overrightarrow{X}}_P$ and $\overrightarrow{X}$ represent the current position vectors of the prey and gray wolf, respectively, and t denotes the present iteration.

Secondly, the hunting behavior involves updating the position of omega (x) using the best solutions from the positions of higher-ranking gray wolves (α, β, and ω). Equations (8)–(14), proposed by Mirjalili et al. [104], govern the calculation of new positions for α, β, and ω.

$$\overrightarrow{D}=\left|\overrightarrow{C}{\overrightarrow{X}}_P\left(t\right)-\overrightarrow{X}\left(t\right)\right| {\overrightarrow{D}}_{\alpha }=\left|{\overrightarrow{C}}_1{\overrightarrow{X}}_{\alpha }(t)-\overrightarrow{X}(t)\right|$$

(8)

$$\overrightarrow{X}(t+1)={\overrightarrow{X}}_p(t)-\overrightarrow{A}·\overrightarrow{D} {\overrightarrow{D}}_{\beta }=|{\overrightarrow{C}}_2{\overrightarrow{X}}_{\beta }(t)-\overrightarrow{X}(t)|$$

(9)

$${\overrightarrow{D}}_{\delta }=|{\overrightarrow{C}}_3{\overrightarrow{X}}_{\delta }(t)-\overrightarrow{X}(t)|$$

(10)

$${\overrightarrow{D}}_1={\overrightarrow{X}}_{\alpha }-{\overrightarrow{A}}_1\left({\overrightarrow{D}}_{\alpha }\right)$$

(11)

$${\overrightarrow{D}}_2={\overrightarrow{X}}_{\beta }-{\overrightarrow{A}}_2\left({\overrightarrow{D}}_{\beta }\right)$$

(12)

$${\overrightarrow{D}}_3={\overrightarrow{X}}_{\delta }-{\overrightarrow{A}}_3\left({\overrightarrow{D}}_{\delta }\right)$$

(13)

$$\overrightarrow{X}\left(t+1\right)=\left({\overrightarrow{X}}_1+{\overrightarrow{X}}_2+{\overrightarrow{X}}_3\right)/3$$

(14)

Lastly, the attacking behavior, which constitutes the final hunting behavior, aims to specify the optimized location of the preys. The wolves’ actions are influenced by the value of $\left|A\right|$, and they can only attack the prey when $\left|A\right|\le 1$ is satisfied. The optimization of the GWO is achieved upon reaching this criterion [104].

2.4. Hybrid Strategy

In this section, we introduce the configuration of the GWO–XGBoost and RF–GWO–XGBoost patterns. Specifically, the GWO algorithm serves as an innovative solution to optimize the XGBoost system, facilitating the broadening of the hyperparameter search domain. This extension enhances the XGBoost model’s capacity to identify optimal performance levels. Notably, the RF–GWO–XGBoost model introduced here stands out for its distinctive feature of amalgamating predictive values from both RF models and the GWO–XGBoost model. To achieve this, the RF approach is initially employed to predict CSGePoCo, utilizing multiple RF models to generate comprehensive predictions for the CSGePoCo. Subsequently, these predictions are utilized in formulating the framework for the XGBoost model. The GWO algorithm plays a crucial role in training the XGBoost model on the basis of predictable values derived from the RF architectures, with the aim of optimizing the hyperparameters of the XGBoost model. The objective function and stopping criterion for both the GWO–XGBoost and RF–GWO–XGBoost models are defined by the RMSE in Equation (15). The model with the smallest fitness value of RMSE is deemed to have the best prediction accuracy. Detailed visual representations of the proposed frameworks for the GWO–XGBoost and RF–GWO–XGBoost models are presented in Figure 5 and Figure 6.

2.5. Performance Evaluation of the Models

To comprehensively assess the efficiency of the proposed models in the present research, various metrics, including the mean average error (MAE), root mean square error (RMSE), coefficient of determination (R²), and a²⁰ index [60,101,102], are employed. These indicators serve to depict the correlations between the measured CSGePoCo values and the estimated CSGePoCo value [105,106,107,108,109]. The mathematical formulas for calculation of these indices are as follows:

$$RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum }_{i=1}^n{\left(m_{\mathrm{CSGePoCo}}-p_{\mathrm{CSGePoCo}}\right)}^2}$$

(15)

$$MAE=\frac{1}{n}{\displaystyle \sum }_{i=1}^n\left|\left(p_{\mathrm{CSGePoCo}}-m_{\mathrm{CSGePoCo}}\right)\right|$$

(16)

$$R^2=\frac{{{\displaystyle \sum }}_{i=1}^r{\left(m_{\mathrm{CSGePoCo}}-{\overline{m}}_{\mathrm{CSGePoCo}}\right)}^2-{{\displaystyle \sum }}_{i=1}^r{\left(m_{\mathrm{CSGePoCo}}-p_{\mathrm{CSGePoCo}}\right)}^2}{{{\displaystyle \sum }}_{i=1}^r{\left(m_{\mathrm{CSGePoCo}}-{\overline{m}}_{\mathrm{CSGePoCo}}\right)}^2}$$

(17)

$$a^{20}-index=\frac{m^{20}}{M}$$

(18)

in which $m_{\mathrm{CSGePoCo}}$ and $p_{\mathrm{CSGePoCo}}$ are the measured and anticipated ith CSGePoCo values, respectively, n stands the number data points, ${\overline{m}}_{\mathrm{CSGePoCo}}$ is the mean of the measured CSGePoCo, ${\overline{p}}_{\mathrm{CSGePoCo}}$ is the mean of the predicted CSGePoCo. In addition, m²⁰ and M indicate total number of data points and the number of points with a ratio “measured value” over “predicted value” between 0.80 and 1.20 [110,111,112,113].

3. Data Preparation

The data for this study were collected from the available literature and encompass 15 parameters [114,115,116], as shown in Table 2. These parameters are FA (kg/m³), SiO₂-Fly (% weight), Al₂O₃-Fly (% weight), CaO-Fly (% weight), GGBS (kg/m³), SiO₂-GGBS (% weight), Al₂O₃-GGBS (% weight), CaO-GGBS (% weight), Fine (kg/m³), Coarse (kg/m³), NaOH (kg/m³), Na₂SiO₃ (kg/m³), SP dosage (kg/m³), NaOH, and CT (°C), and the output parameter of CSGePoCo (MPa), as depicted in Figure 7. Each selected parameter was chosen based on its considerable effect on the strength properties of fly ash-slag-based concretes [117,118,119,120]. Furthermore, the selection of input parameters is conducted based on the suggestions of the literature [121,122,123,124]. Fly ash is a byproduct of coal combustion and is commonly used as a supplementary cementitious material in concrete [63,64]. Its composition, including SiO₂ (silica), Al₂O₃ (alumina), and CaO (calcium oxide), can influence concrete properties such as strength, durability, and workability. Furthermore, GGBS is a byproduct of the iron-making process and is used as a supplementary cementitious material. Its composition, particularly SiO₂, Al₂O₃, and CaO, is crucial in determining its pozzolanic reactivity and impact on concrete performance.

Aggregates contribute to the mechanical properties of concrete. Fine aggregates are typically sand, while coarse aggregates are larger particles like gravel or crushed stone. The size, shape, and gradation of aggregates affect the workability, strength, and durability of concrete [125,126].

Alkaline activators are used in alkali-activated materials to enhance the reactivity of supplementary cementitious materials. NaOH (sodium hydroxide) and Na₂SiO₃ (sodium silicate) are commonly used activators. Their concentrations and ratios can significantly impact the performance of alkali-activated materials [127,128,129]. Superplasticizers are additives that improve the workability of concrete without sacrificing strength. The dosage of superplasticizer affects the fluidity and slump of the concrete mix. Sodium hydroxide (NaOH) molarity refers to the concentration of the alkaline activator. The molarity can influence the rate of chemical reactions and the strength development of alkali-activated materials. Curing temperature is the temperature at which concrete is maintained during the curing period. Curing at different temperatures can impact the development of strength and durability of concrete. The consideration and manipulation, rationale, effect on properties, and collective effects of these parameters are presented in

Table 3. Some information regarding parameters.

Parameter	Consideration and Manipulation	Rationale	Effect on Properties	Collective Effects
Fly Ash	The type and source of fly ash were carefully selected, considering variations in mineral composition and reactivity.	The choice of fly ash can significantly impact the pozzolanic reactions and the overall performance of the concrete.	Different fly ash types can influence strength development, durability, and workability of the concrete.	Combined with other factors, the type of fly ash contributes to the overall concrete properties.
Fly Ash Composition (SiO2-Fly, Al2O3-Fly, CaO-Fly)	Varied compositions of SiO2, Al2O3, and CaO were explored to understand their individual effects.	Different compositions may affect the reactivity and pozzolanic characteristics of fly ash.	SiO2 influences strength, Al2O3 affects sulfate resistance, and CaO influences early strength.	Interactions between these components affect the concrete’s overall performance.
Ground Granulated Blast-Furnace Slag	The source and properties of slag were carefully chosen to provide specific characteristics.	GGBFS contributes to improved workability, reduced heat generation, and enhanced durability.	GGBFS impacts strength development, permeability, and resistance to aggressive environments.	Synergies with other factors determine the concrete’s final characteristics.
GGBFS Composition (SiO2, Al2O3, CaO)	Varied compositions were tested to assess their influence on concrete properties.	The mineral composition of GGBFS affects the pozzolanic activity and reactivity.	SiO2 content influences workability, Al2O3 affects sulfate resistance, and CaO impacts strength.	Combined with other factors, GGBFS composition contributes to the overall performance.
Aggregate (Fine and Coarse)	Different types and gradations of aggregates were tested to understand their impact.	Aggregates affect concrete workability, strength, and durability.	Fine aggregates influence the mix’s cohesion, while coarse aggregates impact strength and workability.	Combined with other factors, aggregate properties contribute to the final concrete characteristics.
Alkaline Activators (NaOH, Na2SiO3)	Various concentrations and combinations of NaOH and Na2SiO3 were explored.	Alkaline activators initiate the activation of supplementary cementitious materials.	Alkaline activators influence setting time, early strength development, and durability.	Interactions with other factors determine the overall performance of the concrete.
Superplasticizer Dosage	Different dosages were considered to optimize workability without compromising strength.	Superplasticizers improve concrete workability by dispersing cement particles.	Superplasticizers influence slump, flowability, and consolidation without excessive water content.	Combined with other factors, the superplasticizer dosage contributes to the overall mix design.
NaOH Molarity	Various concentrations of NaOH were tested to optimize alkaline activation.	The molarity of NaOH affects the rate and extent of chemical reactions in the concrete mix.	The molarity of NaOH influences strength development, setting time, and pore structure.	Interactions with other factors determine the overall performance.
Curing Temperature	Different curing temperatures were applied to study their impact on concrete properties.	Curing temperature influences the rate of hydration and the development of concrete strength.	Higher curing temperatures may accelerate strength gain but can also affect durability.	Combined with other factors, curing temperature contributes to the overall concrete performance.

.

Table 2. The choice of parameters for predicting fly-ash-slag-based concrete by thoroughly examining the literature and utilizing published data.

FA	SiO2-Fly	Al2O3-Fly	CaO-Fly	GGBS	SiO2-GGBS	Al2O3-GGBS	CaO-GGBS	Fine	Coarse	NaOH	Na2SiO3	SP Dosage	NaOH Molarity	CT	CSGePoCo	References
252	60.11	26.53	4	108	34.06	20	32.6	774	1090.8	46.3	115.7	144	8	30	33.83	[124]
252	60.11	26.53	4	108	34.06	20	32.6	774	1090.8	61.7	154.3	144	8	30	25.71
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
225	60.11	26.53	4	225	34.06	20	32.6	760.5	972	64.3	160.7	180	8	60	61.9
225	60.11	26.53	4	225	34.06	20	32.6	760.5	972	77.1	192.9	180	8	60	53.79
293	46	33	2.6	88	21	17	56.1	760	1005	143.3	71.7	0	6	20	37.4	[123]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
293	46	33	2.6	88	21	17	56.1	760	1005	107.5	107.5	0	6	20	26.6
253	46	33	2.60	126	21	17	56.1	760	1005	143.3	71.7	0	4	20	28
237	63.53	27.4	1.26	158	34.26	11.32	38.34	547	1277	52	129	7.9	8	32	28.36	[122]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
360	53.71	27.2	1.90	40	29.96	12.25	45.45	655.9	1218.1	40	100	6	14	23	33.3
200	52.6	34.1	1.32	200	33.8	14.8	38.8	716	1074	9	56	0	0	0	31.7	[121]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
200	52.6	34.1	1.32	200	33.8	14.8	38.8	700	1050	15	93	0	0	0	42.3
360	53.71	27.2	1.9	40	29.96	12.25	45.45	651	1209	45.7	114.3	0	14	22	40	[120]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
340	53.24	26.42	3.65	60	36.77	13.56	37.6	646	1200	53	107	4	12	22	35
320	53.24	26.42	3.65	80	36.77	13.56	37.6	648	1203	53	107	4	12	22	45
300	53.24	26.42	3.65	100	36.77	13.56	37.6	658	1222	53	107	4	12	22	57	[119]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
300	53.24	26.42	3.65	100	36.77	13.56	37.6	659	1223	46	114	4	10	22	45
303.75	45.8	21.4	13.7	101.25	34.52	20.66	32.43	683	1269	81	81	4.05	8	0	10.5	[118]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
303.75	45.8	21.4	13.7	101.25	34.52	20.66	32.43	683	1269	81	81	4.05	10	0	13
303.75	45.8	21.4	13.7	101.25	34.52	20.66	32.43	683	1269	40.5	121.5	4.05	14	0	31.7
0	0	0	0	400	37.73	14.42	37.34	810	990	57.1	143	8	12	25	89.6	[130]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
0	0	0	0	400	37.73	14.42	37.34	810	990	57.1	143	12	12	25	89.2
0	0	0	0	400	37.73	14.42	37.34	810	990	57.1	143	24	12	25	84.1
204.5	65.6	28	1	204.5	30.61	16.24	34.48	554	1293	41	102	0	10	0	53.5	[115]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
102	65.6	28	1	307	30.61	16.24	34.48	554	1293	41	102	0	10	0	55.5
0	65.6	28	1	409	30.61	16.24	34.48	554	1293	41	102	0	10	0	58.6
0	0	0	0	400	31.63	13.42	36.35	740	1110	12.9	82.5	0	0	22	34.6	[114]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
0	0	0	0	400	31.63	13.42	36.35	785	1085	12.9	82.5	0	0	22	53.6
0	0	0	0	400	31.63	13.42	36.35	790	1065	12.9	82.5	0	0	22	66.7

Table 2. The choice of parameters for predicting fly-ash-slag-based concrete by thoroughly examining the literature and utilizing published data.

FA	SiO2-Fly	Al2O3-Fly	CaO-Fly	GGBS	SiO2-GGBS	Al2O3-GGBS	CaO-GGBS	Fine	Coarse	NaOH	Na2SiO3	SP Dosage	NaOH Molarity	CT	CSGePoCo	References
252	60.11	26.53	4	108	34.06	20	32.6	774	1090.8	46.3	115.7	144	8	30	33.83	[124]
252	60.11	26.53	4	108	34.06	20	32.6	774	1090.8	61.7	154.3	144	8	30	25.71
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
225	60.11	26.53	4	225	34.06	20	32.6	760.5	972	64.3	160.7	180	8	60	61.9
225	60.11	26.53	4	225	34.06	20	32.6	760.5	972	77.1	192.9	180	8	60	53.79
293	46	33	2.6	88	21	17	56.1	760	1005	143.3	71.7	0	6	20	37.4	[123]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
293	46	33	2.6	88	21	17	56.1	760	1005	107.5	107.5	0	6	20	26.6
253	46	33	2.60	126	21	17	56.1	760	1005	143.3	71.7	0	4	20	28
237	63.53	27.4	1.26	158	34.26	11.32	38.34	547	1277	52	129	7.9	8	32	28.36	[122]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
360	53.71	27.2	1.90	40	29.96	12.25	45.45	655.9	1218.1	40	100	6	14	23	33.3
200	52.6	34.1	1.32	200	33.8	14.8	38.8	716	1074	9	56	0	0	0	31.7	[121]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
200	52.6	34.1	1.32	200	33.8	14.8	38.8	700	1050	15	93	0	0	0	42.3
360	53.71	27.2	1.9	40	29.96	12.25	45.45	651	1209	45.7	114.3	0	14	22	40	[120]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
340	53.24	26.42	3.65	60	36.77	13.56	37.6	646	1200	53	107	4	12	22	35
320	53.24	26.42	3.65	80	36.77	13.56	37.6	648	1203	53	107	4	12	22	45
300	53.24	26.42	3.65	100	36.77	13.56	37.6	658	1222	53	107	4	12	22	57	[119]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
300	53.24	26.42	3.65	100	36.77	13.56	37.6	659	1223	46	114	4	10	22	45
303.75	45.8	21.4	13.7	101.25	34.52	20.66	32.43	683	1269	81	81	4.05	8	0	10.5	[118]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
303.75	45.8	21.4	13.7	101.25	34.52	20.66	32.43	683	1269	81	81	4.05	10	0	13
303.75	45.8	21.4	13.7	101.25	34.52	20.66	32.43	683	1269	40.5	121.5	4.05	14	0	31.7
0	0	0	0	400	37.73	14.42	37.34	810	990	57.1	143	8	12	25	89.6	[130]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
0	0	0	0	400	37.73	14.42	37.34	810	990	57.1	143	12	12	25	89.2
0	0	0	0	400	37.73	14.42	37.34	810	990	57.1	143	24	12	25	84.1
204.5	65.6	28	1	204.5	30.61	16.24	34.48	554	1293	41	102	0	10	0	53.5	[115]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
102	65.6	28	1	307	30.61	16.24	34.48	554	1293	41	102	0	10	0	55.5
0	65.6	28	1	409	30.61	16.24	34.48	554	1293	41	102	0	10	0	58.6
0	0	0	0	400	31.63	13.42	36.35	740	1110	12.9	82.5	0	0	22	34.6	[114]
…	…	…	…	…	…	…	…	…	…	…	…	…	…	…	…
0	0	0	0	400	31.63	13.42	36.35	785	1085	12.9	82.5	0	0	22	53.6
0	0	0	0	400	31.63	13.42	36.35	790	1065	12.9	82.5	0	0	22	66.7

The Pearson correlation coefficient was employed to discern the relationships among effective parameters and CSGePoCo, as shown in Figure 8. In addition, the pivotal variables influencing the prediction of mechanical strength were assessed using permutation features. Furthermore,

Table 4. Descriptive information of inputs and output variable.

Type	Parameter	Notation	Unit	Mean	Standard Deviation	Minimum	Maximum
Input	Fly ash	FA	kg/m3	252.465	86.271	0	400
	Fly ash composition	SiO2-Fly	% weight	52.764	13.574	0	65.6
		Al2O3-Fly	% weight	25.566	6.757	0	34.1
		CaO-Fly	% weight	4.401	3.774	0	13.7
	ground granulated blast-furnace slag	GGBS	kg/m3	151.439	86.733	0	409
	GGBS composition	SiO2-GGBS	% weight	33.105	3.625	21	37.73
		Al2O3-GGBS	% weight	17.644	3.212	11.32	20.66
		CaO-GGBS	% weight	36.581	6.511	32.43	56.1
	Aggregate	Fine	kg/m3	729.803	67.975	547	810.6
		Coarse	kg/m3	1096.028	117.853	966	1293
	Alkaline activators	NaOH	kg/m3	60.463	26.841	9	143.3
		Na2SiO3	kg/m3	122.984	35.708	54	192.9
	Super plasticizer dosage	SP dosage	kg/m3	77.568	80.983	0	180
	NaOH molarity	NaOH molarity	-	8.564	3.894	0	16
	curing temperature	CT	oC	28.077	20.553	0	60
Output	Compressive Strength of Geopolymer Concrete	CSGePoCo	MPa	42.716	15.328	10.5	89.6

summarizes the statistical properties of the data used, indicating their maximum and minimum based on 156 data samples. Meanwhile, Table 4 presents the summary of the descriptive statistics, including the average, standard deviation, minimum, and maximum. It is noteworthy that the variables incorporated in developing the models exert a significant effect on the robustness of the models. It is acknowledged that the reactivity of raw materials, such as fly ash, can exhibit significant variations depending on their geographical origin and processing conditions. This inherent variability is attributed to differences in mineralogical composition, particle size distribution, and the presence of impurities.

A box plot, also known as a box-and-whisker plot, is a graphical representation of the distribution of a dataset. It provides a visual summary of key statistics, including the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. Box plots are particularly useful for identifying outliers in a dataset.

The box in the plot represents the interquartile range (IQR), which is the range between the first quartile (Q1) and the third quartile (Q3). The line inside the box represents the median (Q2). Furthermore, whiskers extend from the box to the minimum and maximum values within a specified range. They can be determined using different methods, such as 1.5 times the IQR or a fixed percentage of the data. Any data point beyond the whiskers is considered a potential outlier.

Notably, outliers are individual data points that fall significantly outside the overall pattern of the dataset. Outliers can be identified as points beyond the whiskers of the box plot. Outliers may be classified into mild outliers (1.5 to 3 times IQR) and extreme outliers (beyond 3 times IQR). Outliers are often represented as individual points or asterisks outside the whiskers. The shape of the box plot can also provide insights into the symmetry or skewness of the data. A skewed distribution might have one whisker longer than the other. If data points lie beyond the whiskers, they are potential outliers.

The box plot of parameters is depicted in Figure 9. It can be seen that the parameters of CT, SiO₂-GGBS, SiO₂-Fly, Al₂O₃-Fly, and CaO-Fly suffer from outlier data.

4. Developing of the Models

The modeling of CSGePoCo is conventionally approached as a prediction challenge, wherein both the effective parameters and the target value are numerical. To construct an effective predictive model, the dataset needs to be partitioned into distinct training and testing sets. This segregation is accomplished by allocating 80% of the collected database to training datasets and the remaining 20% to testing datasets [114,115,131,132]. Subsequently, the GWO algorithm is employed to explore the optimal combination of variables for learning_rate, maximum_depth, and n_estimators in the XGBoost model. The resultant XGBoost model is then established. Finally, the testing datasets are utilized to assess the proposed model, employing the aforementioned statistical indices. It is crucial to emphasize that each estimation model is constructed and evaluated using the same previously designated data samples.

4.1. XGBoost Model

In the context of XGBoost, two critical stopping criteria, specifically maximum tree depth, n_estimators, and learning_rate, are carefully considered to curb model complexity. The selection of significant values for maximum tree depth and n_estimators is crucial to prevent tree overgrowth and the associated overfitting issues. Accordingly, the maximum tree depth is constrained within the range of 1–3, while n_estimators assume values of 25, 50, 75, 100, and 125, and the range of 0.01–0.15 was set for the learning rate. To specify the optimal combination of these parameters, a systematic trial-and-error procedure is executed, exploring the proposed range of settings. Performance metrics, encompassing RMSE, MAE, R², and the a²⁰ index, are computed to assess the XGBoost models on both the training and the testing datasets (refer to

Table 5. Performance evaluation of XGBoost model.

Model	N Estimators	Max Depth	Learning Rate	Training Phase				Testing Phase
				MAE	R2	RMSE	m20	MAE	R2	RMSE	m20
XGBoost 1	25	1	0.01	3.166	0.897	2.530	0.912	7.820	0.920	8.090	0.512
XGBoost 2	50	2	0.05	3.057	0.903	3.850	0.981	7.400	0.810	9.460	0.405
XGBoost 3	75	3	0.1	2.441	0.947	2.000	0.994	5.161	0.944	5.902	0.516
XGBoost 4	100	1	0.12	2.917	0.914	2.040	0.872	7.010	0.900	8.720	0.465
XGBoost 5	125	2	0.15	2.574	0.919	2.760	0.833	9.720	0.830	7.410	0.485
XGBoost 6	25	3	0.01	3.001	0.912	2.854	0.982	8.300	0.900	7.120	0.427
XGBoost 7	50	1	0.05	3.342	0.887	2.960	0.832	8.470	0.930	7.090	0.471
XGBoost 8	75	2	0.1	3.145	0.899	2.180	0.956	9.380	0.890	6.460	0.506
XGBoost 9	100	3	0.12	3.952	0.854	3.960	0.809	7.570	0.880	9.720	0.454
XGBoost 10	125	3	0.15	3.123	0.900	2.560	0.896	5.450	0.870	6.100	0.434

). Table 5 presents the results of ten developed and evaluated XGBoost models. Notably, the performance metrics for these models are closely aligned, making the selection of the best model challenging. To address this, a straightforward ranking procedure, as proposed by Wang et al. [133] and Zhao et al. [102], is applied to

Table 6. Rating of the obtained statistical indices for XGBoost models.

Model	Training Phase				Testing Phase				Total Rate	Rank
	Rate of MAE	Rate of R2	Rate of RMSE	Rate of m20	Rate of MAE	Rate of R2	Rate of RMSE	Rate of m20
XGBoost 1	3	3	7	6	5	8	4	9	45	4
XGBoost 2	6	6	2	8	7	1	2	1	33	9
XGBoost 3	10	10	10	10	10	10	10	10	80	1
XGBoost 4	8	8	9	4	8	6	3	5	51	2
XGBoost 5	9	9	5	3	1	2	5	7	41	7
XGBoost 6	7	7	4	9	4	6	6	2	45	4
XGBoost 7	2	2	3	2	3	9	7	6	34	8
XGBoost 8	4	4	8	7	2	5	8	8	46	3
XGBoost 9	1	1	1	1	6	4	1	4	19	10
XGBoost 10	5	5	6	5	9	3	9	3	45	4

. The efficiency levels of various proposed models are evaluated based on a rating system. The FR method involves rating R², RMSE, MAE, and a²⁰ values [127,134,135], where a higher rating is accorded to an XGBoost model exhibiting superior R² and a²⁰ values, along with minimized RMSE and MAE values. Notably, the assigned rating is contingent on the number of developed base models for each technique. For instance, if there are 30 models, the top-performing model will receive a rating of 30. The formulation of the FR rating system involves the application of Equation (19):

$$FR={\displaystyle \sum _{i=1}^2\left(r_i^{R^2}+r_i^{RMSE}+r_i^{MAE}+r_i^{a20}\right)}$$

(19)

in which r_i signifies the rate of statistical indices, i is 1 for training rates of indices, and 2 for testing rates of indices.

The XGBoost models are ranked and evaluated based on ranking indicators. The comprehensive results, including the overall rates for XGBoost models 1–10, are summarized in Table 6. As per the table, model 3, with a total rank value of 80 out of 80, attains the highest rank among all the constructed XGBoost models. In other words, XGBoost model 3 outperformed the other models in this study, as evidenced by the ranking and evaluation metrics in Table 6.

4.2. RF Model

In the RF model, the determination of two key parameters, namely the number of trees (n_tree) and the number of variables used to grow each tree (m_try), is paramount. To achieve this, ten RF models were developed with m_try ranging from 3 to 9 and ntree set at 50–200. The assessment of predictive performance on training datasets, gauged through RMSE values, revealed that the optimal value for m_try in predicting CSGePoCo was ten. Subsequently, a grid search technique, employing n_tree in the range of 1–2500 and m_try fixed at 10, was conducted to identify the optimal n_tree. No substantial changes were observed when n_tree was set to 200, leading to the selection of 200 as the optimal value. It is noteworthy that a tenfold cross-validation method was employed to assess the skill of the RF model and select the most suitable RF model for the specific predictive modeling task, such as CSGePoCo prediction. Before constructing the RF model, the dataset underwent standardization using the Box–Cox transformation method [136,137,138] to mitigate overfitting concerns. Beyond predicting CSGePoCo with the RF model, the predictive values generated by a set of RF models are utilized in proposing the innovative RF–GWO–XGBoost model, as previously introduced. Consequently, the best ten RF predictions were chosen according to the achieved results for the subsequent steps (constructing the RF–GWO–XGBoost predictive system), with the efficiency of the ten RF architectures detailed in

Table 7. Performance evaluation of RF model.

Model	ntree	mtry	Training Phase				Testing Phase
			MAE	R2	RMSE	m20	MAE	R2	RMSE	m20
RF 1	50	3	3.971	0.903	3.394	0.942	9.14	0.898	10.69	0.579
RF 2	200	3	3.035	0.879	3.388	0.952	9.33	0.912	10.6	0.529
RF 3	100	5	3.673	0.853	3.266	0.954	10.7	0.899	9.712	0.561
RF 4	150	7	3.161	0.869	3.422	0.95	11.5	0.918	15.095	0.524
RF 5	50	7	3.648	0.868	3.270	0.948	11.4	0.906	8.289	0.557
RF 6	200	9	2.750	0.928	3.259	0.960	6.97	0.918	8.124	0.581
RF 7	100	3	3.007	0.904	3.295	0.958	7.23	0.904	13.24	0.535
RF 8	150	5	3.686	0.923	3.423	0.956	7.61	0.912	13.61	0.578
RF 9	200	7	3.951	0.869	3.908	0.947	9.67	0.909	9.998	0.555
RF 10	100	9	3.427	0.902	3.362	0.953	8.71	0.915	8.124	0.542

. Notably, the RF6 model emerged as the optimal choice based on the rating system proposed by Zhao et al. [102] and was employed as a standalone model for comparison with other models in subsequent sections. It is pertinent to mention that two parameters, namely penalty values (d) and the maximum number of basis functions (f), are utilized to govern the performance of the RF models. The rating of the developed RF model is reported in

Table 8. Rating of the obtained statistical indices for RF models.

Model	Training Phase				Testing Phase				Total Rate	Rank
	Rate of MAE	Rate of R2	Rate of RMSE	Rate of m20	Rate of MAE	Rate of R2	Rate of RMSE	Rate of m20
RF 1	1	7	4	1	6	1	4	9	33	8
RF 2	8	5	5	5	5	6	5	2	41	5
RF 3	4	1	9	7	3	2	7	7	40	6
RF 4	7	3	3	4	1	10	1	1	30	9
RF 5	5	2	8	3	2	4	8	6	38	7
RF 6	10	10	10	10	10	9	9	10	78	1
RF 7	9	8	7	9	9	3	3	3	51	3
RF 8	3	9	2	8	8	6	2	8	46	4
RF 9	2	3	1	2	4	5	6	5	28	10
RF 10	6	6	6	6	7	8	10	4	53	2

. As observed in Table 7, all ten RF models constructed for estimating CSGePoCo in this study exhibit suitability. While certain RF models demonstrate superior performance compared to others, the overall results are remarkably similar. Consequently, determining the optimal RF model becomes challenging due to the closely aligned performances. To address this, an FR ranking technique is employed to discern the best-performing RF model, as detailed in Table 8. Examining Table 4 and Table 5 reveals that RF model 6, attaining a total ranking value of 78 out of 80, emerges as the top-performing model among all developed RF models. Thus, it can be inferred that RF model 6, characterized by n_tree = 200 and m_try = 9, stands out as the superior model within the RF technique for predicting CSGePoCo in this study.

4.3. GWO–XGBoost Model

Determining optimal parameter values for heuristic optimization algorithms during the hyperparameter optimization of machine learning models can be challenging [36,139]. Utilizing random numbers within specific parameter ranges of heuristic algorithms may enhance optimization outcomes. Initially, the relevant hyperparameters for the XGBoost model are initialized. Subsequently, the pertinent parameters for the GWO algorithm are configured. In the case of GWO-XGBoost, following the initialization of the XGBoost model, the parameters for the GWO algorithm are fixed, with the convergence constant linearly decreasing from 2.5 to 0. The population number varies from 50 to 300. A tenfold cross-validation resampling procedure is employed to bolster the effectiveness and robustness of the optimization step. Figure 10 illustrates the change in adaptations in the repetition process. Hence, based on the comprehensive score, the GWO–XGBoost system attains the optimal parameter combination and maximum accuracy with a population size of 150 (MAE of 1.828, R2 of 0.972, RMSE of 2.159, and m20 of 0.965 for the training phase, and MAE of 3.839, R2 of 0.969, RMSE of 4.504, and m20 of 0.742 for the testing phase). Analyzing results reveals that the GWO–XGBoost model demonstrates strong predictive performance for CSGePoCo.

4.4. RF–GWO–XGBoost

While the RF, XGBoost, and GWO–XGBoost models were constructed using the identical original training dataset, the RF–GWO–XGBoost model was formulated by amalgamating the original training data with the prediction values obtained in the RF modeling detailed in

Table 9. Robustness evaluation of developed models in estimating CSGePoCo.

Model	Training Phase				Testing Phase
	MAE	R2	RMSE	m20	MAE	R2	RMSE	m20
RF	2.750	0.928	3.259	0.960	6.968	0.918	8.124	0.581
XGBoost	2.441	0.947	2.854	0.994	5.161	0.944	5.902	0.516
GWO–XGBoost	1.828	0.972	2.159	0.965	3.839	0.969	4.504	0.742
RF–GWO–XGBoost	1.462	0.983	1.712	0.999	3.122	0.981	3.485	0.839

(comprising ten RF models), as illustrated in Figure 6. Following this, the predictive values from ten selected RF models were combined to create an XGBoost model. In essence, another XGBoost model, mirroring the structure of the XGBoost and GWO–XGBoost models, was developed using an alternate training dataset derived from the prediction values obtained in the RF modeling. To optimize this novel XGBoost model, the GWO algorithm was used, employing the same settings as those used for the GWO–XGBoost model. Notably, intriguing outcomes were observed, as detailed in Figure 11. Finally, the optimal RF–GWO–XGBoost model was established, as presented in Table 9. It is essential to emphasize that although the structures of XGBoost, GWO–XGBoost, and RF–GWO–XGBoost models are identical, their hyperparameter values markedly differ concerning the optimization of the GWO algorithm and the impacts of the RF models. Once the CSGePoCo predictive structures were meticulously constructed as aforementioned, CSGePoCo anticipations in the current research were executed using four distinct models: RF, XGBoost, GWO–XGBoost, and RF–GWO–XGBoost. The corresponding results of CSGePoCo estimation utilizing the following four proposed systems are tabulated in Table 9.

5. Results and Discussion

Analyzing the results presented in Table 9 revealed that all four artificial intelligence (AI) models, namely, RF, XGBoost, GWO–XGBoost, and RF–GWO–XGBoost, exhibit relatively low errors, and their accuracy levels are deemed acceptable. Notably, RF’s performance slightly trails that of XGBoost in both the training and testing phases. Interestingly, the optimization features of the GWO algorithm enhance the accuracy of the XGBoost model, leading to superior performance of the GWO–XGBoost model compared to both XGBoost and RF approaches.

This research introduces a hybrid strategy, resulting in the novel hybrid RF–GWO–XGBoost system for anticipating CSGePoCo. The outcomes in Table 9 demonstrate that the developed RF–GWO–XGBoost system achieves acceptable efficiency with a high level of accuracy, surpassing even the GWO–XGBoost system across all datasets. This suggests that the integration plan of stacking and optimization techniques applied to RF and XGBoost approaches provides an alternative training set with improved normalization and regressions, thereby enhancing the predictive capability of the GWO–XGBoost model. Visual representations of these results can be observed in Figure 12, Figure 13, Figure 14 and Figure 15.

Figure 12, Figure 13, Figure 14 and Figure 15 illustrate the correlation of the CSGePoCo value (actual versus estimated) for the RF–GWO–XGBoost model, demonstrating its superiority over the RF, XGBoost, and GWO–XGBoost models, particularly on the training dataset. Notably, the optimization models (GWO–XGBoost and RF–GWO–XGBoost) exhibit significantly improved correlation, with the proposed hybrid RF–GWO–XGBoost model performing exceptionally well. In the testing phase, the regression levels of the optimization models surpass those of other models, with the proposed RF–GWO–XGBoost model standing out.

A further assessment of the developed models is conducted by comparing their performance against measured values of CSGePoCo in Figure 16. To provide a comprehensive evaluation, violin plots and Taylor diagrams are employed on both the training and testing datasets, as illustrated in Figure 17 and Figure 18, respectively. Figure 17 reveals that the violin plots exhibit a close mean value of predicted CSGePoCo by the proposed RF–GWO–XGBoost model to measured CSGePoCo. Moreover, the Taylor diagram demonstrates that the proposed RF–GWO–XGBoost model excels in predicting CSGePoCo, closely aligning with the actual values.

In order to gain deeper insights into the operational mechanism of the proposed RF–GWO–XGBoost model and to elucidate the contributions of input variables in the modeling process, an investigation into the significance levels of these effective parameters was conducted using an analysis of the sensitivity. Sensitivity analysis is an integral technique applied across diverse fields, such as engineering, economics, and environmental sciences, aiming to assess the impact of input parameters or assumptions on the output of a model or system. Within sensitivity analysis, the cosine amplitude method (CAM), a specific approach, was employed to gauge how changes in input parameters influence the variability in the model’s output. This method systematically varies individual input parameters while keeping other factors constant, measuring resultant changes in the model’s output. The nomenclature of this method is derived from the cosine function, which defines the amplitude of the input parameter variations. Through this methodology, researchers can quantitatively measure the sensitivity of the model to specific input variations and pinpoint parameters exerting the most substantial influence on the model’s behavior. This analysis enables researchers to identify critical parameters contributing significantly to output variability, facilitating the prioritization of resources and efforts toward addressing and optimizing these influential factors. Moreover, the CAM offers a systematic and structured approach for exploring the impact of parameter changes, allowing researchers to assess how sensitive the model is to both small and large fluctuations in input parameters [140,141]. By conducting sensitivity analysis utilizing the CAM, researchers can make informed decisions regarding the model’s design, input parameter selection, and overall robustness. This enhances the model’s predictive capabilities and ensures its applicability in real-world scenarios [142]. The effectiveness and relative significance of the influential parameters were assessed through sensitivity analysis using the CAM, employing the following two renowned techniques [113,143,144,145]:

$$s_{ij}=\frac{{\displaystyle \sum _{k=1}^m{x}_{ik}\cdot x_{jk}}}{\sqrt{\left({\displaystyle \sum _{k=1}^m{x}_{ik}^2}\right)\cdot \left({\displaystyle \sum _{k=1}^m{x}_{jk}^2}\right)}}$$

(20)

where x_ik and x_jk are the input and output parameters, and m stands for the number of datasets.

The importance of the parameters in the proposed RF–GWO–XGBoost model can be presented as CaO-Fly < SP dosage < NaOH < FA < CT < NaOH < Al₂O₃-Fly < SiO₂-Fly < CaO-GGBS < Al₂O₃-GGBS < Coarse < Na₂SiO₃ < GGBS < SiO₂-GGBS < Fine with sensitivity values of 0.609, 0.71, 0.813, 0.814, 0.822, 0.832, 0.884, 0.892, 0.916, 0.921, 0.922, 0.933, 0.938, 0.947, and 0.948. The findings presented in Figure 19 reveal that the variables Fine, SiO₂-GGBS, GGBS, Na₂SiO₃, Coarse, Al₂O₃-GGBS, and CaO-GGBS exert considerable influence over CSGePoCo, with Al₂O₃-Fly and SiO₂-Fly playing particularly significant roles. Notably, the variable CaO-Fly and SP dosage exhibit the least effect on CSGePoCo, and its exact application in predicting CSGePoCo remains indeterminate. Furthermore, the variables CaO-GGBS, Al₂O₃-GGBS, Coarse, Na₂SiO₃, GGBS, SiO₂-GGBS, and Fine demonstrate high sensitivity to CSGePoCo, especially CaO-GGBS and Al₂O₃-GGBS. These variables should be diligently considered and incorporated into the predictive modeling of CSGePoCo. Additionally, the variable CaO-Fly, while showing minimal impact, lacks precision in its role in CSGePoCo modeling.

In this step, for validation of the prediction results and to evaluate the performance of the developed models, a set of data points comprising ten unseen data points was employed as shown in

Table 10. Validation of the predictions using ten unseen data points.

No	Al2O3	CaO	GGBS	SiO2	Al2O3	CaO	Fine	Coarse	NaOH	Na2SiO3	SP Dosage	NaOH	T
1	26.53	4	126	34.06	20	32.6	810.6	966	60	150	168	8	60
2	26.53	4	126	34.06	20	32.6	810.6	966	66	165	168	8	60
3	26.53	4	126	34.06	20	32.6	810.6	966	72	180	168	8	60
4	26.53	4	135	34.06	20	32.6	760.5	972	57.9	144.6	180	8	60
5	26.53	4	135	34.06	20	32.6	760.5	972	64.3	160.7	180	8	60
6	26.53	4	135	34.06	20	32.6	760.5	972	70.7	176.8	180	8	60
7	26.53	4	135	34.06	20	32.6	760.5	972	77.1	192.9	180	8	60
8	26.53	4	144	34.06	20	32.6	774	1090.8	46.3	115.7	144	8	60
9	26.53	4	144	34.06	20	32.6	774	1090.8	51.4	128.6	144	8	60
10	26.53	4	144	34.06	20	32.6	774	1090.8	56.6	141.4	144	8	60
No	CS	RF	XGBoost	GWO–XGBoost	RF–GWO–XGBoost	Error of RF	Error of XGBoost	Error of GWO–XGBoost			Error of RF–GWO–XGBoost
1	43.5	42.75	40.29	43.31	41.69	0.75	3.21	0.19			1.81
2	31.24	35.35	32.79	31.21	32.95	4.11	1.55	0.03			1.71
3	26.89	23.52	27.23	27.26	25.01	3.37	0.34	0.37			1.88
4	38.63	37.08	41.33	40.62	40.81	1.55	2.7	1.99			2.18
5	44.49	41.92	41.51	43.01	42.76	2.57	2.98	1.48			1.73
6	35.2	33.92	32.1	37.79	35.79	1.28	3.1	2.59			0.59
7	29.46	34.32	26.71	28.3	28.72	4.86	2.75	1.16			0.74
8	55.57	52.23	54.65	57.41	53.16	3.34	0.92	1.84			2.41
9	57.37	58.41	53.93	53.73	54.56	1.04	3.44	3.64			2.81
10	53.39	49.02	49.8	50.36	53.09	4.37	3.59	3.03			0.3

.

6. Conclusions

This research addresses the pressing need for sustainable alternatives to traditional Portland cement production for landscape concrete by introducing a novel hybrid RF–GWO–XGBoost algorithm for anticipating the CSGePoCo. GePoCo presents challenges as an eco-friendly alternative due to its complex cementitious matrix and intricate mix design, necessitating accurate predictive models for optimizing its performance. Through the utilization of machine learning approaches, specifically the integration of random forest (RF), the gray wolf optimization (GWO) algorithm, and extreme gradient boosting (XGBoost), this study successfully developed the RF–GWO–XGBoost model. The stacking strategy, involving multiple RF models with diverse hyperparameters and subsequent optimization through the GWO algorithm, resulted in the superior RF–GWO–XGBoost model. Comparative analysis with stand-alone RF and XGBoost models, and a proposed GWO–XGBoost system, revealed the remarkable performance enhancement achieved by the proposed methodology. The RF–GWO–XGBoost model exhibited the highest accuracy and reliability, as indicated by the RMSE, MAE, R², and a²⁰ index values. This comprehensive evaluation demonstrated the model’s effectiveness in predicting GePoCo compressive strength, emphasizing the significant impact of certain variables, such as Fine, SiO₂-GGBS, GGBS, Na₂SiO₃, Coarse, Al₂O₃-GGBS, and CaO-GGBS. Importantly, this study highlighted the limited influence of the CaO-Fly variable on GePoCo, underlining its imprecise role in the modeling process. Overall, the findings of this research contribute to the advancement of predictive modeling for GePoCo and underscore the RF–GWO–XGBoost algorithm’s potential in addressing the intricate challenges associated with alternative and sustainable concrete production. This novel approach has practical implications for the construction industry, providing a reliable tool for optimizing geopolymer concrete formulations, thereby promoting environmentally conscious practices in the field of civil engineering.