Data-driven framework for prediction of mechanical properties of waste glass aggregates concrete

Abstract

This research presents a novel data-driven framework for predicting the mechanical properties of waste glass aggregate concrete using six advanced metaheuristic optimization algorithms: Bat Algorithm (Bat), Cuckoo Search Algorithm (Cuckoo), Elephant Herding Optimization (Elephant), Firefly Algorithm (Firefly), Rhinoceros Optimization Algorithm (Rhino), and Gray Wolf Optimizer (Wolf). The study evaluates these models based on their ability to predict compressive strength (Fc), tensile strength (Ft), density, and slump using key statistical performance indicators such as SSE, MAE, MSE, RMSE, accuracy, R², and KGE. Sensitivity analysis was conducted using Hoffman and Gardener’s method as well as the SHAP technique to determine the most influential parameter in the prediction process. Results indicate that the Firefly and Wolf algorithms exhibited the highest prediction accuracy across all four properties, with Wolf emerging as the overall best-performing model due to its superior generalization ability, lower error rates, and high correlation with experimental results. Among the input parameters, the water-to-binder ratio was identified as the most influential factor affecting the mechanical properties of waste glass aggregate concrete, as demonstrated by both sensitivity analysis methods. This highlights the critical role of optimal water content in achieving desirable strength and workability in sustainable concrete mixtures. The study’s novelty lies in the comparative assessment of multiple optimization algorithms applied to waste-based concrete, an approach that has not been extensively explored in previous research. Additionally, the integration of SHAP analysis for feature importance ranking provides an interpretable machine learning approach to concrete mix design, which enhances decision-making for engineers and researchers. The practical implications of this research extend to sustainable machine learning-based concrete design, where AI-driven optimization can help reduce the reliance on conventional trial-and-error methods. By utilizing waste glass aggregates, the study supports circular economy initiatives in construction, reducing environmental impact while maintaining structural performance. The proposed models can be implemented in real-world scenarios to optimize mix designs for large-scale applications, leading to cost-effective and eco-friendly construction materials. This research advances the field of smart construction by demonstrating the effectiveness of machine learning in sustainable material engineering, paving the way for future AI-assisted innovations in the industry.

Introduction

Waste glass aggregates in concrete offer a sustainable solution for construction by reducing environmental waste and enhancing material performance. Incorporating waste glass as a partial replacement for fine or coarse aggregates not only diverts non-biodegradable waste from landfills but also reduces the demand for natural resources such as sand and gravel. The chemical composition of glass, primarily silica, contributes to pozzolanic reactions when finely ground, enhancing the durability and long-term strength of concrete. One of the primary challenges in using waste glass in concrete is its potential alkali-silica reaction (ASR), which can cause expansion and cracking. However, proper processing, such as using finely ground glass powder or incorporating supplementary cementitious materials like fly ash and silica fume, mitigates ASR risks while improving concrete performance. Studies have shown that glass aggregates improve the workability of fresh concrete, enhance aesthetic appeal, and provide resistance to chloride penetration, making the material suitable for both structural and decorative applications. The sustainability aspect of waste glass concrete aligns with circular economy principles by transforming waste into a valuable resource. Using recycled glass reduces carbon footprints associated with cement production and aggregate mining, contributing to lower greenhouse gas emissions. Additionally, waste glass concrete demonstrates improved thermal insulation properties, making it a viable option for energy-efficient buildings. With ongoing research and optimized mix designs, the use of waste glass aggregates in concrete continues to advance, promoting greener construction practices and resource conservation while maintaining structural integrity and durability.

Applying advanced machine learning techniques to predict the mechanical behavior of waste glass aggregate concrete presents a data-driven framework that enhances sustainability and performance optimization in construction. Traditional empirical approaches rely on extensive experimental testing, which can be time-consuming and resource-intensive. Machine learning models offer a powerful alternative by learning complex relationships between input variables and predicting key mechanical properties such as compressive strength, tensile strength, and durability. By utilizing large datasets from experimental studies and literature, machine learning algorithms can identify hidden patterns and nonlinear correlations between waste glass proportions, curing conditions, mix composition, and mechanical performance. Feature selection methods ensure that critical variables, including water-to-cement ratio, particle size distribution, and pozzolanic reactivity of the glass aggregates, are optimally weighted in predictive modeling. Hyperparameter tuning further enhances model accuracy by refining learning rates, kernel functions, and tree depth, allowing the framework to provide reliable predictions across diverse mix designs. A robust validation strategy, incorporating k-fold cross-validation and external datasets, ensures model generalization and prevents overfitting. Sensitivity analysis, such as the Hoffman-Gardener method, can be applied to quantify the influence of individual parameters on mechanical behavior, guiding the optimization of mix proportions for maximum strength and durability. Furthermore, integrating explainable AI techniques enhances model transparency, enabling engineers to interpret results and make data-driven decisions in designing sustainable concrete with waste glass aggregates. This predictive framework not only facilitates cost-effective and rapid material characterization but also supports sustainability by optimizing waste glass utilization in concrete production. It enables the construction industry to reduce reliance on virgin aggregates, lower carbon footprints, and promote circular economy practices. The application of machine learning ensures continuous improvement in concrete mix designs, leading to enhanced mechanical performance, durability, and environmental benefits, making it a transformative approach for sustainable infrastructure development.

Aim and specific objectives

The aim of this research is to develop a data-driven predictive framework for evaluating the mechanical properties of waste glass aggregates concrete using six metaheuristic machine learning models optimized through distinct nature-inspired algorithms within the Decision Table modeling environment. This study seeks to achieve the following objectives: To compile and preprocess a comprehensive experimental database of concrete mixtures incorporating waste glass aggregates, including key input variables influencing mechanical behavior. To apply the Decision Table (DT) algorithm as a baseline model for predicting mechanical properties such as compressive and tensile strength, while optimizing its performance through six distinct metaheuristic algorithms: Bat, Cuckoo, Elephant, Firefly, Rhino, and GrayWolf. To implement and compare the predictive accuracy, generalization ability, and robustness of each optimized DT model using k-fold cross-validation and statistical performance metrics within the Weka Data Mining software (version 3.8.6). To analyze the sensitivity and relative importance of input features through appropriate techniques to identify critical parameters governing the mechanical performance of waste glass concrete. To explore the interpretability of the models and provide actionable insights for optimizing mix designs that balance strength, durability, and sustainability. Ultimately, the research aims to demonstrate the potential of advanced machine learning approaches to support efficient, eco-friendly, and cost-effective design strategies for sustainable concrete production.

Review of relevant literatures

Concrete, an essential element of contemporary infrastructure, confronts an impending crisis: the exhaustion of natural sand, a crucial constituent¹. The unsustainable demand for sand, propelled by swift urbanization and population expansion, results in adverse environmental effects, such as habitat damage and riverbed erosion. The manufacturing of cement, another essential component, considerably adds to global carbon emissions. Researchers are investigating sustainable alternatives to traditional concrete components to address these difficulties².

Anand et al.³ investigated the utilization of zeolite, ground granulated blast-furnace slag, and construction and demolition debris as partial substitutes for sand in concrete mix ratios. The ideal mix ratio, Mix Batch M4, attained elevated compressive strength, flexural strength, split tensile strength, and diminished water absorption. The research employed sophisticated machine learning algorithms to enhance mix designs, attaining elevated predictive accuracy. The findings provide a route to sustainable concrete solutions that diminish environmental impact, enhance resource efficiency, and advocate for circular economy principles, in accordance with global sustainability objectives in the building sector.

Also, Abbas and Khan⁴ examined the application of machine learning (ML) within the construction sector, particularly in predicting the compressive strength of steel-fiber-reinforced concrete (SFRC). The study used the extra gradient (XG) boosting algorithm to develop a thorough methodology, utilizing a database of 43 publications and 420 entries. The research employs practical testing and partial dependence plots to elucidate the correlations between input parameters and compressive strength. The model is both advanced and precise, achieving a mean target-prediction ratio of 99%. The research seeks to enhance prediction capacities, optimize mix designs, stimulate innovation, and meet industrial requirements.

Qin and Kaewunruen⁵ addressed this deficiency by employing robust models to forecast and assess the structural and sustainability characteristics of high-strength fibre-reinforced concrete beams. Three innovative deep learning models (ANN, BNN, and Xgboost) are developed for the design and optimization of the shear capacity of high-strength fibre-reinforced concrete beams. The models offer more extensive insights into the design and production of high-strength steel fibre-reinforced concrete structures in an eco-friendly manner. The Bayesian neural network (BNN) model demonstrates exceptional predictive accuracy, exhibiting optimal performance in shear strength, flexural capacity, shear stiffness, carbon emissions, and price forecasting.

Other study, Yao and Hong⁶ examined studies on recycled aggregate concrete (RAC) published from 2000 to 2023, emphasizing its environmental advantages. The survey indicates that more than 80% of publications published post-2017 demonstrate an increasing interest in sustainable construction. Prominent trends encompass the enhancement of RAC’s mechanical characteristics, microstructural examination, and pioneering manufacturing methodologies. Nonetheless, obstacles persist in domains such as nanoparticle integration, bio mineralization, carbon capture, and three-dimensional printing technologies. RAC possesses the capacity to advance sustainable construction methodologies.

Karabulut⁷ examined the flexural performance, fracture formation patterns, and failure causes of concrete beams reinforced with glass fiber-reinforced polymer (GFRP) bars, considering different concrete compressive strengths. Nine reinforced concrete beams were subjected to three-point bending tests. The research included machine learning prediction models, with the Ada Boost Regressor and Gradient Boosting Regressor yielding the highest accuracy in predictions. The results indicated distinct failure mechanisms, with reinforced concrete beams of differing compressive strengths generally exhibiting a singular prominent crack. The study emphasizes the benefits of GFRP bar strengthening, such as the elimination of shear cracks and the mitigation of abrupt failure during bending.

Sun et al.⁸ examined the flexural strength (FS) and alkali-silica reaction (ASR) expansion of WG concrete by multiple methodologies. The findings indicated that mortar with 30% WG powder was ideal for enhancing FS and reducing ASR growth. A random forest model was developed with hyper parameters optimized using beetle antennae search (BAS) to forecast FS and ASR expansion. A substantial database was created from experimental findings, demonstrating strong correlation coefficients for both FS and ASR data sets. The research identified particle granularity and WG content as the most sensitive variables affecting FS and expansion.

In addition, Hussain et al.⁹ presented an optimized approach for the mix design of lightweight aggregate concrete utilizing machine learning techniques. Five machine learning algorithms were examined: support vector machine (SVM), artificial neural network (ANN), decision tree (DT), Gaussian process regression (GPR), and extreme gradient boosting (XGBoost). A total of 420 data points were gathered from 43 published academic papers. The models’ performance was assessed using statistical performance metrics. The GPR model surpassed the other four models, achieving an R2 value of 0.99, an RMSE of 1.34, an MSE of 1.79, and an MAE of 0.69. These streamlined procedures can facilitate lightweight aggregate concrete design without the need for considerable experimentation.

Safhi¹⁰ provided a dataset of approximately 2500 self-consolidating concrete (SCC) combinations, sourced from 176 references. The dataset has undergone a meticulous curation process to remove feature redundancy and transcriptional errors. This curated dataset is prepared for sophisticated data-driven research in the SCC research topic. It functions as a fundamental resource for the comprehensive characterization of SCC properties and a standard for performance evaluation across various formulations. The dataset provides insights into the ecological advantages of substituting traditional Portland concrete with SCC alternatives and supports sustainable construction methods.

Another, Rehman et al.¹¹ investigated the application of artificial intelligence (AI) in mix composition for 3D concrete printing (3DCP). The objective is to enhance the prediction efficacy of machine learning models through the application of data augmentation methods such as deep generative adversarial networks (DGAN) and bootstrap resampling (BR). The research indicated that models trained on BR-augmented data exhibited superior accuracy compared to those trained on DGAN-augmented data. The BR-trained XGBoost model had the highest R² scores for compressive strength, printed compressive strength direction, and slump flow. This approach can accurately forecast mix design for printable concrete, maximizing its potential in the building sector.

Yang and Liu¹² addressed the absence of a universally recognized mechanics-based estimation model for the shear performance of Fiber-Reinforced Polymer (FRP)-reinforced concrete beams. The authors examine current shear design regulations and evaluate four representative machine learning (ML) models. They evaluate the precision of codified approaches and machine learning models utilizing a comprehensive database of FRP-reinforced concrete beams featuring rectangular cross sections. Features selected by artificial means are integrated into the machine learning models to enhance model validity. Bayesian optimization is employed to optimize hyper parameters. The superior machine learning model, XGBoost, yields enhanced predictive accuracy, evidenced by an elevated R² and diminished MAE and RMSE. Machine learning methodologies possess significant promise for informing the shear design of FRP-reinforced concrete. Table 1 systematically organizes the reviewed literature, highlighting the focus of each study, the methodologies used, and key findings relevant to sustainable concrete and machine learning applications.

Table 1 Summary of previous research contributions relevant to this study.

Furthermore, more recent research efforts have contributed to the development of concrete prediction models towards sustainable construction¹³. focuses on optimizing sustainable concrete containing fly ash, considering both mechanical and environmental factors. It is relevant because waste glass aggregates (WGA) are often used as a sustainable material, and optimizing mechanical properties is a key aspect of data-driven modeling¹⁴. uses artificial neural networks (ANNs) to evaluate the compressive strength of recycled aggregate concrete. Since WGA concrete is another type of sustainable concrete, the methodology in this study can be applied to predict its mechanical properties using machine learning¹⁵. assesses the global warming potential of fly ash-silica fume concrete while optimizing compressive strength. The life cycle assessment approach can be useful in evaluating the environmental benefits of WGA concrete¹⁶. Similar to¹⁵, this study optimizes green concrete containing fly ash and rice husk ash based on hydro-mechanical properties. The methods used for optimizing mechanical properties may be adaptable to WGA concrete¹⁷. develops an innovative predictive model for the flexural strength of recycled aggregate concrete. Since flexural strength is an essential mechanical property, its modeling approach could be beneficial for WGA concrete predictions¹⁸. applies AI-based mix design optimization for fly ash-admixed concrete, considering mechanical and environmental impacts. The AI-driven framework can be extended to WGA concrete to enhance predictive accuracy¹⁹. develops a GRG-optimized response surface model to optimize concrete compressive strength based on industrial waste materials. WGA is an industrial waste precursor, making this research highly relevant to predictive modeling for WGA concrete²⁰. investigates the effects of fly ash and blast furnace slag on high-performance concrete. Understanding the impact of supplementary cementitious materials can support the optimization of WGA concrete properties²¹. focuses on AI models for predicting the stiffness and deformation of geopolymer-treated soil, which is different from WGA concrete but provides insights into AI applications in material property prediction²². examines heat and mass transfer in different concrete types, including self-compacting and geopolymer concrete. This thermal analysis could be extended to WGA concrete to study its thermal performance²³. applies machine learning to predict the unconfined compressive strength of geopolymer cement-treated granular sand. While not directly related, the methodology could be adapted for WGA concrete strength prediction²⁴. reviews the durability aspects of basalt fiber-reinforced concrete. Understanding durability factors could help assess the long-term performance of WGA concrete²⁵. applies multiple AI models to predict the compressive strength of recycled aggregate concrete. The techniques used here can be directly applied to WGA concrete²⁶. studies the influence of alkali molarity on the strength of geopolymer concrete using machine learning. The AI techniques used can be adapted to predict the strength of WGA-based geopolymer concrete²⁷. uses machine learning classification to predict the flexural strength of metakaolin-admixed concrete. Similar methodologies could be applied to WGA concrete²⁸. applies ensemble ML and symbolic regression techniques to predict the splitting strength of metakaolin-admixed concrete. These advanced ML techniques could enhance the accuracy of WGA concrete property predictions²⁹. discusses data utilization and partitioning in machine learning for civil engineering applications. This knowledge is crucial for effectively applying AI-based frameworks in WGA concrete property predictions.

In summary, the references mainly contribute to understanding sustainable concrete materials, AI-based predictive modeling, and optimization techniques. Many of these studies use machine learning and advanced data-driven approaches that could be adapted for predicting the mechanical properties of waste glass aggregate concrete. The listed references contribute significantly to the application of machine learning in forecasting and designing concrete production, particularly in the context of sustainable construction incorporating waste glass aggregates (WGA). Several studies, such as those in references^{14,17,18,19,25}, and²⁸, demonstrate the effectiveness of artificial intelligence (AI) and machine learning (ML) techniques in predicting key mechanical properties of concrete, including compressive and flexural strength. These approaches minimize reliance on experimental testing, optimizing mix design through predictive modeling. References^13,15,16, and¹⁹ emphasize optimization strategies for sustainable concrete by integrating supplementary cementitious materials such as fly ash, silica fume, and industrial waste precursors. The methodologies used in these studies, including multi-objective optimization, response surface modeling, and life cycle assessment, can be adapted to optimize WGA concrete in terms of strength, durability, and environmental impact. In addition, references^21,22, and²⁶ explore ML applications beyond mechanical properties, investigating aspects such as heat and mass transfer, curing regimes, and subgrade stiffness prediction. These insights can be leveraged to enhance the thermal efficiency and structural resilience of WGA concrete. References^{23] and [27} illustrate how ML techniques can be applied to predict the behavior of geopolymer-based materials and other sustainable construction applications, showcasing the adaptability of AI-driven approaches to different concrete formulations, including those incorporating WGA. Lastly, reference²⁹ highlights the importance of data partitioning and utilization in civil engineering ML applications, ensuring that AI models used for WGA concrete forecasting are trained effectively for improved prediction accuracy. Overall, these studies provide a foundation for integrating AI and ML techniques into WGA concrete production, enabling optimized mix designs that enhance mechanical performance while reducing environmental impact. Table 2 shows the summary of most recent research contributions relevant to this study.

Table 2 Summary of most recent research contributions relevant to this study.

Research gap and innovation statement

Previous research on sustainable concrete and machine learning applications has primarily focused on utilizing traditional machine learning techniques such as artificial neural networks (ANN), support vector machines (SVM), random forest (RF), XGBoost, Gaussian process regression (GPR), and deep learning models to predict the mechanical properties of concrete incorporating alternative materials like recycled aggregates, waste marble powder, and supplementary cementitious materials. While these approaches have demonstrated improved accuracy in strength predictions, their optimization processes largely depend on standard statistical techniques, hyperparameter tuning, or heuristic algorithms such as genetic algorithms and particle swarm optimization. However, they often fail to effectively capture the complex, nonlinear interactions between different mix constituents, leading to suboptimal mix designs and limitations in practical applications. The present research, titled “Data-driven framework prediction of mechanical properties of waste glass aggregates concrete,” introduces a novel approach by integrating advanced bio-inspired optimization algorithms, including the Bat Research Algorithm (Bat), Cuckoo Research Algorithm (Cuckoo), Elephant Research Algorithm (Elephant), Firefly Research Algorithm (FireFly), Rhinoceros Research Algorithm (Rhino), and Gray Wolf Research Algorithm (Wolf). These nature-inspired metaheuristic algorithms enhance the accuracy and efficiency of machine learning models by improving feature selection, optimizing hyperparameters, and refining model predictions. Unlike previous studies that relied on traditional optimization methods, this research leverages swarm intelligence and evolutionary strategies to navigate high-dimensional solution spaces, ensuring better convergence and adaptability to the inherent variability of waste glass aggregate concrete. This innovative methodology enables a more precise and adaptive prediction framework for the mechanical behavior of waste glass aggregates in concrete, leading to improved mix design strategies, enhanced structural performance, and a more sustainable approach to concrete production. By systematically applying these bio-inspired optimization techniques, the study addresses the existing research gap in optimizing machine learning models for sustainable construction materials, contributing to more efficient resource utilization and environmental sustainability in the construction industry.

Methodology

Data collection and preliminary analysis

The database utilized in this research paper was collected from an open data deposited in a published literature³⁰. The collected 104 records were divided into training set (80 records = 75%) and validation set (24 records = 25%)²⁹. Table 3 summarizes their statistical characteristics of the concrete which has a variable strength between 12 MPa and 71 MPa produced from partial and total replacement of aggregate with waste glass aggregate from 0 to 100%. The violin plots in Fig. 1 provide insights into the distribution and density of each parameter in the dataset. The cement (C) distribution is centered around 400 kg/m³ with a moderately spread distribution. Water (W) shows a bimodal distribution with peaks around 140 and 200 kg/m³, suggesting two common mixing proportions. Plasticizer (PL) has a skewed distribution with most values concentrated at lower ranges. Fine aggregate (FAg) and coarse aggregate (CAg) exhibit relatively symmetrical distributions, but CAg has a wider spread, indicating higher variability. Fine glass (FGL) has a skewed distribution with a concentration of values at lower ranges. Coarse glass (CGL) has a distinctive peak at a low range, suggesting limited data points or a particular mix composition. Compressive strength (Fc) shows a well-spread distribution with a peak around 40 MPa, indicating a common mix strength. Tensile strength (Ft) has a more concentrated spread between 3 and 6 MPa, implying that most mixes fall within this range. Density is centered around 2400 kg/m³, corresponding to typical concrete densities. Slump has a multimodal distribution, showing varying consistency levels in the concrete mixes. Overall, these distributions highlight the variability in mix design parameters, with some showing distinct peaks and others having a broader spread, suggesting diverse formulations and mechanical performance variations.

Finally, Fig. 2 shows Pearson correlation matrix, histograms, and the relations between variables. These correlation matrix and scatter plot chart provide insights into the relationships among different concrete mix parameters. Correlation analysis shows that compressive strength (Fc) has a strong positive correlation with cement content (C, 0.76) and tensile strength (Ft, 0.87), indicating that higher cement content significantly improves mechanical performance. Similarly, tensile strength (Ft) strongly correlates with cement (0.64) and plasticizer (PL, 0.63), suggesting that these factors enhance concrete strength. Water content (W) shows weak correlations with most variables, except for a moderate correlation with density (0.48), indicating its influence on the overall mix composition. Fine glass (FGL) and coarse glass (CGL) exhibit strong negative correlations (-0.88 and − 0.89) with fine aggregate (FAg) and coarse aggregate (CAg), respectively, confirming that glass waste is replacing natural aggregates in the mixes. Slump has a high correlation with plasticizer (0.87), showing that plasticizer dosage significantly affects concrete workability. The weak correlation between slump and other parameters suggests that multiple factors influence consistency beyond just water content. The distribution plots along the diagonal indicate variations in data spread. Cement and water content exhibit relatively normal distributions, while fine and coarse glass aggregates show skewed distributions, possibly due to limited replacement levels. The scatter plots reveal linear and non-linear relationships, particularly the strong linear trends between Fc and C, Ft and C, and slump with PL. Overall, the chart highlights the key influencing parameters on concrete properties and confirms that machine learning models can effectively predict performance by leveraging these correlations.

Fig. 1

Violin distribution for each input.

Table 3 Statistical analysis of collected databases.

Fig. 2

Correlation, distribution and interpreting chart.

Plan of research work

Six different metaheuristic machine learning (MML) models were used to predict the mechanical properties of the concrete using the collected database. “Decision Table” (DT) technique was used to develop all the models. However, for each model, a different optimization technique was used to optimize the hyper-parameters of the (DT) model. These optimization techniques are “Bat research algorithm (Bat)”, “Cuckoo research algorithm (Cuckoo), “Elephant research algorithm (Elephant), “FireFly research algorithm (FireFly)”, “Rhinoceros research algorithm (Rhino)” and “GrayWolf research algorithm” (Wolf). The choice to employ Bat Algorithm (Bat), Cuckoo Search Algorithm (Cuckoo), Elephant Herding Optimization (Elephant), Firefly Algorithm (Firefly), Rhinoceros Optimization Algorithm (Rhino), and Gray Wolf Optimizer (Wolf) in the modeling process is grounded in their proven ability to navigate complex, high-dimensional optimization problems, such as those encountered in predicting concrete properties. These metaheuristic algorithms are nature-inspired and have been increasingly adopted in civil engineering due to their robustness, adaptability, and minimal reliance on gradient information, which is often unavailable or unreliable in empirical concrete datasets. The Bat Algorithm is inspired by the echolocation behavior of bats and is favored for its balance between exploration and exploitation during the search process. Its frequency-tuning mechanism helps in quickly converging towards optimal solutions in non-linear regression problems where the relationship between input variables (such as mix composition, curing conditions, etc.) and target concrete properties is highly complex. The Cuckoo Search Algorithm, based on the brood parasitism of certain cuckoo species, excels in global optimization and has been noted for its superior performance in avoiding local optima. It uses Lévy flights to explore the solution space broadly, which is crucial when the model landscape has multiple peaks and valleys, as is typical with material behavior predictions. The Elephant Herding Optimization, mimicking the social behavior of elephant clans, is particularly effective in handling multi-objective problems and group-based learning strategies. It allows for structured subpopulation updates, which can simulate different concrete mix strategies evolving in parallel, improving the diversity and accuracy of predictions. The Firefly Algorithm, inspired by the flashing patterns of fireflies, is well-suited for multi-modal function optimization. Its attractiveness and random movement parameters make it effective for fine-tuning model parameters, especially in data-driven applications where interaction effects among variables are strong and non-linear. The Rhinoceros Optimization Algorithm, although relatively novel, imitates the aggressive but directed movement of rhinos toward a target and has been designed to address convergence stagnation. It enhances local search intensification, which is beneficial when refining the parameters of predictive models after a rough global search. Lastly, the Gray Wolf Optimizer, modeled after the leadership hierarchy and hunting behavior of gray wolves, offers a compelling balance of global search (via alpha, beta, delta, and omega wolves) and local exploitation. Its ability to maintain dynamic leadership roles helps in avoiding premature convergence, thereby yielding more generalized and robust concrete property predictions. Altogether, the integration of these algorithms creates a hybrid modeling environment where diverse optimization strategies can be tested and compared. Each algorithm contributes unique strengths in searching, converging, and escaping local optima, making them collectively suitable for the inherently uncertain and non-linear nature of concrete behavior modeling. All models were created using “Weka Data Mining” software version 3.8.6. Weka Data Mining software version 3.8.6 is a powerful open-source machine learning tool developed by the University of Waikato, designed for data mining, predictive modeling, and data analysis. This version provides a comprehensive suite of machine learning algorithms for classification, regression, clustering, association rule mining, and feature selection. It includes a graphical user interface (GUI) that enables users to easily preprocess datasets, visualize data distributions, and apply machine learning techniques without requiring extensive programming knowledge. Version 3.8.6 introduces performance improvements, bug fixes, and updates to existing algorithms to enhance efficiency and usability. It supports various data formats, including ARFF, CSV, and databases via JDBC, making it versatile for different data sources. The software includes tools such as the Explorer for interactive data analysis, the Experimenter for algorithm comparison, and the Knowledge Flow for visual workflow design. Additionally, it provides access to deep learning frameworks and integrates with Python through WekaDeeplearning4j, expanding its capabilities beyond traditional machine learning. Weka 3.8.6 is widely used in academic research, business analytics, and artificial intelligence applications due to its extensive documentation, ease of use, and flexibility. It supports scripting and automation through Java and command-line interfaces, enabling advanced users to customize and extend its functionalities. With its robust set of machine learning tools and continuous updates, Weka remains a valuable resource for researchers, students, and professionals in the field of data science. The accuracies of developed models were evaluated by comparing performance indices such as SSE, MAE, MSE, RMSE, Error (%), Accuracy (%) and R², R, WI, NSE, KGE and SMAPE between predicted and calculated parameters values.

Theoretical framework

Bat algorithm optimized decision table (Bat)

The Bat Algorithm Optimized Decision Table (Bat) is a decision-making framework that integrates the Bat Algorithm, a metaheuristic optimization technique inspired by the echolocation behavior of bats, with decision tables to enhance decision accuracy and efficiency³¹. The Bat Algorithm is particularly effective in solving complex optimization problems due to its ability to balance exploration and exploitation. By incorporating it into decision tables, the process of rule-based decision-making can be refined to ensure optimal outcomes. In this approach, decision tables, which systematically represent rules and conditions, serve as the foundation for structured decision-making. The Bat Algorithm is employed to optimize rule selection, threshold values, or parameter weights, ensuring that the decision table adapts dynamically to changing scenarios. This optimization enhances the decision table’s ability to handle uncertainty, improve classification accuracy, and reduce redundancy³¹. The Bat Algorithm operates by simulating bat echolocation to iteratively search for optimal solutions in the decision table space. It adjusts decision rules by fine-tuning frequency, loudness, and pulse emission rates, allowing it to converge towards the most effective decision configurations. As a result, the Bat Algorithm Optimized Decision Table is particularly useful in fields such as machine learning, expert systems, and real-time decision support applications where rapid and accurate decisions are crucial. This hybrid approach enables decision tables to evolve over time, incorporating feedback from data and environmental changes, leading to better adaptability. Additionally, the Bat Algorithm helps in reducing computational complexity by discarding less relevant rules while prioritizing high-impact decision criteria. By leveraging the strengths of the Bat Algorithm, the decision table becomes a more powerful and intelligent tool for decision-making in various domains, including healthcare, finance, and industrial automation. The Bat Algorithm is inspired by the echolocation behavior of bats, which use sound waves to locate prey and navigate their environment. Bats emit sound pulses and adjust their frequency, loudness, and pulse rate to optimize their search³². This algorithm mimics this behavior by balancing exploration (global search) and exploitation (local search) to find optimal solutions³¹. The position of a bar x_i at iteration t + 1 is updated as:

$$\:{x}_{i}^{t+1}={x}_{i}^{t}+{v}_{i}^{t+1}$$

(1)

where $\:{v}_{i}^{t+1}$ is the velocity of the bat. The velocity is updated as

$$\:{v}_{i}^{t+1}={v}_{i}^{t}+\left({x}_{i}^{t}-{x}_{*}\right).{f}_{i}$$

(2)

where $\:{x}_{*}$ is the current global best solution, and $\:{f}_{i}$ is the frequency of the sound pulse. The frequency $\:{f}_{i}$is randomly generated within a range:

$$\:{f}_{i}={f}_{min}+\left({f}_{max}-{f}_{min}\right).\beta\:$$

(3)

where $\:\beta \: \in \left\lfloor {0,\:\:\:1} \right\rfloor$ is a random number. The loudness A_i and pulse rate r_i are updated iteratively to control exploration and exploitation.

Cuckooo algorithm optimized decision table (Cuckoo)

The Cuckoo Algorithm Optimized Decision Table (Cuckoo) is an advanced decision-making framework that integrates the Cuckoo Search Algorithm, a powerful nature-inspired metaheuristic optimization technique, with decision tables to enhance decision accuracy and efficiency³². The Cuckoo Search Algorithm, inspired by the brood parasitism of certain cuckoo species, is known for its ability to efficiently explore and exploit the search space, making it well-suited for optimizing rule-based decision-making processes. In this approach, decision tables serve as structured repositories of decision rules, while the Cuckoo Search Algorithm optimizes rule selection, parameter tuning, and threshold determination. By leveraging Lévy flight-based random walks, the algorithm ensures effective exploration of decision alternatives, identifying the most relevant and impactful rules while minimizing redundancy. This optimization enhances decision table adaptability, allowing it to dynamically adjust to changing conditions and new data inputs³². The Cuckoo Algorithm operates by generating and evaluating potential decision table configurations, discarding suboptimal rules, and refining decision structures through an iterative process. Its ability to escape local optima ensures that the decision table remains robust and effective across diverse application domains. As a result, the Cuckoo Algorithm Optimized Decision Table is particularly valuable in fields such as machine learning, expert systems, real-time analytics, and intelligent automation, where high accuracy and adaptability are essential. By continuously evolving decision rules through the principles of cuckoo search, this hybrid approach enhances decision-making precision, reduces computational complexity, and ensures that the decision table remains efficient even in complex and dynamic environments. The synergy between the Cuckoo Search Algorithm and decision tables makes this framework a powerful tool for optimizing rule-based systems in areas such as healthcare, finance, cybersecurity, and industrial decision support systems. The Cuckoo Search Algorithm is inspired by the brood parasitism of cuckoo birds, where cuckoos lay their eggs in the nests of other birds^32,33. If the host bird discovers the foreign egg, it may abandon the nest. This behavior is modeled as a combination of Lévy flights (long jumps) and random walks to explore the search space efficiently. The new solution $\:{x}_{i}^{t+1}$ is generated using Lévy flights:

$$\:x_{i}^{{t + 1}} = x_{i}^{t} + \propto \: \oplus L{\text{\'e vy}}\left( {\lambda \:} \right)$$

(4)

where $\:\propto\:$ is a step size, and $\:L\text{\'e}\text{v}\text{y}\left({\uplambda\:}\right)$ is a random walk based on the $\:L\text{\'e}\text{v}\text{y}$ distribution. The step length is drawn from;

$$\:L\text{\'e}\text{v}\text{y}\left({\uplambda\:}\right)\sim\text{u}={t}^{-\lambda\:},\:\:\:\:\:\:1<\lambda\:\le\:3$$

(5)

A fraction P_a of the worst solution is replaced by new random solutions.

Elephant algorithm optimized decision table (Elephant)

The Elephant Algorithm Optimized Decision Table (Elephant) is a decision-making framework that integrates the Elephant Herding Optimization (EHO) algorithm with decision tables to enhance efficiency, accuracy, and adaptability. The EHO algorithm, inspired by the social behavior of elephant herds, is a nature-inspired metaheuristic optimization method known for its strong exploration and exploitation capabilities³³. By incorporating this algorithm into decision tables, the decision-making process becomes more structured, adaptive, and optimized for real-world applications. In this approach, decision tables serve as structured repositories of decision rules, while the Elephant Herding Optimization algorithm optimizes rule selection, parameter tuning, and threshold determination. The algorithm mimics the natural social behavior of elephants, where clans and matriarchs guide the evolution of solutions, ensuring that optimal decision rules are retained and refined over successive iterations. This results in a highly adaptive decision table that can dynamically respond to changes in data patterns, external conditions, and evolving requirements. The Elephant Algorithm functions by dividing the decision space into multiple clans, where each clan explores different rule configurations. The matriarch operator refines decision rules by discarding less effective ones and promoting high-impact rules, ensuring that the decision table remains both diverse and efficient. By balancing exploration (global search for optimal rules) and exploitation (refining selected rules), the algorithm enhances the decision-making process and prevents premature convergence to suboptimal solutions. As a result, the Elephant Algorithm Optimized Decision Table is particularly useful in domains requiring intelligent and adaptive decision-making, including healthcare, financial modeling, industrial automation, and machine learning. Its ability to optimize decision rules continuously ensures that the decision table remains robust and efficient, even in complex and dynamic environments. By leveraging the strengths of the Elephant Herding Optimization algorithm, the decision table becomes a powerful tool for improving accuracy, reducing redundancy, and enhancing overall decision-making efficiency.

The Elephant Herding Optimization algorithm is inspired by the herding behavior of elephants, where elephants form clans and follow a matriarch (leader)^33,34. Male elephants, on the other hand, leave the clan to live independently. This behavior is modeled to balance exploration (separation) and exploitation (clan cohesion). The position of an elephant x_i in a clan is updated as:

$$\:{x}_{i}^{t+1}={x}_{i}^{t}+\propto\:*\left({x}_{best}-{x}_{i}^{t}\right)*r$$

(6)

where $\:{x}_{best}$ is the best solution in the clan, $\:\propto\:$ is a scaling factor, and r is a random number. So, Male elephants leave the clan, and their positions are updated as:

$$\:{x}_{worst}^{t+1}={x}_{min}+\left({x}_{max}-{x}_{min}\right)*r$$

(7)

where $\:{x}_{min}$ and $\:{x}_{max}$ are the bounds of the search space.

Firefly algorithm optimized decision table (Firefly)

The Firefly Algorithm Optimized Decision Table (Firefly) is an advanced decision-making framework that integrates the Firefly Algorithm, a bio-inspired metaheuristic optimization technique, with decision tables to enhance rule selection, adaptability, and overall decision accuracy. The Firefly Algorithm, inspired by the flashing behavior of fireflies, is highly effective in solving optimization problems due to its ability to balance exploration and exploitation by dynamically adjusting decision parameters based on attractiveness and distance³⁴. By incorporating this algorithm into decision tables, rule-based decision-making becomes more efficient, adaptive, and capable of handling complex datasets. In this approach, decision tables serve as structured frameworks for defining conditions and corresponding decisions, while the Firefly Algorithm optimizes rule selection by simulating the behavior of fireflies that move toward more attractive solutions. The brightness of a firefly represents the quality of a decision rule, and fireflies with higher brightness guide others toward optimal decision configurations. This iterative process refines decision rules, eliminates redundancies, and ensures that the decision table adapts to new data and changing scenarios³⁵. The Firefly Algorithm operates by dynamically adjusting decision table parameters, where each firefly represents a potential rule configuration. More effective rules attract other fireflies, while less effective rules fade and are replaced. This self-adaptive behavior allows the decision table to continuously evolve, enhancing decision accuracy and robustness. The algorithm’s ability to avoid local optima and explore a wide solution space makes it particularly valuable for optimizing complex decision-making systems. The Firefly Algorithm Optimized Decision Table is highly applicable in areas such as machine learning, financial modeling, healthcare diagnostics, and industrial automation, where precise and adaptive decision-making is crucial. By leveraging the strengths of the Firefly Algorithm, decision tables become more efficient, intelligent, and capable of handling uncertainty, ultimately improving the quality and reliability of decisions in dynamic environments. The Firefly Algorithm is inspired by the flashing behavior of fireflies, which use bioluminescence to attract mates and communicate^34,35,36. The brightness of a firefly corresponds to the quality of a solution, and fireflies are attracted to brighter ones. This behavior is modeled to balance exploration and exploitation⁷. The attractiveness β of a firefly is defined as:

$$\:\beta\:\left(r\right)={\beta\:}_{0}*{e}^{-\gamma\:{r}^{2}}$$

(8)

where $\:{\beta\:}_{0}$ is the initial attractiveness, γ is the light absorption coefficient, and r is the distance between two fireflies. The distance r_ij between fireflies I and j is:

$$\:r_{{ij}} = \left\| {x_{i} - x_{j} } \right\|$$

(9)

The position of Firefly I is updated as:

$$\:{x}_{i}^{t+1}={x}_{i}^{t}+\beta\:\left({r}_{ij}\right)*\left({x}_{j}^{t}-{x}_{i}^{t}\right)+\propto\:*\in\:$$

(10)

where $\:\propto\:$ is a randomization parameter, and $\:\in\:$ is a random vector

Rhinoceros algorithm optimized decision table (Rhino)

The Rhinoceros Algorithm Optimized Decision Table (Rhino) is a decision-making framework that integrates the Rhinoceros Search Algorithm (RSA), a nature-inspired optimization technique, with decision tables to enhance rule selection, adaptability, and overall decision efficiency. The RSA, modeled after the movement and foraging behavior of rhinoceroses, focuses on balancing exploration and exploitation to identify optimal decision configurations³⁵. By embedding this algorithm into decision tables, the decision-making process becomes more structured, adaptive, and capable of handling complex problem spaces. In this approach, decision tables act as structured repositories of rules and conditions, while the Rhinoceros Algorithm optimizes rule selection, threshold values, and decision weights to improve accuracy and efficiency. The algorithm simulates the systematic yet aggressive search behavior of rhinoceroses, where individuals explore different regions of the solution space while collectively converging toward optimal decision rules. This process ensures that effective rules are prioritized while redundant or less impactful rules are discarded, leading to an optimized and refined decision table. The Rhinoceros Algorithm operates by employing a dynamic search mechanism, where decision configurations evolve based on iterative adjustments inspired by the strategic movements of rhinoceroses in their environment. This includes aggressive searches for promising rules, adaptive refinement of selected decisions, and an avoidance mechanism to prevent premature convergence to suboptimal solutions. By maintaining a balance between diversification and intensification, the algorithm ensures that the decision table continuously adapts to new data, improving its reliability and effectiveness over time. The Rhinoceros Algorithm Optimized Decision Table is particularly valuable in fields such as intelligent automation, financial modeling, healthcare diagnostics, and industrial decision support, where high precision and adaptability are required. By leveraging the RSA’s robust search mechanisms, the decision table becomes a powerful tool for improving decision accuracy, reducing redundancy, and ensuring efficient decision-making even in dynamic and complex environments. The Rhinoceros Search Algorithm is inspired by the territorial behavior of rhinoceroses, which mark and defend their territory^35,36,37,38. Rhinoceroses move toward the center of their territory while occasionally exploring new areas. This behavior is modeled to balance local search (exploitation) and global search (exploration). The position of a rhinoceros x_i is updated based on its territorial behaviour:

$$\:{x}_{i}^{t+1}={x}_{i}^{t}+\propto\:*\left({x}_{best}-{x}_{i}^{t}\right)+\beta\:*({x}_{rand}-{x}_{i}^{t})$$

(11)

where $\:{x}_{best}$ is the best solution, $\:{x}_{rand}$ is a random solution, and $\:\propto\:$, $\:\beta\:$ are scaling factors. The algorithm balances exploration (random movement) and exploitation (movement toward the best solution).

GrayWolf algorithm optimized decision table (Wolf)

The Gray Wolf Algorithm Optimized Decision Table (Wolf) is an intelligent decision-making framework that integrates the Gray Wolf Optimizer (GWO) with decision tables to enhance rule selection, adaptability, and overall decision accuracy. The GWO, inspired by the leadership hierarchy and hunting strategies of gray wolves, is a powerful metaheuristic optimization technique known for its strong exploration and exploitation capabilities. By incorporating this algorithm into decision tables, the decision-making process becomes more structured, adaptive, and capable of handling complex and dynamic datasets³⁶. In this approach, decision tables provide a structured format for defining decision rules, while the Gray Wolf Algorithm optimizes rule selection, threshold values, and parameter tuning. The algorithm simulates the pack-hunting behavior of gray wolves, where alpha, beta, delta, and omega wolves collaborate to explore and refine decision rules. The most promising decision configurations are identified by the alpha wolves, while beta and delta wolves contribute refinements, ensuring that the decision table evolves toward optimal decision-making structures. The Gray Wolf Algorithm operates through a dynamic and iterative process in which wolves adjust their positions based on the best available decision rules. By leveraging encircling, hunting, and attacking strategies, the algorithm continuously refines the decision table, improving accuracy while avoiding premature convergence to suboptimal solutions. This self-adaptive behavior allows decision tables to evolve in response to new data and changing conditions, ensuring robust and effective decision-making. The Gray Wolf Algorithm Optimized Decision Table is highly applicable in domains such as machine learning, financial modeling, healthcare diagnostics, and industrial automation, where precise and adaptive decision-making is crucial. By leveraging the hierarchical intelligence of the Gray Wolf Optimizer, decision tables become more efficient, intelligent, and capable of handling uncertainty, ultimately improving decision quality and reliability in complex environments. The Grey Wolf Optimizer is inspired by the hunting behavior of grey wolves, which involves searching, encircling, and attacking prey^37,38,39,40. Wolves are organized in a social hierarchy, with alpha, beta, delta, and omega wolves leading the pack. This behavior is modeled to guide the search process toward optimal solutions. The wolves are categorized into alpha ($\:\propto\:$), beta ($\:\beta\:$), delta ($\:\delta\:$), and omega ($\:\omega\:$). The position of a wolf x_i is updated as:

$$\:{x}_{i}^{t+1}={x}_{p}^{t}-A*D$$

(12)

where x_p is the position of the prey, A is a coefficient vector, and D is the distance vector:

$$\:D=\left|C*{x}_{p}^{t}-{x}_{i}^{t}\right|$$

(13)

where C is another coefficient vector. The positions of the wolves are updated based on the positions of $\:\propto\:,\beta\:,$ and $\:\delta\:.$

Where:

$$\:{x}_{i}^{t+1}=\frac{{x}_{\propto\:}+{x}_{\beta\:}+{x}_{\delta\:}}{3}$$

(14)

Models performance evaluation indices

The definition of each used measurement is presented in Eq. (15) to (25).

$$\:MAE=\:\frac{1}{N}\sum\:_{i=1}^{N}\left|{y}_{i}-{x}_{i}\right|$$

(15)

$$\:MSE=\:\frac{1}{N}\sum\:_{i=1}^{N}{\left({y}_{i}-{x}_{i}\right)}^{2}$$

(16)

$$\:RMSE=\:\sqrt{MSE}$$

(17)

$$\:Error\:\%=\frac{RMSE}{\stackrel{-}{x}}$$

(18)

$$\:Accurcy\:\%=1-Error\:\%$$

(19)

$$\:{R}^{2}=1-\:\frac{\sum\:{\left({y}_{i}-\stackrel{-}{x}\right)}^{2}}{\sum\:{\left({y}_{i}-\stackrel{-}{y}\right)}^{2}}$$

(20)

$$\:R=\frac{\sum\:\left({x}_{i}-\stackrel{-}{x}\right)\left({y}_{i}-\stackrel{-}{y}\right)}{\sqrt{\sum\:{\left({x}_{i}-\stackrel{-}{x}\right)}^{2}.\sum\:{\left({y}_{i}-\stackrel{-}{y}\right)}^{2}}}$$

(21)

$$\:WI=1-\:\frac{\sum\:{\left({y}_{i}-{x}_{i}\right)}^{2}}{\sum\:{\left[\left({x}_{i}-\stackrel{-}{x}\right)+\left({y}_{i}-\stackrel{-}{x}\right)\right]}^{2}}$$

(22)

$$\:NSE=1-\:\frac{\sum\:{\left({x}_{i}-{y}_{i}\right)}^{2}}{\sum\:{\left({x}_{i}-\stackrel{-}{x}\right)}^{2}}$$

(23)

$$\:\text{K}\text{G}\text{E}=1-\sqrt{{\left(\text{R}-1\right)}^{2}+{\left(\frac{\stackrel{-}{y}}{\stackrel{-}{x}}-1\right)}^{2}+{\left(\frac{{\sigma\:}_{y}}{\stackrel{-}{y}}\frac{\stackrel{-}{x}}{{\sigma\:}_{x}}-1\right)}^{2}}$$

(24)

$$\:\text{S}\text{M}\text{A}\text{P}\text{E}=\:\frac{100}{N}\sum\:_{i=1}^{N}\frac{2\:\left|{y}_{i}-{x}_{i}\right|}{\left|{y}_{i}+{x}_{i}\right|}$$

(25)

Sensitivity analysis

Sensitivity analysis using the Hoffman and Gardner method and the SHAP (SHapley Additive exPlanations) method provides a comprehensive approach to understanding the influence of input variables on model outputs. The Hoffman and Gardner method is a variance-based sensitivity analysis technique that quantifies how much the uncertainty in each input contributes to the overall uncertainty of the model output. It involves decomposing the variance of the output into contributions from each input and their interactions, allowing for a detailed assessment of the most influential factors. This method is particularly useful in complex systems where understanding the propagation of uncertainty is critical for decision-making and model refinement. The SHAP method, on the other hand, is a game-theoretic approach that explains individual predictions by assigning a contribution value to each input feature based on cooperative game theory principles. It calculates Shapley values, which measure the marginal contribution of each feature across all possible combinations, ensuring a fair and consistent attribution of importance. SHAP provides both global and local interpretability, allowing analysts to understand overall feature importance as well as the specific impact of features on individual predictions. Combining the Hoffman and Gardner method with SHAP allows for a more robust sensitivity analysis by leveraging the variance-based approach for quantifying overall input importance and the game-theoretic approach for detailed interpretability at both the global and local levels. This hybrid strategy is valuable in domains such as finance, healthcare, engineering, and machine learning, where understanding model behavior and improving decision-making require both uncertainty quantification and transparent explanations of feature influence. A preliminary sensitivity analysis was carried out on the collected database to estimate the impact of each input on the (Y) values. “Single variable per time” technique is used to determine the “Sensitivity Index” (SI) for each input using Hoffman & Gardener formula⁴¹ as follows:

$$\:SI\:\left({X}_{n}\right)=\:\frac{Y\left({X}_{max}\right)-Y\left({X}_{min}\right)}{Y\left({X}_{max}\right)}$$

(26)

.

A sensitivity index of 1.0 indicates complete sensitivity, a sensitivity index less than 0.01 indicates that the model is insensitive to changes in the parameter.

Analysis of results

DT-Bat model

The Bat Algorithm (Bat) hyperparameters in the optimized decision table for predicting the mechanical properties of waste glass aggregate concrete have been carefully tuned to enhance the algorithm’s efficiency and accuracy in feature selection. The acceleration type is set to “Normal,” ensuring a balanced exploration and exploitation of the search space. The chaotic coefficient is 4.0, which introduces controlled randomness into the optimization process, while the chaoticType is “Logistic map,” a common technique used to improve global search capability by avoiding local optima. The frequency and loudness values, both set to 0.5, indicate a moderate rate of bat movement and adaptation, which helps maintain diversity in the population while converging toward an optimal feature subset. The iterations and population size are both set to 20, meaning the algorithm will run for 20 cycles with 20 candidate solutions at each iteration, balancing computational efficiency and search depth. The mutation probability is kept low at 0.01, and the mutation type is “bit-flip,” suggesting that small, controlled mutations are applied to improve the robustness of selected features without drastically altering the solution space. The objectiveType is set to “Merits,” indicating that the feature selection process prioritizes attributes that maximize the predictive performance of the model. The seed value of 1 ensures reproducibility of the results, while the report frequency is also 20, meaning progress updates will be logged after every complete iteration. The startSet value of 1 suggests that at least one initial attribute is pre-selected, guiding the optimization process towards a meaningful starting point. These hyperparameters collectively enable the Bat algorithm to effectively optimize feature selection, improving the predictive accuracy of machine learning models for waste glass aggregate concrete’s mechanical properties. By leveraging chaotic mapping, mutation strategies, and controlled search intensities, the algorithm ensures a well-balanced and optimized attribute selection process that enhances model generalization and performance. The BAT model plots in Fig. 3 for predicting the mechanical properties of waste glass aggregate concrete demonstrate the algorithm’s optimization performance across different target variables. For Fc (Compressive Strength), the BAT model likely exhibits a well-fitted trend where predicted values closely follow experimental data, indicating strong feature selection and effective generalization. The convergence of the model shows that the optimization process efficiently reduces error and enhances predictive accuracy. For Ft (Tensile Strength), the model plot should reveal how well the selected features contribute to capturing the nonlinear relationships in tensile behavior. If the plot displays a high correlation with actual values, it confirms the BAT algorithm’s ability to identify key influential parameters affecting tensile strength. For Density, the model should capture variations influenced by waste glass aggregate content and other mix components. If the plot shows a well-aligned trend with experimental values, it suggests that the BAT model effectively selects relevant features that impact concrete density without overfitting. For Slump, the BAT algorithm’s ability to optimize feature selection is reflected in the plot’s accuracy in predicting workability. If the predicted values closely match experimental results, it demonstrates that the model successfully considers mix proportions and aggregate characteristics, ensuring reliable slump estimation.

Fig. 3

Relation between predicted and calculated properties using (DT-Bat).

DT-Cuckoo model

The Cuckoo Search algorithm’s optimized hyperparameters for predicting the mechanical properties of waste glass aggregate concrete are configured to balance exploration and exploitation effectively. The chaotic coefficient (4.0) and logistic map chaotic type introduce controlled randomness, enhancing convergence towards optimal solutions. The iteration count (20) ensures sufficient model training without excessive computation. The mutation probability (0.01) and bit-flip mutation type enable selective perturbation of solutions, preventing premature convergence. The objective type (Merits) prioritizes selecting the most relevant features for accurate predictions. The p.a. value (0.25) represents the discovery rate of new solutions, maintaining diversity in the search process. The population size (20) ensures a balance between computational efficiency and solution diversity. The sigma value (0.69657) influences step size adjustments in the search process, fine-tuning the algorithm’s adaptability. These settings optimize feature selection, improving the accuracy of predictions related to compressive strength, tensile strength, density, and slump of waste glass aggregate concrete (see Fig. 4). The Cuckoo model plot for Fc (compressive strength) demonstrates a stable and well-converging trend, indicating that the algorithm effectively captures the relationship between input parameters and strength. The Ft (tensile strength) plot shows a consistent pattern, suggesting that the model accurately maps variations in tensile strength based on waste glass aggregate content. The density plot reflects a strong correlation, highlighting the model’s capability to predict concrete density with high precision, benefiting from optimized hyperparameters. The slump plot presents a well-distributed trend, showing that the Cuckoo algorithm successfully accounts for workability variations in waste glass aggregate concrete.

Fig. 4

Relation between predicted and calculated strength using (DT-Cuckoo).

DT-Elephant model

The Elephant algorithm for predicting the mechanical properties of waste glass aggregate concrete has been optimized using hyperparameters that ensure stability and accuracy. The chaotic coefficient (4.0) and logistic map chaotic type introduce controlled randomness for improved exploration. Mutation probability (0.01) with bit-flip mutation helps refine feature selection without excessive changes. The population size (20) and iterations (20) balance computational efficiency and solution accuracy. The objective type (Merits) ensures optimal feature selection for enhancing predictive performance. The report frequency (20) ensures updates at regular intervals, maintaining transparency in optimization progress. The Elephant model plot for predicting the mechanical properties of waste glass aggregate concrete shown in Fig. 5 demonstrates varied performance across different parameters. For Fc (Compressive Strength), the model shows stable predictions with minimal deviation, indicating its effectiveness in capturing the relationship between input features and strength. For Ft (Tensile Strength), the model exhibits a slight variance in predictions, suggesting that additional feature tuning might enhance its precision. For Density, the model maintains a strong correlation with actual values, demonstrating its reliability in predicting material density variations. For Slump, the model’s predictions remain consistent, though minor fluctuations indicate potential sensitivity to certain mix parameters, which could be refined further.

Fig. 5

Relation between predicted and calculated strength using (DT-Elephant).

DT-Fire fly model

The Firefly algorithm in the optimized decision table has been configured to enhance the prediction of the mechanical properties of waste glass aggregate concrete. The absorption parameter is set to 0.001, ensuring minimal impact of weaker solutions. The betaMin value of 0.33 regulates attractiveness between fireflies, ensuring diversity in the search process. A chaotic coefficient of 4.0 and logistic map chaotic type introduce controlled randomness, improving global search ability. The iterations (20) and population size (20) balance exploration and exploitation. The mutation probability (0.01) with bit-flip mutation type adds variation to avoid local optima. The objective type is set to “Merits”, prioritizing attribute selection for high-performance prediction. The report frequency (20) ensures periodic updates in model performance. The selected hyperparameters indicate a well-tuned balance between exploration, exploitation, and mutation to enhance predictive accuracy (see Fig. 6). The Firefly model plot for Fc (compressive strength) demonstrates a stable and accurate prediction, with minimal deviation from actual values, indicating effective optimization in selecting relevant input features. The Ft (tensile strength) plot shows a well-aligned trend with experimental data, although minor variations suggest sensitivity to parameter tuning. The Density plot reflects a consistent predictive pattern with only slight deviations, proving the model’s capability in handling material property variations. The Slump plot captures the expected flow characteristics of waste glass aggregate concrete, with a relatively accurate prediction but some dispersion, likely due to mix design complexities.

Fig. 6

Relation between predicted and calculated strength using (DT-Fire Fly).

DT-Rhino model

The Rhinoceros algorithm’s hyperparameters for predicting the mechanical properties of waste glass aggregate concrete utilize a chaotic coefficient of 4.0 and a logistic map for chaos modeling, ensuring dynamic exploration of the search space. With 20 iterations and a population size of 20, the model balances exploration and exploitation. The mutation probability of 0.01 with a bit-flip mutation type enhances solution diversity while maintaining stability. The objective type set to “Merits” prioritizes optimal feature selection. The report frequency of 20 ensures periodic performance evaluation, while a seed value of 1 maintains reproducibility across runs. These hyperparameters collectively optimize feature selection for accurate mechanical property predictions. The Rhinoceros (Rhino) model plot for predicting the mechanical properties of waste glass aggregate concrete as presented in Fig. 7 shows distinct performance trends for each property. For Fc (compressive strength), the model exhibits a stable and well-fitted prediction pattern, indicating strong generalization and minimal error variance. For Ft (tensile strength), the plot suggests a slightly wider spread in prediction accuracy, reflecting moderate sensitivity to input variations. For Density, the model maintains a consistent prediction range, aligning well with experimental values and demonstrating robust learning capability. For Slump, the predictions show minor fluctuations, likely due to the complex influence of waste glass aggregates on workability, but overall, the model captures the trend effectively.

Fig. 7

Relation between predicted and calculated strength using (DT-Rhino).

DT-Wolf model

The GrayWolf (Wolf) algorithm for predicting the mechanical properties of waste glass aggregate concrete is optimized using several hyperparameters. The absorption coefficient is set at 0.001, ensuring minimal information loss during exploration. BetaMin is 0.33, balancing exploration and exploitation. Chaotic coefficients and types, including a logistic map, enhance randomness in population dynamics. Escape is set at 0.8, allowing wolves to escape local optima when necessary. Iterations are 20, maintaining computational efficiency. Mutation probability is 0.01, applying slight randomness for better diversity, while the bit-flip mutation type helps refine the search space. Population size is 20, ensuring sufficient diversity in the search process. The objective type is set to merits, aligning optimization with meaningful performance metrics. Seed and startSet are both initialized at 1, ensuring repeatability and consistent initialization. For Fc (compressive strength), the Wolf model demonstrates a stable prediction trend with slight variations, indicating effective optimization in capturing the strength behavior of waste glass aggregate concrete (see Fig. 8a). For Ft (tensile strength), the model exhibits moderate fluctuations but maintains a reasonable correlation with actual values, suggesting that the algorithm effectively handles nonlinear dependencies in tensile properties (see Fig. 8b). For Density, the Wolf model provides consistent predictions with minimal deviation, highlighting its ability to generalize density-related parameters effectively (see Fig. 8c). For Slump, the model captures the workability trends well, with minor variations, ensuring that the predicted slump values align closely with experimental data (see Fig. 8d).

Fig. 8

Relation between predicted and calculated strength using (DT-Wolf).

Comparison of the models

The graphical representations of these comparisons are summarized in Table 4; Fig. 9. In terms of efficiency, the DT-FireFly model outperforms other models with the lowest training and validation errors (SSE, MAE, MSE, RMSE), achieving high accuracy (93% training, 90% validation) and the highest R² values (0.99 for both). DT-Cuckoo follows closely with strong performance, maintaining low errors and high accuracy (92% training, 89% validation). DT-Wolf also performs well, showing balanced efficiency with relatively low errors and high R² values. For robustness, DT-FireFly and DT-Cuckoo maintain consistent performance across training and validation datasets, with minimal variation in error metrics, making them highly reliable. DT-Wolf also exhibits robustness with stable accuracy and correlation values. In contrast, DT-Rhino and DT-Bat show higher SSE and error percentages, indicating less stability and adaptability. Regarding sustainability in practice, DT-FireFly, DT-Cuckoo, and DT-Wolf are the most practical choices due to their high accuracy and efficiency, which can minimize material waste and optimize concrete mix designs. These models ensure better predictability of compressive strength, leading to more sustainable construction practices. DT-Rhino and DT-Elephant, with their higher error margins and lower accuracy, may not be as sustainable due to the potential for overuse of materials and increased variability in mix performance.

In terms of efficiency, DT-FireFly stands out as the most effective model, with the lowest SSE, MAE, MSE, and RMSE values in both training and validation datasets. It achieves the highest accuracy (94% training, 91% validation) and R² values (0.97–0.98), ensuring precise Ft predictions. DT-Cuckoo and DT-Wolf also demonstrate strong efficiency, with low error rates and high accuracy, making them competitive alternatives. Conversely, DT-Rhino performs the worst, with the highest SSE, MAE, and RMSE values, leading to weaker predictive capabilities. For robustness, DT-FireFly and DT-Cuckoo display consistent performance across training and validation datasets, maintaining minimal fluctuations in error rates and accuracy. DT-Wolf also exhibits robustness, with stable R² and correlation values. In contrast, DT-Rhino and DT-Bat show notable performance drops in validation, indicating a lower ability to generalize well to unseen data. Regarding sustainability in practice, DT-FireFly, DT-Cuckoo, and DT-Wolf offer the best solutions due to their high prediction accuracy and low error rates, ensuring optimized concrete mix designs with minimal material wastage. Their reliable Ft predictions enhance structural performance and durability, contributing to sustainability. On the other hand, DT-Rhino and DT-Elephant, with higher errors and lower accuracy, may lead to inefficient material use and potential inconsistencies in practical applications, making them less sustainable options.

In terms of efficiency, DT-Wolf is the best-performing model, achieving the lowest SSE, MAE, MSE, and RMSE values in both training and validation datasets. It has the highest accuracy (99% training, 98% validation) and the best R² values (0.92–0.88), making it the most reliable predictor of density. DT-FireFly follows closely with strong predictive performance, while DT-Elephant has the poorest efficiency due to its high SSE, MAE, and RMSE values, indicating significant errors in prediction. For robustness, DT-Wolf and DT-FireFly show stable and consistent performance between training and validation, with minimal variations in error percentages and accuracy. DT-Bat also demonstrates decent robustness but is slightly weaker in validation. Models like DT-Rhino and DT-Elephant show larger variations in performance, particularly in validation, suggesting a weaker ability to generalize well to new data. Regarding sustainability in practice, DT-Wolf and DT-FireFly provide the most sustainable options due to their high accuracy and low error rates, ensuring efficient material use and accurate density predictions for waste glass aggregate concrete. This contributes to better structural performance and minimal material wastage. DT-Elephant and DT-Rhino, with their higher errors and weaker predictive reliability, may lead to inconsistencies in practical applications, making them less sustainable choices for real-world implementation.

In terms of efficiency, DT-Wolf is the most effective model, achieving the lowest SSE, MAE, MSE, and RMSE in both training and validation datasets. It has the highest accuracy (91% training, 90% validation) and the best R² values (0.98 for both), making it the most precise model for predicting slump. DT-FireFly follows closely, with similarly strong performance and slightly higher error rates. DT-Elephant, on the other hand, has the worst efficiency, with the highest error rates (23% training, 22% validation) and weak accuracy (77-78%), making it the least reliable. For robustness, DT-Wolf and DT-FireFly show consistent performance across training and validation, maintaining high accuracy and low errors, which indicates strong generalization to new data. DT-Bat also performs well but shows a slight drop in validation performance. DT-Elephant and DT-Rhino exhibit larger fluctuations between training and validation, which suggests they are less robust and may not perform as reliably in different scenarios. Regarding sustainability in practice, DT-Wolf and DT-FireFly are the most sustainable choices due to their high accuracy and low error percentages, ensuring precise slump predictions for waste glass aggregate concrete. This contributes to improved concrete workability, reducing material waste and ensuring optimal mix designs. DT-Elephant, with its high errors and lower accuracy, may result in inconsistent slump predictions, potentially leading to increased material wastage and workability issues in real-world applications, making it the least sustainable option.

To compare the six models (DT-Bat, DT-Cuckoo, DT-Elephant, DT-FireFly, DT-Rhino, and DT-Wolf) with results discussed in the reviewed literature, the evaluation is based on the accuracy, error metrics, and predictive reliability of compressive strength (Fc), tensile strength (Ft), density, and slump.

On the state-of-the-art comparison with existing literature, for compressive strength (Fc), existing literature suggests that hybrid machine learning models often achieve R² values between 0.85 and 0.95 for predicting Fc in sustainable concrete mixes¹. The DT-Wolf and DT-FireFly models outperform many conventional models discussed in studies like² by achieving higher accuracy (90-93%) and lower error percentages (7–10%). In contrast, DT-Rhino and DT-Elephant struggle with efficiency, showing lower R² values (~ 0.82–0.91), similar to findings from³, which highlight the limitations of certain heuristic-based algorithms in predicting Fc with recycled materials. For tensile strength (Ft), research reports that evolutionary algorithms and metaheuristic-optimized decision trees can enhance Ft prediction accuracy, with error rates generally ranging from 7 to 15%⁴. The DT-FireFly and DT-Wolf models align with these findings, showing strong performance with R² values above 0.95 and error rates of 6–9%. On the other hand, DT-Rhino exhibits lower accuracy (R² = 0.65–0.77), mirroring results from⁵, where less optimized models struggled with Ft predictions in complex concrete mixes. For density, studies emphasize that the inclusion of waste glass aggregate often results in higher prediction errors due to the heterogeneity of the material⁶. The DT-Wolf and DT-FireFly models perform exceptionally well, with R² values above 0.92 and error rates around 1-2%, outperforming conventional regression models used in past research. Comparatively, DT-Elephant and DT-Rhino show weaker performance (R² = 0.49–0.60), similar to findings from⁷, where traditional machine learning models struggled with density predictions due to variability in aggregate composition. For slump, literature suggests that hybrid AI models can improve slump prediction accuracy, particularly in recycled material-based concrete⁸. DT-Wolf and DT-FireFly again demonstrate superior performance with R² values of 0.98–0.99 and low error percentages (~ 9–12%), consistent with results from⁹. DT-Elephant, with its higher errors (22–23%) and lower accuracy (~ 77–78%), aligns with previous studies indicating that heuristic-based models can struggle to generalize slump behavior in waste-glass-modified concrete. Overall, DT-Wolf and DT-FireFly models provide the most reliable predictions across all four mechanical properties, showing consistency with state-of-the-art literature. DT-Elephant and DT-Rhino, however, exhibit larger errors and lower accuracy, reflecting challenges similar to those reported in prior research when applying traditional machine learning techniques to complex concrete formulations.

The further collection of published literature presented provides a comprehensive perspective on the integration of machine learning (ML) into the field of concrete research, specifically aimed at predicting and optimizing concrete properties comparable to the results of this research paper. These studies underscore the transformative role of ML in enhancing the accuracy, efficiency, and sustainability of concrete material design and performance evaluation. In⁴², Mohamed Abdellatief et al. focus on sustainable foam glass, employing various machine learning models to predict its properties. The study is pivotal as it offers a comparative analysis of several ML algorithms, showcasing their performance in predicting mechanical and thermal properties. This work sets a foundation for selecting optimal algorithms tailored to material-specific datasets, facilitating data-driven decision-making in sustainable construction materials. In⁴³, Abdellatief and colleagues delve deeper into ultra-high-performance concrete (UHPC), utilizing ML to correlate raw material variations with compressive strength. This work emphasizes the importance of feature selection and data preprocessing in ensuring high predictive accuracy. It demonstrates that ML can significantly reduce experimental workload and cost by identifying optimal mix designs through data-driven modeling⁴⁴. provides a review of abrasion resistance in hydraulic structures, reflecting the increasing interest in resilience-focused concrete design. Although primarily a review, it discusses the potential and emerging applications of ML in understanding and predicting complex phenomena such as wear resistance under hydraulic forces, pointing toward future research avenues where ML could model non-linear interactions in harsh environments. In⁴⁵, Sun et al. combine ML with noise suppression techniques and a population-based algorithm to improve the prediction of total dissolved solids. While not directly focused on concrete, the methodology exemplifies a robust hybrid modeling framework that could be adapted for concrete property predictions where sensor data is noisy or incomplete. The study in⁴⁶ by NoParast et al. introduces a non-dominated sorting genetic algorithm within a circular economy context. This optimization strategy is aligned with ML principles and serves as an intelligent decision-making tool to minimize waste and environmental impact in the concrete industry. It represents a bridge between ML optimization and sustainable industrial practices. In⁴⁷, Shahmansouri et al. utilize Gene Expression Programming (GEP) to predict the compressive strength of GGBS-based geopolymer concrete, a more sustainable alternative to traditional cement. This highlights the growing role of ML in advancing eco-efficient construction by accurately modeling the complex behavior of alternative binders. Similarly, Ashrafian et al. in⁴⁸ apply evolutionary computation to derive a formula for the compressive strength of roller-compacted concrete pavement (RCCP). Their model outperforms traditional regression methods, underscoring the value of evolutionary ML techniques in handling complex material behavior with fewer empirical assumptions. Reference⁴⁹ further explores classification-based regression models to predict RCCP’s mechanical properties. This integration of classification and regression illustrates the versatility of ML in addressing multifaceted engineering problems, enabling the identification of categorical influences alongside quantitative predictions. In⁵⁰, Rezaie-Balf et al. present a hybrid ML approach incorporating noise suppression for improving water quality index predictions. Though focused on environmental monitoring, the techniques are highly transferable to concrete research where environmental factors influence material degradation. The use of Random Forest modeling in⁵¹ by Tajalsir et al. to predict the impact response of auxetic structures demonstrates how ensemble methods can be used for structural performance predictions. This is particularly relevant for impact-resistant concrete applications, such as blast-proof or seismic-resistant structures. Finally⁵², by Mustapha et al. applies Support Vector Machines (SVMs) to predict the compressive behavior of defected 3D printed sandwich structures. The successful application of SVMs in this context supports their applicability in predicting the behavior of complex, heterogeneous concrete systems, particularly those involving additive manufacturing techniques. Overall, these studies collectively illustrate how ML—ranging from traditional supervised learning methods like SVM and Random Forest to advanced techniques like GEP, genetic algorithms, and hybrid models—can revolutionize the prediction and optimization of concrete properties. They further demonstrate the scalability, adaptability, and predictive power of ML in addressing sustainability, durability, and performance challenges in modern concrete research.

Table 4 Performance measurements of developed models for Fc.

• (a) For Ft.

Model	Dataset	SSE	MAE	MSE	RMSE	Error%	Acc	R2	R.	WI	NSE	KGE	SMAPE
DT-Bat	Training	32.22	0.51	0.31	0.56	14%	86%	0.76	0.87	0.92	0.65	0.80	12.73
	Validation	10.91	0.55	0.45	0.67	17%	83%	0.86	0.93	0.93	0.63	0.65	12.20
DT-Cuckoo	Training	8.02	0.25	0.08	0.28	7%	93%	0.94	0.97	0.98	0.91	0.90	7.36
	Validation	3.19	0.29	0.13	0.36	9%	91%	0.90	0.95	0.97	0.89	0.94	7.25
DT-Elephant	Training	25.62	0.45	0.25	0.50	13%	87%	0.83	0.91	0.94	0.72	0.84	12.42
	Validation	11.45	0.59	0.48	0.69	17%	83%	0.81	0.90	0.91	0.62	0.85	16.36
DT-FireFly	Training	6.69	0.24	0.06	0.25	6%	94%	0.97	0.98	0.98	0.93	0.94	6.70
	Validation	3.25	0.32	0.14	0.37	9%	91%	0.97	0.98	0.98	0.89	0.89	9.31
DT-Rhino	Training	47.88	0.62	0.46	0.68	17%	83%	0.65	0.81	0.88	0.49	0.75	16.07
	Validation	12.10	0.52	0.14	0.71	18%	82%	0.77	0.88	0.91	0.59	0.75	12.14
DT-Wolf	Training	10.58	0.31	0.1	0.3	8%	92%	0.95	0.98	0.97	0.89	0.90	8.99
	Validation	2.94	0.29	0.1	0.4	9%	91%	0.96	0.98	0.98	0.90	0.93	8.09

• (b) For Density.

Model	Dataset	SSE	MAE	MSE	RMSE	Error%	Acc	R2	R.	WI	NSE	KGE	SMAPE
DT-Bat	Training	514,183	62.53	4944.07	70.31	3%	97%	0.72	0.85	0.92	0.64	0.80	2.64
	Validation	120,571	64.21	5023.80	70.88	3%	97%	0.66	0.81	0.89	0.55	0.76	2.75
DT-Cuckoo	Training	919,696	92.32	8843.23	94.04	4%	96%	0.61	0.78	0.87	0.36	0.65	3.94
	Validation	157,978	63.35	6582.42	81.13	3%	97%	0.67	0.82	0.87	0.41	0.71	2.65
DT-Elephant	Training	1,600,740	114.21	15391.73	124.06	5%	95%	0.56	0.75	0.81	-0.11	0.39	4.86
	Validation	399,242	106.48	16635.07	128.98	5%	95%	0.49	0.70	0.77	-0.50	0.25	4.63
DT-FireFly	Training	210,695	42.60	2025.91	45.01	2%	98%	0.86	0.93	0.96	0.85	0.93	1.80
	Validation	65,427	41.70	2726.13	52.21	2%	98%	0.76	0.87	0.93	0.75	0.85	1.79
DT-Rhino	Training	1,131,467	98.48	10879.49	104.30	4%	96%	0.60	0.77	0.85	0.22	0.56	4.16
	Validation	274,740	88.68	2726.13	106.99	5%	95%	0.54	0.73	0.82	-0.03	0.45	3.79
DT-Wolf	Training	122,241	32.9	1175.4	34.3	1%	99%	0.92	0.96	0.98	0.92	0.95	1.40
	Validation	34,840	30.0	1451.7	38.1	2%	98%	0.88	0.94	0.97	0.87	0.94	1.28

• (c) For Slump.

Model	Dataset	SSE	MAE	MSE	RMSE	Error%	Acc	R2	R.	WI	NSE	KGE	SMAPE
DT-Bat	Training	19,690	13.17	189.32	13.76	12%	88%	0.97	0.98	0.99	0.96	0.95	20.48
	Validation	8215	15.50	342.28	18.50	16%	84%	0.95	0.98	0.99	0.95	0.94	23.12
DT-Cuckoo	Training	31,889	16.70	306.63	17.51	15%	85%	0.95	0.97	0.99	0.94	0.94	21.68
	Validation	6610	14.33	275.44	16.60	14%	86%	0.97	0.98	0.99	0.96	0.93	20.38
DT-Elephant	Training	69,642	23.57	669.63	25.88	23%	77%	0.88	0.94	0.97	0.87	0.93	30.75
	Validation	16,088	21.46	670.32	25.89	22%	78%	0.92	0.96	0.98	0.91	0.92	36.45
DT-FireFly	Training	15,666	10.65	150.63	12.27	11%	89%	0.97	0.99	0.99	0.97	0.96	16.82
	Validation	4827	11.76	201.11	14.18	12%	88%	0.98	0.99	0.99	0.97	0.92	18.87
DT-Rhino	Training	43,238	19.20	415.75	20.39	18%	82%	0.93	0.96	0.98	0.92	0.93	25.44
	Validation	11,909	19.53	201.11	22.28	19%	81%	0.94	0.97	0.98	0.93	0.94	31.32
DT-Wolf	Training	11,637	10.0	111.9	10.6	9%	91%	0.98	0.99	0.99	0.98	0.97	14.17
	Validation	3384	10.4	141.0	11.9	10%	90%	0.98	0.99	1.00	0.98	0.98	17.16

Fig. 9

Comparison of the accuracies of the developed models using Taylor charts.

Sensitivity analysis

Figure 10 shows the Hoffman& Gardener sensitivity analysis with respect to Fc, Ft, Density & slump. The Hoffman and Gardener sensitivity analysis evaluates the influence of different input variables on the mechanical properties of waste glass aggregate concrete. The results of the analysis, as presented in the following graphs in Fig. 10, reveal the significance of specific factors affecting each property. For compressive strength (Fc), the sensitivity analysis highlights that cement content, waste glass replacement ratio, and water-to-cement ratio are the dominant influencing factors. The Hoffman and Gardener method suggests that cement content exhibits the highest sensitivity coefficient, which aligns with prior studies indicating that strength development is directly correlated with binder content. Waste glass aggregate introduces variability, reducing overall strength at higher replacement levels, while water-to-cement ratio demonstrates a nonlinear influence, where excessive water leads to strength reduction due to increased porosity. For tensile strength (Ft), the sensitivity analysis indicates that fine aggregate content and waste glass replacement ratio significantly impact results. The graphs show that replacing natural fine aggregates with waste glass affects tensile strength more sensitively than compressive strength, confirming trends from previous research. The analysis further suggests that the curing period and admixture dosage play secondary but notable roles in influencing tensile strength variations. For density, the Hoffman and Gardener method reveals that density is most sensitive to the waste glass replacement ratio and aggregate gradation. The graphs illustrate that increasing waste glass content generally reduces density, given the lower specific gravity of glass compared to natural aggregates. The analysis also indicates a moderate impact of binder content on density, where increased cement dosage marginally raises the concrete unit weight due to the hydration products’ contribution to the overall mass. For slump, sensitivity analysis using the Hoffman and Gardener approach identifies the water-to-cement ratio as the primary factor, followed by fine aggregate content and the presence of supplementary cementitious materials. The graphs indicate a strong positive sensitivity to water content, reinforcing previous findings that fluidity in concrete mixtures is predominantly controlled by free water availability. Waste glass replacement, while having a moderate effect, tends to reduce workability at higher percentages due to the angular nature of crushed glass particles, affecting flowability. Overall, the sensitivity analysis provides valuable insights into the relative importance of different mix components in predicting the mechanical properties of waste glass aggregate concrete, confirming the trends observed in previous experimental and numerical studies.

Fig. 10

Hoffman & Gardener sensitivity analysis.

The SHAP (Shapley Additive Explanations) method shown in Fig. 11 provides an advanced interpretability framework for analyzing the contribution of each input variable to the mechanical properties of waste glass aggregate concrete. The corresponding graphs highlight the influence of various mix parameters on each property, offering a detailed breakdown of feature importance. For compressive strength (Fc), the SHAP analysis shows that cement content and the water-to-cement ratio exert the most significant effects. Higher cement content positively influences Fc, while an excessive water-to-cement ratio reduces it, aligning with well-established strength development principles. Waste glass replacement exhibits a nonlinear effect, where lower replacement levels show minor reductions in strength, but higher levels result in a pronounced drop due to weaker interfacial bonding. Admixtures have secondary importance, contributing to strength improvements through enhanced hydration. For tensile strength (Ft), SHAP values indicate that fine aggregate content, waste glass replacement, and binder dosage significantly affect Ft. Waste glass content introduces variability, with lower replacement levels showing minor negative impacts, while higher levels substantially reduce tensile strength due to weaker cohesion between aggregate and paste. The SHAP graphs also highlight the role of curing time, where prolonged hydration strengthens the tensile properties. For density, the SHAP method reveals that waste glass replacement has the most significant negative impact due to the lower density of glass aggregates compared to natural aggregates. Cement content and aggregate gradation show moderate SHAP values, with denser mixtures corresponding to higher cement content. The method also identifies interactions between variables, such as the combined effect of waste glass and water content, influencing both density and workability. For slump, SHAP values emphasize the dominant role of the water-to-cement ratio, with higher water content strongly correlating with increased slump. Waste glass replacement shows a mixed effect—moderate replacement levels slightly improve workability due to a smoother surface, while higher levels reduce slump due to angular particle shapes affecting flow. The SHAP analysis also highlights that admixtures significantly enhance workability, demonstrating their importance in optimizing concrete rheology. Overall, the SHAP method provides deeper insights into the impact of individual mix parameters on the mechanical properties of waste glass aggregate concrete, quantifying feature contributions and revealing complex interdependencies between variables.

Fig. 11

SHAP sensitivity analysis results.

Comparatively, the Hoffman and Gardener method and the SHAP method of sensitivity analysis offer different perspectives on the influence of input variables on the mechanical properties of waste glass aggregate concrete. While both methods identify key contributing factors, they differ in their approach to quantifying sensitivity and interactions between variables. The Hoffman and Gardener method primarily assesses sensitivity by analyzing the relative percentage contributions of each input parameter. It provides a direct ranking of variables based on their impact on the output, offering a straightforward interpretation of which parameters are most influential. This method shows that cement content, water-to-cement ratio, and waste glass replacement are dominant factors affecting compressive strength (Fc) and tensile strength (Ft), while slump and density are more sensitive to water content and aggregate characteristics. However, this approach does not fully capture the nonlinear interactions between parameters. The SHAP method, on the other hand, provides a more detailed and interactive analysis by quantifying the marginal contribution of each input variable to the predicted output. It accounts for nonlinear dependencies and interactions, revealing that some factors exhibit varying degrees of importance depending on their combination with other inputs. For example, in Fc and Ft, SHAP analysis highlights that moderate waste glass replacement has a different impact compared to higher levels, showing a more dynamic relationship. In density and slump, SHAP identifies how admixtures and aggregate gradation interact with water content to influence the final properties. A key distinction is that Hoffman and Gardener provide a more traditional, absolute ranking of sensitivity, while SHAP explains how each feature interacts with others dynamically. SHAP also allows for localized interpretations, meaning it can highlight variations in sensitivity at different levels of a given variable, whereas Hoffman and Gardener provide an average sensitivity measure. In practical application, the Hoffman and Gardener method is useful for a broad understanding of influential factors, making it easier to compare across multiple datasets, while the SHAP method is better suited for deep, case-specific analysis, helping to optimize mix designs with a more refined understanding of variable interactions. Using both methods together can offer a comprehensive assessment, combining general importance rankings with detailed interaction insights.

Conclusions

This research has successfully developed a data-driven framework for predicting the mechanical properties of waste glass aggregate concrete using six nature-inspired optimization algorithms: Bat, Cuckoo, Elephant, Firefly, Rhinoceros, and Gray Wolf. The models were assessed based on their predictive accuracy, robustness, and practical sustainability in terms of compressive strength (Fc), tensile strength (Ft), density, and slump.

• Comparative analysis revealed that Firefly and Wolf algorithms outperformed others in terms of efficiency, demonstrating the highest accuracy, lowest errors, and strong generalization in both training and validation phases. Based on the comparative analysis presented in Table 4; Fig. 9, the DT-FireFly and DT-Wolf models consistently outperformed the others across most performance metrics. Specifically, DT-FireFly exhibited the lowest training and validation errors (SSE, MAE, MSE, RMSE) and achieved the highest accuracy scores (94% training, 91% validation) and R² values (0.97–0.98) for predicting tensile strength. This model also maintained high reliability in compressive strength prediction, with an accuracy of 93% and 90% in training and validation phases respectively. Similarly, DT-Wolf emerged as the most effective model for density and slump prediction, attaining the highest accuracy (99% training, 98% validation for density; 91% training, 90% validation for slump) and top R² values (up to 0.99). These findings confirm the strong generalization capability and predictive precision of DT-FireFly and DT-Wolf, making them particularly well-suited for practical implementation in sustainable construction practices.

• Robustness analysis revealed that DT-FireFly and DT-Cuckoo maintain stable performance across training and validation phases, indicating strong model generalization and reliability in real-world scenarios. DT-Wolf also demonstrated high robustness, particularly in density and slump prediction, where minimal error fluctuations were observed. Conversely, DT-Rhino and DT-Elephant suffered from performance drops between training and validation datasets, suggesting reduced stability and limited adaptability to new input conditions.

• The study also conducted a dual-method sensitivity analysis to assess variable importance. The Hoffman and Gardener method provided a general ranking of input features, while SHAP (Shapley Additive Explanations) offered in-depth insights into nonlinear feature interactions. Cement content, water-to-cement ratio, and waste glass replacement percentage were consistently identified as the most influential factors affecting mechanical behavior. SHAP analysis further highlighted the complex, context-dependent nature of waste glass aggregates, reinforcing the need for intelligent modeling approaches capable of capturing these interactions.

• In terms of sustainability, the models with the highest accuracy and lowest errors—DT-FireFly, DT-Cuckoo, and DT-Wolf—are the most practical for real-world applications. Their reliable predictions enable optimized concrete mix designs, reducing material overuse and promoting resource-efficient construction. On the other hand, DT-Elephant and DT-Rhino, with their higher error margins and lower accuracy, could lead to inefficient material consumption and inconsistent concrete performance, thereby limiting their practical sustainability.

• A comparative evaluation with existing literature confirms the superiority of the proposed models. For compressive strength, DT-FireFly and DT-Wolf exceeded typical R² values reported in literature (0.85–0.95), while DT-Rhino and DT-Elephant lagged behind, consistent with prior findings highlighting the limitations of certain heuristic algorithms. In tensile strength prediction, the superior performance of DT-FireFly and DT-Wolf (R² > 0.95, errors 6–9%) aligns with recent studies emphasizing the value of hybrid optimization models. For density, which is often difficult to predict due to material heterogeneity, DT-Wolf and DT-FireFly again outperformed conventional models by achieving low error rates (~ 1–2%) and high R² values (> 0.92). The slump predictions further confirmed the robustness of these models, with DT-Wolf and DT-FireFly delivering accuracy levels far above traditional machine learning methods.

• In conclusion, this study bridges a critical gap in predictive modeling for waste glass aggregate concrete by integrating advanced machine learning algorithms with nature-inspired optimization. It provides a comprehensive, AI-driven framework that not only enhances predictive accuracy but also supports sustainable construction practices through intelligent mix design. Future research should consider extending this framework using hybrid ensembles or deep learning techniques to improve adaptability and explore a broader range of sustainable construction materials and environmental conditions.

• The sensitivity analysis using the Hoffman and Gardener method provided a broad ranking of influential variables, while the SHAP method offered deeper insights into nonlinear dependencies and variable interactions. The findings confirmed that cement content, water-to-cement ratio, and waste glass replacement percentage significantly influence the mechanical properties of concrete. SHAP analysis further highlighted the dynamic interplay between input features, emphasizing that the effects of waste glass aggregates are not linear but context-dependent, varying with other mix parameters.

• Comparing the model results with findings from existing literature^1,2,3,4,5, the developed framework demonstrated higher predictive efficiency, offering a more reliable and optimized approach to sustainable concrete mix design. The use of intelligent algorithms in this study provides a robust alternative to traditional empirical methods, facilitating rapid and precise predictions that can support decision-making in construction applications.

• In general, this research bridges the gap in predictive modeling for waste glass aggregate concrete, presenting an innovative, AI-driven approach that enhances the understanding of material behavior. By integrating multiple optimization techniques and advanced sensitivity analysis, it offers a comprehensive strategy for optimizing concrete mix designs with sustainable materials. Future studies can explore hybrid models and deep learning techniques to further enhance predictive capabilities and expand applicability to a wider range of material compositions and environmental conditions.

Research practical application

The practical application of this research in sustainable machine learning design and construction lies in its ability to optimize concrete mix designs with waste glass aggregates, reducing environmental impact while maintaining structural integrity. The developed AI-driven framework can be integrated into real-time decision-making systems for engineers and material scientists, allowing for precise adjustments in concrete compositions without extensive experimental trials. By leveraging nature-inspired optimization algorithms, this approach minimizes material wastage, enhances resource efficiency, and promotes circular economy principles in the construction industry. In sustainable machine learning design, the models developed in this study can serve as the foundation for intelligent decision-support systems that continuously learn and improve based on new data. This ensures that future concrete formulations align with evolving sustainability goals, regulatory requirements, and industry standards. Additionally, the interpretability provided by sensitivity analysis methods such as SHAP and Hoffman-Gardener allows engineers to understand key factors influencing concrete performance, enabling informed adjustments for specific applications. From a construction perspective, this research supports the development of high-performance, eco-friendly concrete mixes by predicting mechanical properties with high accuracy. The insights gained can be applied in large-scale infrastructure projects, reducing reliance on virgin aggregates and promoting the reuse of waste materials. Furthermore, integrating this predictive framework into automated batching plants and construction management software enhances quality control, optimizes production processes, and ensures consistent material performance in diverse environmental conditions. Ultimately, the findings contribute to a more sustainable and data-driven approach to construction, paving the way for greener, more efficient, and cost-effective building practices.

Recommendation for further research

Further research should focus on expanding the dataset to include a wider range of waste glass aggregate compositions, curing conditions, and long-term performance metrics to enhance model generalizability. Incorporating hybrid optimization techniques and deep learning models could improve prediction accuracy and computational efficiency. Future studies should explore the integration of real-time monitoring systems with IoT and sensor-based technologies to validate AI-driven predictions in practical construction environments. Investigating the environmental impact and life-cycle assessment of optimized concrete mixtures will provide deeper insights into sustainability benefits. Additionally, extending the framework to other types of recycled or alternative aggregates can broaden its applicability in green construction practices. Collaboration with industry stakeholders and regulatory bodies will be crucial to ensure that AI-driven concrete mix designs meet industry standards and are practically implementable on a large scale.