The production of ordinary Portland cement (OPC), which is extensively used in construction, is a significant contributor to carbon dioxide emissions and the depletion of non-renewable resources [1, 2]. With global cement production surpassing 3.5 billion tons annually, the cement industry alone accounts for approximately 8% of global carbon dioxide emissions, intensifying concerns about the issue of global warming [3, 4]. Given the pressing challenges posed by the environmental impact and the depletion of non-renewable energy sources, it is crucial to identify sustainable alternatives to cement that can mitigate the environmental footprint of the construction industry and reduce reliance on non-renewable resources [5].
Geopolymer, a novel building material with environmental and sustainable attributes [6, 7], is formed through alkali activation of aluminosilicate precursors [8, 9]. Due to its energy-saving and widespread sourcing properties, it is considered promising green building material and has garnered extensive attention in construction industry, potentially replacing OPC [10]. Geopolymer has high strength, low permeability, and excellent durability, making it suitable for practical engineering projects [11–13]. Ternary geopolymers, composed of fly ash (FA), granulated blast furnace slag (GBFS), and steel slag (SS), exhibit not only higher compressive strength but also excellent durability with minimal environmental pollution. The combination of FA, GBFS, and SS can lead to synergistic effects that enhance the geopolymerization process and improve the strength of the final product. Each material contributes different reactive components, such as silica, alumina, and calcium, which can react with alkalis to form additional binding phases [14]. However, the design of ternary geopolymers considering strength, cost and carbon emission presents certain difficulties. The components of ternary geopolymers exhibit significant differences in properties, and their interactions are complex. A rational mix proportion necessitates a comprehensive consideration of the characteristics of each component, requiring extensive experimentation and adjustment. This poses intricate challenges in mix proportion design and component balance.
To overcome the limitations of traditional mix design methods and to refine mix proportions for ternary geopolymers, formula analysis and statistical methodologies have been introduced as viable alternatives [15]. Formula analysis approaches are grounded in empirical equations and the interrelation between system components, deriving new mix designs. However, these methods rely upon specific formulas, limiting their reliability and scalability in practical application [16, 17]. Statistical methods seek to address the drawbacks of formula analysis by employing standard statistical procedures to construct empirical models tailored for optimizing mix designs [18]. Nonetheless, this technique necessitates an ample dataset to train statistical models that accurately predict concrete performance, potentially falling short of meeting the diverse objectives of specific projects [19, 20]. In addition, the statistical methods may not capture the complex relationship between the components of ternary geopolymers and their multiple objectives.
In order to surpass the constraints associated with traditional approaches, the utilization of computational optimization methodologies has emerged as a viable alternative solution for geopolymer mixture optimization [21, 22]. This approach establishes a relationship between decision variables (geopolymer components) and objectives (geopolymer properties), and uses optimization algorithms to find the optimal geopolymer mixture. In recent years, researchers have started applying machine learning (ML) methods to model the properties of geopolymers [23–25].
ML methods have the capability to automatically learn from and extract useful information from extensive datasets, aiding in the identification of optimal geopolymer mixture proportions [26, 27]. This approach offers a higher level of automation, reducing the reliance on manual intervention and enhancing design efficiency. Furthermore, advances in computational power and the ease of data collection have made it increasingly convenient to acquire sufficient data. Due to the above advantages, scholars have used ML models to predict the mechanical properties, shrinkage behavior, and strength of geopolymer mixtures, with favorable results [28, 29]. Additionally, ensemble learning algorithms have been introduced to improve the accuracy and stability of geopolymer mixture performance prediction [30]. Unlike traditional independent models (such as ANN and SVR), bagging learning improves the prediction accuracy of geopolymer mixtures by combining the predictions of multiple base models. This reduces model bias and variance, lowers the risk of overfitting, and enhances the generalization overall stability of the model [31–33]. Among these, the bagging-based ensemble learning algorithms such as random forest regressors (RFR), extreme random trees (ERT), gradient boosting regressors (GBR), and extreme gradient boosting regressors (XGBR) are widely used [34, 35]. Recent research has shown that these tree-based ensemble learning methods typically outperform independent and traditional empirical models when addressing engineering problems [36–38]. Therefore, in this study, on the foundation of using ANN and SVR, tree-based ensemble learning algorithms, ERT, and GBR, are introduced to establish a predictive model for geopolymer mixtures.
In the context of multi-objective optimization (MOO) of geopolymer mixtures, it is a proper choice to introduce metaheuristic algorithms in order to satisfy multiple objectives such as high UCS, low cost, and low carbon emissions, and to further improve optimization efficiency and accuracy [39]. Metaheuristic algorithms are a class of optimization algorithms based on iterative and adaptive search that simulate heuristic search strategies inspired by natural systems or artificial intelligence [40]. One commonly used metaheuristic algorithm is Evolutionary Algorithm (EA), which is based on Darwin's theory of evolution and simulates evolutionary processes such as selection, reproduction, and mutation [41]. EA maintains a population, evaluates individual fitness using a fitness function, and generates new generations of solutions through genetic operations (such as selection, crossover, and mutation) to gradually optimize the objective function. The advantages of evolutionary algorithms include their global search ability and adaptability to multi-objective optimization problems. In previous studies, some researchers have used NSGA-II to optimize the design of concrete [42]. NSGA-II is a MOO algorithm that achieves a balance between optimization objectives and diversity by maintaining non-dominated rankings and crowding distance of the population to find a set of non-dominated solutions. In previous studies, some researchers have used NSGA-II to optimize the design of concrete [43–45], but there are few reports on using NSGA-II to solve the MOO problem of geopolymer mixtures. Therefore, this study applies NSGA-II to optimize the design of geopolymer mixtures, achieving efficient and accurate optimization of multiple objectives for ternary geopolymer mixtures.
This study established a MOO model using machine learning and NSGA-II algorithm. Initially, a dataset was compiled based on experimental tests, and subsequently, four typical ML models, namely SVR, ANN, GBR, and ERT, were trained using the dataset. The nonlinear mapping relationship between the UCS of ternary geopolymer mixtures and mix proportions was established. The variable importance and sensitivity studies were conducted to elucidate the influence of different components on UCS of ternary geopolymers. Based on the trained ML model, combined with the NSGA-II algorithm, a MOO framework was established to find the Pareto frontier for trade-offs between UCS, cost, and CO2 emission of the ternary geopolymers.