Intelligent Mixture Design of Limestone Calcined Clay Cement Based on Ensemble Learning and Multi-Objective Optimization

Limestone Calcined Clay Cement (LC³) has attracted attention as a promising low-carbon cementitious material due to its reduced CO₂ emissions and satisfactory mechanical performance. However, its properties are strongly affected by raw-material composition, processing conditions, and mixture proportions. In this study, a database encompassing diverse material parameters and preparation processes was developed, and multiple machine-learning models were applied to predict the compressive strength of LC³ systems. The predictive accuracy of these models was further enhanced through the Bayesian optimization and the Boosting-based ensemble strategies. Based on the optimized predictive models, a multi-objective optimization framework was proposed to integrate compressive strength, materials cost, and embodied carbon emissions. A genetic algorithm was subsequently applied to identify optimal mixture proportions for LC³ matrices. The results showed that the proposed approach could achieve a balanced trade-off between mechanical performance and sustainability, thereby improving both the scientific robustness and practical applicability of LC³ mixture design. This work could provide a data-driven pathway for performance-oriented optimization of emerging low-carbon cementitious materials.

A database of 291 LC³ mixtures was compiled, covering a wide range of compositions and curing conditions. Input variables included clinker, calcined clay, limestone, gypsum, water-to-binder ratio, calcination parameters, curing conditions, and curing age. The compressive strength served as an output. Correlation analysis and variance inflation factor (VIF) evaluation were applied to reduce multicollinearity. Four machine learning models (i.e., Multilayer Perceptron (MLP), Random Forest (RF), Gaussian Process Regression (GPR), and Extreme Gradient Boosting (XGB)) were trained and tuned via the Bayesian optimization. An ensemble framework was then constructed with MLP as the meta-learner and XGB, RF, and GPR as base models within a Boosting strategy to enhance accuracy.

In parallel, a multi-objective optimization model was formulated, targeting compressive strength, material cost, and embodied carbon emissions. Cost and emission factors were drawn from market and life cycle databases. Practical constraints on binder fractions, water-to-binder ratio, and curing requirements ensured a feasibility. The non-dominated Sorting Genetic Algorithm Ⅱ (NSGA-Ⅱ) was used to search for Pareto-optimal mixtures that reflect different trade-offs among strength, cost, and carbon footprint.

The ensemble learning notably improves prediction compared with individual models. The XGB provides the strongest performance among single algorithms, while GPR and RF also yield the good results. The MLP alone is weaker, but the predictive accuracy is further enhanced when integrating as a meta-learner in the Boosting ensemble. This underscores the advantage of combining diverse learners to model a complex LC³ behavior.

The variable importance analysis identifies curing age as a dominant positive factor, followed by calcined clay fineness and curing temperature. In contrast, the excessive replacement of calcined clay and limestone has a negative effect, revealing threshold behaviors. The interactions among clinker, calcined clay, and limestone confirm synergistic benefits in moderate levels, but dilution effects at a higher dosage. These findings clarify the nonlinear mechanisms affecting LC³ strength and validate the interpretability of the model.

The NSGA-Ⅱ optimization generates a Pareto front of candidate solutions. A strength-prioritized mixture achieves mechanical properties, comparable to OPC concrete with a reduced carbon impact. A carbon-prioritized mixture minimizes emissions, while maintaining an acceptable strength, making it suitable for sustainability-driven projects. A balanced solution achieves compromise among all three objectives, representing a practical option for general engineering applications. The verification against experimental results confirms the reliability of predictions, demonstrating that the proposed framework can simultaneously address the performance, economic, and environmental targets.

This study introduced an integrated framework that could combine ensemble learning with a multi-objective optimization for LC³ mixture design. The main contributions involved, 1) Boosting-based ensemble learning significantly enhanced the accuracy of compressive strength prediction; 2) Curing age, calcined clay fineness, and curing temperature were identified as key positive drivers, while excessive calcined clay and limestone replacement exerted negative influences; 3) NSGA-Ⅱ effectively produced Pareto-optimal mixtures balancing strength, cost, and carbon emissions, offering flexible solutions under different priorities; and 4) The experimental validation confirmed that optimized LC³ mixtures could maintain competitive strength, while substantially reducing both cost and carbon footprint.

The integration of predictive modeling and optimization provided a powerful pathway for advancing LC³ research and practice. It could contribute a methodological innovation and demonstrate a clear potential for sustainable, design of low-carbon cementitious materials in the construction industry.