Multi-Objective Optimization for Nano-Silica-Modified Concrete Based on Explainable Machine Learning

Abstract

Nano-silica modified concrete (NSC) has been widely applied in engineering practice. However, conventional manual mix proportion design is both time-consuming and costly. In this study, four machine learning models—XGBoost, CatBoost, Random Forest, and AdaBoost—were trained to predict the compressive strength of NSC. Based on the best-performing model, the NSGA-II algorithm was employed to develop a multi-objective optimization framework, considering compressive strength, cost, and carbon emissions as objectives. The results indicated that XGBoost achieved the highest accuracy, with R2 = 0.99 and RMSE = 1.80 MPa. Feature importance analysis further revealed that nano-silica content was strongly correlated with strength (0.82) and cost (0.85). Using NSGA-II, a set of Pareto-optimal solutions was generated. The NSGA-II algorithm produced Pareto-optimal solutions, highlighting the trade-offs among the three objectives. This integrated approach effectively reduces experimental workload and provides a valuable reference for sustainable NSC mix proportion design.