Multi-Objective Optimization of Low-Carbon Concrete Mix Proportions Considering Carbon Emissions and Creep Behavior

This study proposes a physical-prior and residual-learning method for creep prediction of low-carbon concrete and integrates it into a multi-objective optimization framework for mix proportion design. After cleaning and normalizing 1066 creep test records, the B4 model served as the physical prior backbone, and a sparse variational Gaussian process (SVGP) was used to fit the residuals between measured and theoretical values. Global linear calibration, a Matérn-5/2 kernel with automatic relevance determination, and length-scale regularization were used to suppress kernel collapse and overfitting. The B4+SVGP model was compared with random forest, extreme gradient boosting, and a backpropagation neural network under a unified dataset, feature set, and training protocol, and Shapley additive explanations (SHAP) were used to analyze mixture effects on creep compliance. The B4+SVGP model that performed best under record-level validation was then embedded in NSGA-II to optimize net carbon emissions and 1000-day creep compliance simultaneously; TOPSIS was used to derive mix proportions under carbon-emission-oriented, balanced, and creep-oriented weight preferences. Under a unified record-level 10-fold cross-validation protocol, B4+SVGP achieved favorable prediction accuracy (R2 = 0.9660) and retained a relative advantage in the target mix proportion region. Loading duration, age at loading, and 28-day compressive strength were the most influential factors, consistent with the physical mechanisms of the B4 model. Under strength and mix-feasibility constraints, the Pareto front exhibited an L shape with an inflection at approximately 205 kg/m3 net carbon emissions. The balanced (5:5) scenario yielded a candidate with a water-to-binder ratio of 0.4227, a binder content of 300.03 kg/m3, and fly ash/slag/silica fume replacements of 6.76%/6.70%/14.82%; it reduced net carbon emissions by approximately 18.7% while increasing creep compliance by only approximately 2.1%. The resulting mixtures are computational candidates whose fresh-state properties, compressive strength, and long-term creep behavior require experimental verification before engineering recommendation.