GreenMix-pareto: Uncertainty-aware, physics-guided multi-objective optimization of low-carbon concrete mix designs

Concrete mix design increasingly requires balancing mechanical performance with climate and resource impacts. Most existing data-driven studies either optimize a single target (often strength) or report point predictions without calibrated uncertainty, which limits reliability-aware and constructible Pareto decision-making. GreenMix-Pareto addresses this gap through an end-to-end workflow that combines (i) physics-guided multi-task learning with monotonicity constraints, (ii) distribution-free conformal calibration for decision-grade uncertainty, (iii) data-driven feasibility screening, and (iv) hybrid multi-objective optimization to produce robust Pareto sets. Using a dataset of N = 1000 mixes (cement, water, superplasticizer, coarse/fine aggregates, age), the method derives domain ratios (e.g., water–cement ratio, sand ratio, paste fraction) and trains a monotone-constrained, multi-output gradient-boosting model to jointly predict compressive strength, embodied carbon dioxide (CO 2 ), energy, and resource use. Conformalized quantile regression provides calibrated prediction intervals that support chance constraints on strength using robust lower bounds. A learned feasibility filter (one-class support vector machine (SVM) + kernel density estimation (KDE)), together with broad domain bounds, restricts the search to plausible and constructible mixtures. The optimization stage combines Expected Hypervolume Improvement (EHVI) Bayesian optimization with Non-dominated Sorting Genetic Algorithm II (NSGA-II) refinement to discover dense, uncertainty-aware Pareto fronts. On held-out tests, the physics-guided model achieves strong accuracy for strength (RMSE = 0.58 MPa, R 2 = 0.997 ) while preserving physically credible gradients. For strength, conformal prediction reaches near-nominal marginal coverage (e.g., 0.92 at 90%). The resulting Pareto fronts expose actionable eco–strength trade-offs; a representative knee solution achieves ∼ 50 MPa strength with ∼ 220 kg CO 2 and ∼ 1159 MJ per m 3 inside the learned feasible region. Evaluation uses five independent stratified 80/20 splits with age-bin control; reported test metrics are averaged across splits. SHAP and partial-dependence analyses align with mixture science (impacts driven by cement; strength governed by w / c and age). The workflow supports reliability-aware strength targeting while reducing embodied impacts in low-carbon concrete design.