To address insufficient carbon integration, weakly verifiable quality constraints, and unstable Pareto-set generation in construction-stage green decision-making, this study develops a multi-objective optimization model for construction mode configuration and an engineering-oriented genetic algorithm (GA) framework for Pareto solution generation under hard feasibility constraints. In a construction organization scenario, duration, cost, and carbon emissions are formulated as parallel objectives, while a quality threshold, explicit process logic, and basic resource and workface-feasibility conditions are incorporated to ensure engineering implementability. Construction-stage carbon emissions are quantified using the emission factor method under an auditable activity-level accounting framework. The configured GA framework is compared with the conventional GA, the Non-dominated Sorting Genetic Algorithm II, and the Non-dominated Sorting Genetic Algorithm III through repeated-run statistics and multi-metric evaluation. On the main case, it achieves the highest mean hypervolume (0.723 ± 0.074, mean ± standard deviation), the lowest mean spacing (0.076 ± 0.207), and the smallest average convergence generation (18.49 ± 2.57). The Pareto results reveal a clear trade-off among duration, cost, and carbon emissions, in which high-load beam-and-slab formwork and concrete-related activities dominate cost and carbon variation, whereas schedule advantage mainly depends on stronger compression of critical-chain activities and inter-floor handover.