Construction project management often involves optimizing time and cost while ensuring minimal environmental impact. This study presents an innovative hybrid approach combining non-dominated sorting genetic algorithm III (NSGA-III) and multi-objective particle swarm optimization (MOPSO) to address the time-cost-environmental sustainability trade-off (TCEST) in construction projects. The proposed model aims to minimize project completion time and cost while maximizing environmental sustainability. A case study is conducted to validate the model, incorporating diverse construction activities and their respective time, cost, and environmental sustainability metrics. The results reveal Pareto-optimal solutions demonstrating significant trade-offs among the three objectives. The hybrid approach outperforms standalone algorithms in terms of solution diversity, convergence, and hypervolume indicators. Weighted sum methods are employed to select the most suitable solution from the Pareto front based on project priorities. Correlation analysis further explores interdependencies among objectives, emphasizing the feasibility of balancing these critical factors. The study contributes a robust decision-support tool for sustainable project planning, facilitating informed decision-making in modern construction management.