Cross-docking is an excellent way to reduce the space required to store goods, inventory management costs, and customer order delivery time. This paper focuses on cost optimization, scheduling incoming and outgoing trucks, and green supply chains with multiple cross-docking. The three objectives are minimizing total operating costs, truck transportation sequences, and carbon emissions within the supply chain. Since the linear programming model is an integer of zero and one and belongs to NP-hard problems, its solution time increases sharply with increasing dimensions. Therefore, the non-dominated sorting genetic algorithm-II (NSGA-II) and the multi-objective particle swarm optimization (MOPSO) were used to find near-optimal solutions to the problem. Then, these algorithms were compared with criteria such as execution time and distance from the ideal point, and the superior algorithm in each criterion was identified.