An improved MOEA/D for low-carbon many-objective flexible job shop scheduling problem

•A model with four objectives, minimizing the make-span, delay time, processing load rate and carbon emissions, is built.•An initialization strategy with five heuristic methods is designed, which provides guarantees for the final solutions.•A restart strategy considering both the carbon emissions and the limit of restarts can protect the machine.•A local reinforcement strategy that provides the convergence to a part of inferior sub-problems is designed.