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. The low-carbon many-objective flexible job shop scheduling problem (LCMa-FJSP) has developed into a major topic of current research owing to global warming and energy crises. In this study on the LCMa-FJSP, a comprehensive scheduling model with four objectives, such as minimizing the completion time, total delay time, processing load rate of the bottleneck machine and total carbon emissions of the system is built. To solve this complex LCMa-FJSP, a novel multi-objective evolutionary algorithm (MOEA) with three modified strategies, named IMOEA/D-HS, is proposed. First, a novel hybrid initialization strategy combining five heuristic methods is used to obtain a reliable initial population. Second, a new restart strategy that considers limited restarts is applied to reduce carbon emissions while protecting the lifetime of the machine. Third, a local reinforcement strategy is proposed that can efficiently improve the convergence of a part of sub-problems identified by distance and angle-based evaluation indicator (APD). To impartially and comprehensively analyze and evaluate the performance of IMOEA/D-HS, it is compared with four state-of-the-art algorithms, i.e., MOEA/D-DRA, MOEA/DD, NSGA-III and RVEA on 15 numerical tests. The results demonstrate that IMOEA/D-HS outperforms these four algorithms in the terms of convergence and diversity, which proves its ability to solve complex LCMa-FJSPs.