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Recently, energy-saving scheduling issues have attracted more and more attention in the manufacturing field. Meanwhile, in practical production, maintenance planning is viewed as a vital task in the workshop. However, the existing literature about energy-saving scheduling problems rarely consider the effect of preventive maintenance. Therefore, this paper investigates an energy-saving flexible job shop scheduling problem with preventive maintenance. A mathematical model is proposed considering the minimization of total energy consumption. To solve the problem, a novel discrete elephant herding optimization algorithm (NDEHO) is proposed according to the problem's characteristics. To test the NDEHO's performance, the Taguchi design of experiment approach is adopted to get the best combination of parameters in the algorithm. Numerical experiments are conducted based on twenty-four instances, including four benchmark instances and twenty randomly generated instances. Computational data indicate that NDEHO outperforms other compared algorithms for solving the considered problem. [ABSTRACT FROM AUTHOR]