In recent years, people have paid more and more attention to traditional manufacturing's environmental impact, especially in terms of energy consumption and related emissions of carbon dioxide. Except for adopting new equipment, production scheduling could play an important role in reducing the total energy consumption of a manufacturing plant. Machine tools waste a considerable amount of energy because of their underutilization. Consequently, energy saving can be achieved by switching machines to standby or off when they lay idle for a comparatively long period. Herein, we first introduce the objectives of minimizing non-processing energy consumption, total weighted tardiness and earliness, and makespan into a typical production scheduling model-the job shop scheduling problem, based on a machine status switching framework. The multi-objective genetic algorithm U-NSGA-III combined with MME (a heuristic algorithm combined with the MinMax (MM) and Nawaz-Enscore-Ham (NEH) algorithms) population initialization method is used to solve the problem. The multi-objective optimization algorithm can generate a Pareto set of solutions so that production managers can flexibly select a schedule from these non-dominated schedules based on their priorities. Three sets of numerical experiments have been carried out on the extended Taillard benchmark to verify this three-objective model's effectiveness and the multi-objective optimization algorithm. The results show that U-NSGA-III has obtained better Pareto solutions in most test problem instances than NSGA-II and NSGA-III. Furthermore, the non-processing energy consumption is reduced by 46%-69%, which is 13-83% of the total energy consumption.