Abstract:  To solve the low-carbon scheduling problems of multi-objective flexible job-shops taking equipment energy consumption， tool wear and cutting fluid consumption as carbon emission sources and energy consumption and labor cost as processing cost， a low-carbon scheduling model was formulated to minimize carbon emission， makespan and processing cost， and an improved elitist NSGA-Ⅱ was proposed to solve the problem. Firstly， the chromosome composition was dynamically adjusted by encoding based on Tent chaotic map and greedy decoding based on analytic hierarchy process to improve the quality of the initial population. Then， an adaptive genetic strategy was proposed based on genetic parameters， which adjusted the crossover and mutation rates according to the population evolution stage and the population non dominated state dynamically. Finally， based on external archives an improved elite retention strategy was designed to improve the population diversity in the later stages of the algorithm and retain high-quality individuals in the evolution processes. The effectiveness of the improved algorithm was verified by standard scheduling examples and a practical case. 

Key words: low-carbon, flexible job-shop, multi-objective scheduling, non-dominated sorting genetic algorithm（NSGA-Ⅱ）

摘要： 为解决以设备能耗、刀具磨损和切削液消耗为碳排放来源，能耗和人工费用为加工成本的多目标柔性作业车间低碳调度问题，建立以最小化碳排放量、最长完工时间和加工成本为目标的低碳调度模型，提出一种改进带精英策略的非支配遗传算法（NSGA-Ⅱ）并进行求解。首先通过基于Tent混沌映射的编码与融合了层次分析法（AHP）的贪婪解码来动态调整染色体组成，提高初始种群质量；然后提出了一种基于遗传参数的自适应遗传策略，根据种群进化阶段与种群非支配状态动态调整交叉、变异率；最后设计了一种基于外部档案集的改进精英保留策略，提高了算法后期的种群多样性并保留了进化过程中的优质个体。通过标准调度算例与实际案例验证了改进算法的有效性。

关键词: 低碳, 柔性作业车间, 多目标调度, 非支配排序遗传算法