The energy-efficient distributed job shop scheduling problem (EEDJSP) is studied in this paper with the criteria of minimizing both makespan and energy consumption. A mathematical model is presented and an effective modified multi-objective evolutionary algorithm with decomposition (MMOEA/D) is proposed. First, the encoding scheme and decoding scheme are designed based on the characteristics of the EEDJSP. Second, several initialization rules are fused together to produce a diverse population with certain diversity. Third, a collaborative search is proposed to exchange the information between individuals for exploring good solutions. Fourth, three problem-specific local intensification heuristics are designed. Moreover, an adaptive selection strategy is proposed to adjust the utilization of local search operators dynamically. Besides, an energy adjustment strategy is designed for further improvement. We carry out extensive numerical tests with the benchmarking instances. The effectiveness of local intensification as well as energy adjustment strategy is verified via the statistical comparisons. It also shows that the MMOEA/D outperforms other algorithms.

本文以最小化制造时间和能耗为标准，研究了节能分布式作业车间调度问题（EEDJSP）。提出了一个数学模型，并提出了一种有效的改进的多目标分解进化算法（MMOEA / D）。首先，根据EEDJSP的特性设计编码方案和解码方案。第二，将几个初始化规则融合在一起，以产生具有一定多样性的多样化种群。第三，提出了协作搜索以在个人之间交换信息以探索好的解决方案。第四，设计了三种针对特定问题的局部强化启发法。此外，提出了一种自适应选择策略来动态调整本地搜索运算符的利用率。除了，设计了能量调整策略以进一步改进。我们使用基准测试实例进行了广泛的数值测试。通过统计比较验证了局部集约化以及能源调整策略的有效性。它还显示MMOEA / D优于其他算法。