Production scheduling is of great significance in improving production effectiveness while the energy-efficient problem is one of most concerned problems for researchers and manufacturers. Thus, this study investigates the energy-efficient distributed permutation flow shop scheduling problem (DPFSP) with the objectives of makespan and energy consumption. The DPFSP is an extension of permutation flow shop problem (PFSP) considering a set of identical factories. This paper presents a multi-objective mixed integer programming model based on the three sub-problems: allocating jobs among factories, scheduling the jobs in each factory and determining speed upon each job. A multi-objective whale swarm algorithm (MOWSA) is proposed to solve this energy-efficient DPFSP. A new problem-dependent local search is developed to improve the exploitation capability of MOWSA. Moreover, the updating exploitation mechanism is presented to enhance energy efficiency without affecting production efficiency. Finally, the extensive comparison experiments are designed to demonstrate the effectiveness of proposed MOWSA, problem-dependent local search and updating exploitation mechanism. The results indicate the effectiveness of MOWSA and the superior performance over NSGA-II, SPEA2, PAES and MDEA, and also demonstrate that the proposed algorithm can significantly reduce the energy consumption compared with other algorithms.

生产计划对提高生产效率具有重要意义，而节能问题是研究人员和制造商最关注的问题之一。因此，本研究以制造期和能耗为目标，研究了节能分布式排列流水车间调度问题（DPFSP）。DPFSP是置换流水车间问题（PFSP）的扩展，它考虑了一组相同的工厂。本文提出了一个基于三个子问题的多目标混合整数规划模型：在工厂之间分配作业，在每个工厂中调度作业以及确定每个作业的速度。提出了一种多目标鲸群算法（MOWSA）来解决这种节能的DPFSP。开发了一种新的基于问题的局部搜索以提高MOWSA的开发能力。此外，提出了更新的开发机制以提高能源效率而不影响生产效率。最后，设计了广泛的比较实验，以证明所提出的MOWSA，依赖问题的局部搜索和更新开发机制的有效性。结果表明，MOWSA的有效性和优于NSGA-II，SPEA2，PAES和MDEA的性能，也证明了与其他算法相比，该算法可以显着降低能耗。设计了广泛的比较实验，以证明所提出的MOWSA，依赖问题的局部搜索和更新开发机制的有效性。结果表明，MOWSA的有效性和优于NSGA-II，SPEA2，PAES和MDEA的性能，也证明了与其他算法相比，该算法可以显着降低能耗。设计了广泛的比较实验，以证明所提出的MOWSA，依赖问题的局部搜索和更新开发机制的有效性。结果表明，MOWSA的有效性和优于NSGA-II，SPEA2，PAES和MDEA的性能，也证明了与其他算法相比，该算法可以显着降低能耗。