Because of COVID-19, factories are facing many difficulties, such as shortage of workers and social alienation. How to improve production performance under limited labor resources is an urgent problem for global manufacturing factories. This work studies an energy-efficient job-shop scheduling problem with limited workers. Those workers can have multiskills. A many-objective model with five objectives, that is: 1) makespan; 2) total tardiness; 3) total idle time; 4) total worker cost; and 5) total energy, is built. To solve this many-objective optimization problem (MaOP), a novel fitness evaluation mechanism (FEM) based on fuzzy correlation entropy (FCE) is adopted. Two construction methods for reference points are proposed to build the bridge between MaOP and a fuzzy set. Based on FCE and cluster methods, an environmental selection mechanism (ESM) is proposed to achieve a balance between solution convergence and diversity. With the proposed FEM and ESM, two many-objective evolutionary algorithms are proposed to solve MaOP. The effect of FCE-based FEM and ESM on the performance of algorithms is verified via experiments. The proposed algorithms are compared with four well-known peers to test their performance. The extensive experimental results show that they are very competitive for the considered many-objective scheduling problem.

中文翻译：

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基于参考点的模糊关联熵的多目标进化算法用于节能型有限工人的车间调度。

由于COVID-19，工厂面临许多困难，例如工人短缺和社会疏远。对于全球制造工厂来说，如何在有限的劳动力资源下提高生产性能是一个迫在眉睫的问题。这项工作研究了有限的工人的高能效的车间调度问题。那些工人可以有多种技能。具有五个目标的多目标模型，即：1）制作时间；2）总体迟到；3）总的空闲时间；4）职工总费用；5）建立了总能量。为了解决这个多目标优化问题（MaOP），采用了一种基于模糊相关熵（FCE）的适应性评估机制（FEM）。提出了两种参考点的构造方法来建立MaOP和模糊集之间的桥梁。基于FCE和聚类方法，提出了一种环境选择机制（ESM）以实现解决方案收敛和多样性之间的平衡。通过提出的有限元和ESM，提出了两种多目标进化算法来求解MaOP。通过实验验证了基于FCE的FEM和ESM对算法性能的影响。将所提出的算法与四个著名的对等体进行比较，以测试其性能。大量的实验结果表明，它们在考虑的多目标调度问题上具有很高的竞争力。将所提出的算法与四个著名的对等体进行比较，以测试其性能。大量的实验结果表明，它们在考虑的多目标调度问题上具有很高的竞争力。将所提出的算法与四个著名的对等体进行比较，以测试其性能。大量的实验结果表明，它们在考虑的多目标调度问题上具有很高的竞争力。