In order to solve the flexible job shop scheduling problem with variable batches, we propose an improved multi-objective optimization algorithm, which combines the idea of inverse scheduling. First, a flexible job shop problem with the variable batches scheduling model is formulated. Second, we propose a batch optimization algorithm with inverse scheduling in which the batch size is adjusted by the dynamic feedback batch adjusting method. Moreover, in order to increase the diversity of the population, two methods are developed. One is the threshold to control the neighborhood updating, and the other is the dynamic clustering algorithm to update the population. Finally, a group of experiments are carried out. The results show that the improved multi-objective optimization algorithm can ensure the diversity of Pareto solutions effectively, and has effective performance in solving the flexible job shop scheduling problem with variable batches.

中文翻译：

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求解可变批次柔性作业车间调度问题的改进多目标优化算法

为了解决具有可变批次的灵活的车间调度问题，我们提出了一种改进的多目标优化算法，该算法结合了逆调度的思想。首先，提出了具有可变批次计划模型的柔性车间作业问题。其次，提出了一种具有逆向调度的批处理优化算法，其中通过动态反馈批处理调整方法来调整批处理大小。此外，为了增加人口的多样性，开发了两种方法。一种是控制邻域更新的阈值，另一种是用于更新种群的动态聚类算法。最后，进行了一组实验。结果表明，改进的多目标优化算法可以有效地保证帕累托解的多样性，