The distributed assembly permutation flow-shop scheduling problem (DAPFSP) is a typical NP-hard combinatorial optimization problem that has wide applications in advanced manufacturing systems and modern supply chains. In this work, an innovative three-dimensional matrix-cube-based estimation of distribution algorithm (MCEDA) is first proposed for the DAPFSP to minimize the maximum completion time. Firstly, a matrix cube is designed to learn the valuable information from elites. Secondly, a matrix-cube-based probabilistic model with an effective sampling mechanism is developed to estimate the probability distribution of superior solutions and to perform the global exploration for finding promising regions. Thirdly, a problem-dependent variable neighborhood descent method is proposed to perform the local exploitation around these promising regions, and several speedup strategies for evaluating neighboring solutions are utilized to enhance the computational efficiency. Furthermore, the influence of the parameters setting is analyzed by using design-of-experiment technique, and the suitable parameters are suggested for different scale problems. Finally, a comprehensive computational campaign against the state-of-the-art algorithms in the literature, together with statistical analyses, demonstrates that the proposed MCEDA produces better results than the existing algorithms by a significant margin. Moreover, the new best-known solutions for 214 instances are improved.

分布式装配置换流水车间调度问题（DAPFSP）是典型的NP硬组合优化问题，在先进制造系统和现代供应链中具有广泛的应用。在这项工作中，为DAPFSP提出了一种创新的基于三维矩阵的基于分布的估计算法（MCEDA），以最大程度地减少了最大完成时间。首先，设计一个矩阵立方体，以从精英那里学习有价值的信息。其次，建立了基于矩阵多维数据集的概率模型，该概率模型具有有效的采样机制，可以估计优良解的概率分布，并进行全局探索以寻找有希望的区域。第三，提出了一种与问题相关的可变邻域下降方法，以在这些有希望的地区周围进行局部开发，并采用几种加速策略来评估相邻解决方案，以提高计算效率。此外，通过实验设计技术分析了参数设置的影响，并针对不同规模的问题提出了合适的参数。最后，针对文献中最先进算法的全面计算活动以及统计分析表明，提出的MCEDA比现有算法产生的结果要好得多。此外，针对214个实例的新的最著名解决方案得到了改进。并针对不同规模的问题提出了合适的参数。最后，针对文献中最先进算法的全面计算活动以及统计分析表明，提出的MCEDA比现有算法产生的结果要好得多。此外，针对214个实例的新的最著名解决方案得到了改进。并针对不同规模的问题提出了合适的参数。最后，针对文献中最先进算法的全面计算活动以及统计分析表明，提出的MCEDA比现有算法产生的结果要好得多。此外，针对214个实例的新的最著名解决方案得到了改进。