Abstract As an important part of batch chemical industry scheduling problems, the multi-stage multi-product batch plant scheduling problem (MMSP) has been widely studied for decades. This problem is characterized by multiple stages with non-identical parallel units and operate based on customer orders. In this paper, we focus on the large scale MMSP and treat the minimization of make-span as the objective function. An efficient cooperative hybrid evolutionary algorithm is proposed based on the framework of cooperative co-evolution. First, a novel two-line encoding scheme is developed to represent the unit assignment and sequencing for orders respectively. Second, modified estimation of distribution algorithm (EDA) and differential evolutionary (DE) operations are proposed according to the feature of MMSP. EDA operation with a novel population-based incremental learning strategy is applied to handle the unit assignment variables. And novel DE operation based on a novel encoding method is adopted to deal with sequence variables. Then, two selection strategies are applied to preserve optimal and sub-optimal solutions for the proposed algorithm. The critical path based local search algorithm is adopted to further improve the efficiency of local optimization. The proposed algorithm has been tested by several instances with different sizes and characteristics. The numerical results and comparisons show that the proposed work is very competitive in solving large scale MMSP.

中文翻译：

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大规模多阶段多产品批量工厂调度问题的协同混合进化算法

摘要 作为批量化工调度问题的重要组成部分，多阶段多产品批量工厂调度问题（MMSP）已被广泛研究了几十年。这个问题的特点是多阶段具有不同的并联单元，并根据客户订单进行操作。在本文中，我们专注于大规模 MMSP 并将最小化跨度作为目标函数。基于协同协同进化的框架，提出了一种高效的协同混合进化算法。首先，开发了一种新颖的两行编码方案来分别表示订单的单元分配和排序。其次，根据MMSP的特点，提出了改进的分布估计算法（EDA）和差分进化（DE）操作。应用具有新颖的基于群体的增量学习策略的 EDA 操作来处理单元分配变量。并且采用基于新颖编码方法的新颖DE操作来处理序列变量。然后，应用两种选择策略来保留所提出算法的最优解和次优解。采用基于关键路径的局部搜索算法，进一步提高了局部优化的效率。所提出的算法已经通过具有不同大小和特征的多个实例进行了测试。数值结果和比较表明，所提出的工作在解决大规模 MMSP 方面非常有竞争力。然后，应用两种选择策略来保留所提出算法的最优解和次优解。采用基于关键路径的局部搜索算法，进一步提高了局部优化的效率。所提出的算法已经通过具有不同大小和特征的多个实例进行了测试。数值结果和比较表明，所提出的工作在解决大规模 MMSP 方面非常有竞争力。然后，应用两种选择策略来保留所提出算法的最优解和次优解。采用基于关键路径的局部搜索算法，进一步提高了局部优化的效率。所提出的算法已经通过具有不同大小和特征的多个实例进行了测试。数值结果和比较表明，所提出的工作在解决大规模 MMSP 方面非常有竞争力。