In the flowshop scheduling literature, the insertion-based neighborhood search method is often considered to obtain high-quality solutions. It will lead to expending extensive computational effort when evaluating the objective function. Rapid evaluation methods based on Taillard's acceleration can reduce the time complexity of function evaluation. However, existing rapid evaluation methods cannot be applied directly to the distributed flowshop group scheduling problem (DFGSP), especially to minimize the total tardiness time objective. Thus, we first proposed two theorems and their proofs based on the critical machine. Then, two rapid evaluation methods based on these theorems are proposed to accelerate the evaluation of the objective. Considering the multiple coupled sub-problems in the DFGSP, we proposed a cooperative iterated greedy algorithm (CIG) combining two rapid evaluation methods, in which inter-group and intra-group neighborhood search strategies are proposed to enhance the search depth and breadth. Comprehensive statistical experiments show that computational effort is extensively decreased in the calculation of total tardiness time, and the CIG algorithm significantly outperforms the eight compared algorithms.

在流水作业调度文献中，通常考虑使用基于插入的邻域搜索方法来获得高质量的解决方案。在评估目标函数时，这将导致花费大量的计算工作。基于Taillard加速的快速评估方法可以降低函数评估的时间复杂度。然而，现有的快速评估方法不能直接应用于分布式流水作业组调度问题（DFGSP），特别是最小化总延迟时间目标。因此，我们首先基于临界机提出了两个定理及其证明。然后，基于这些定理提出了两种快速评估方法来加速目标的评估。考虑DFGSP中的多个耦合子问题，我们提出了一种结合两种快速评估方法的合作迭代贪婪算法（CIG），其中提出了组间和组内邻域搜索策略以增强搜索深度和广度。综合统计实验表明，CIG算法在总迟到时间的计算中大大减少了计算量，并且CIG算法显着优于八种对比算法。