This study investigates a flow shop group scheduling problem where both sequence-dependent setup time between groups and round-trip transportation time between machines are considered. The objective is to minimize makespan. To solve the problem, we first develop a mixed integer linear programming model and then propose an efficient co-evolutionary discrete differential evolution algorithm (CDDEA). In the CDDEA, several problem-specific heuristic rules are generated to construct initial population. A novel discrete differential evolution mechanism and a cooperative-oriented optimization strategy are proposed to synergistically evolve both the sequence of jobs in each group and the sequence of groups. In addition, two lower bounds are developed to evaluate the solution quality of CDDEA. Extensive computational experiments are carried out. The results show that the proposed CDDEA is effective in solving the studied problem.

这项研究调查了一个流水车间组调度问题，其中考虑了组间序列相关的建立时间和机器之间的往返运输时间。目的是最小化制造时间。为了解决这个问题，我们首先开发了一个混合整数线性规划模型，然后提出了一种有效的协同进化离散差分进化算法（CDDEA）。在CDDEA中，生成了一些特定于问题的启发式规则来构造初始种群。提出了一种新颖的离散差分进化机制和面向合作的优化策略，以协同地演化每个组中的作业序列和组中的序列。此外，还开发了两个下限来评估CDDEA的溶液质量。进行了广泛的计算实验。