Abstract In a flexible job-shop scheduling problem (FJSP), an operation can be assigned to one of a set of eligible machines. Therefore, the problem is to simultaneously determine both the assignment of operations to machines and their sequences. Accordingly, the solution encoding of many regular genetic algorithms (RGAs) developed in literature has two parts: one part encodes the assignment decision and the other the sequencing decision. The genetic search determines both the assignment and the sequencing of the operations simultaneously through a random process guided by the principles of natural selection and evolution. In this paper, we develop a two-stage genetic algorithm (2SGA) with the first stage being different from a typical RGA for FJSP found in the literature. The first stage of 2SGA has a solution encoding that only dictates the sequence in which the operations are considered for assignment. Whenever an operation is considered for assignment, the machine that can complete this operation the soonest is selected while taking into account the operations that are already assigned to this machine. The order in which the operations are assigned to machines determines their sequence. The second stage, starting from the solutions of the first stage, follows the common approach of genetic algorithm for FJSP to enable the algorithm to search the entire solution space by including solutions that might have been excluded because of the greedy nature of the first stage. We tested the proposed algorithm by solving many benchmark problems and several other large-size problems of a comprehensive FJSP model with sequence-dependent setup, machine release date, and lag-time. The performance of the proposed two-stage algorithm greatly exceeds that of the common approach of genetic algorithm for FJSP. We also show that further performance improvement of the proposed algorithm can be achieved using high-performance parallel computation. However, the more interesting result we found was that the sequential version of the proposed algorithm (using a single CPU) outperformed a parallel implementation of the regular genetic algorithm that uses many CPUs. We also noted that the superiority of the proposed algorithm over RGA is much greater when solving large-size problems, rendering the proposed algorithm as a viable choice for solving practical problems that are typically encountered in industries.

中文翻译：

---

一种有效的两阶段遗传算法，用于具有序列相关的附加/分离设置、机器发布日期和滞后时间的灵活作业车间调度问题

摘要 在灵活作业车间调度问题 (FJSP) 中，可以将操作分配给一组符合条件的机器中的一个。因此，问题是同时确定机器的操作分配及其顺序。因此，文献中开发的许多常规遗传算法（RGA）的解决方案编码有两部分：一部分编码分配决策，另一部分编码排序决策。遗传搜索通过以自然选择和进化原理为指导的随机过程同时确定操作的分配和顺序。在本文中，我们开发了一种两阶段遗传算法 (2SGA)，第一阶段与文献中发现的 FJSP 的典型 RGA 不同。2SGA 的第一阶段有一个解决方案编码，它只规定了考虑分配操作的顺序。每当考虑分配操作时，在考虑已经分配给该机器的操作的同时，选择能够最快完成该操作的机器。操作分配给机器的顺序决定了它们的顺序。第二阶段，从第一阶段的解开始，遵循 FJSP 遗传算法的通用方法，使算法能够搜索整个解空间，包括可能因第一阶段的贪婪性质而被排除的解。我们通过解决具有序列相关设置、机器发布日期和滞后时间的综合 FJSP 模型的许多基准问题和其他几个大型问题来测试所提出的算法。所提出的两阶段算法的性能大大超过了 FJSP 遗传算法的常用方法。我们还表明，使用高性能并行计算可以实现所提出算法的进一步性能改进。然而，我们发现更有趣的结果是，所提出算法的顺序版本（使用单个 CPU）优于使用多个 CPU 的常规遗传算法的并行实现。我们还注意到，在解决大型问题时，所提出的算法比 RGA 的优越性要大得多，