The unrelated parallel machine scheduling problem with sequence-dependent setup times is addressed in this paper with the objective of minimizing the elapsed time between the start and finish of a sequence of operations in a set of unrelated machines. The machines are considered unrelated because the processing speed is dependent on the job being executed and not on the individual machines. Generally, the problem is considered NP-hard, as it presents additional complexity to find an optimal solution in terms of minimum makespan. An advanced firefly metaheuristic optimization algorithm is introduced to solve this problem. The proposed method, called the FAII algorithm, aims to improve the standard firefly algorithm's performance by incorporating an enhanced global best solution update mechanism and adaptive mutation-based local and global neighborhood search scheme to improve the quality of the proposed algorithm's generated solution. Several experiments were conducted to compare and validate the proposed algorithms' performance on small and large-scale benchmarked problem instances with up to 12 machines and 120 job combinations. Moreover, the performance of the FAII was also compared with eight other metaheuristic algorithms, which were implemented in parallel with the FAII method. Furthermore, the numerical results of the FAII algorithm were compared with the scheduling results of six other well-known metaheuristics from the literature. The comparison results backed with a comprehensive statistical analysis showed the superiority of the enhanced FA-style scheduling optimization over other metaheuristic methods to find good quality solutions or minimum average makespan.

中文翻译：

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具有基于自适应变异的邻域搜索的高级离散萤火虫算法，用于调度具有序列相关设置时间的不相关并行机

本文解决了与序列相关的设置时间无关的并行机器调度问题，目的是最小化一组不相关机器中一系列操作的开始和结束之间的经过时间。这些机器被认为是不相关的，因为处理速度取决于正在执行的作业而不是单个机器。通常，该问题被认为是 NP-hard，因为它提出了额外的复杂性来找到最小制造时间方面的最佳解决方案。引入了一种先进的萤火虫元启发式优化算法来解决这个问题。所提出的方法称为 FAII 算法，旨在改进标准萤火虫算法' 通过结合增强的全局最佳解决方案更新机制和基于自适应变异的局部和全局邻域搜索方案来提高所提出算法生成解决方案的质量。进行了几个实验来比较和验证所提出的算法在具有多达 12 台机器和 120 个作业组合的小型和大型基准问题实例上的性能。此外，还将 FAII 的性能与其他八种元启发式算法进行了比较，这些算法与 FAII 方法并行实现。此外，将 FAII 算法的数值结果与文献中其他六种著名的元启发式算法的调度结果进行了比较。