This work presents a novel parallel branch and bound algorithm to efficiently solve to optimality a set of instances of the multi-objective flexible job shop scheduling problem for the first time, to the very best of our knowledge. It makes use of the well-known NSGA-II algorithm to initialize its upper bound. The algorithm is implemented for shared-memory architectures, and among its main features, it incorporates a grid representation of the solution space, and a concurrent priority queue to store and dispatch the pending sub-problems to be solved. We report the optimal Pareto front of thirteen well-known instances from the literature, which were unknown before. They will be very useful for the scientific community to provide more accuracy in the performance measurement of their algorithms. Indeed, we carefully analyze the performance of NSGA-II on these instances, comparing the results against the optimal ones computed in this work. Extensive computational experiments show that the proposed algorithm using 24 cores achieves a speedup of 15.64x with an efficiency of 65.20%.

这项工作提出了一种新颖的并行分支定界算法，以我们所知，这是第一次有效地将一组多目标柔性作业车间调度问题的实例最佳化。它利用著名的NSGA-II算法来初始化其上限。该算法是针对共享内存体系结构实现的，其主要功能包括合并解决方案空间的网格表示以及并发优先级队列，以存储和调度要解决的未解决子问题。我们从文献中报告了13个著名实例的最优Pareto前沿，这些实例以前是未知的。它们对于科学界非常有用，可以在其算法的性能测量中提供更高的准确性。的确，我们仔细分析了NSGA-II在这些情况下的性能，并将结果与​​这项工作中计算出的最佳结果进行了比较。大量的计算实验表明，所提出的使用24个核的算法实现了15.64倍的加速，效率为65.20％。