The NP-hard scheduling problem P||C_max encompasses a set of tasks with known execution time which must be mapped to a set of identical machines such that the overall completion time is minimized. In this work, we improve existing techniques for optimal P||C_max scheduling with a combination of new theoretical insights and careful practical engineering. Most importantly, we derive techniques to prune vast portions of the search space of branch-and-bound (BnB) approaches. We also propose improved upper and lower bounding techniques which can be combined with any approach to P||C_max. Moreover, we present new benchmarks for P||C_max, based on diverse application data, which can shed light on aspects which prior synthetic instances fail to capture. In an extensive evaluation, we observe that our pruning techniques reduce the number of explored nodes by 90$\times$ and running times by 12$\times$. Compared to a state-of-the-art ILP-based approach, our approach is preferable for short running time limits and for instances with large makespans.

翻译：NP难调度问题P||C_max涉及一组已知执行时间的任务，这些任务必须被映射到一组同构机器上，以最小化总体完成时间。在本工作中，我们结合新的理论洞见与细致的工程实践，改进了现有最优P||C_max调度技术。最重要的是，我们推导出可大幅剪枝分支定界（BnB）方法搜索空间的技术。我们还提出了改进的上下界技术，这些技术可与任何P||C_max求解方法结合使用。此外，基于多样化的应用数据，我们提出了新的P||C_max基准测试集，这些数据能够揭示以往合成实例未能捕捉的问题特性。在广泛评估中，我们观察到所提出的剪枝技术将探索节点数减少了90倍，运行时间缩短了12倍。与基于整数线性规划（ILP）的先进方法相比，我们的方法在短时间运行限制下以及对于具有较大完工时间的实例更具优势。