The NP-hard problem of task scheduling with communication delays ($P|prec,c_{ij}|C_{\max }$) is often tackled using approximate methods, but guarantees on the quality of these heuristic solutions are hard to come by. Optimal schedules are therefore invaluable for properly evaluating these heuristics, as well as being very useful for applications in time critical systems. Optimal solving using branch-and-bound algorithms like A* has been shown to be promising in the past, with a state-space model we refer to as exhaustive list scheduling (ELS). The obvious weakness of this model is that it leads to the production of large numbers of duplicate states during a search, requiring special techniques to mitigate this which cost additional time and memory. In this paper we define a new state-space model (AO) in which we divide the problem into two distinct sub-problems: first we decide the allocations of all tasks to processors, and then we order the tasks on their allocated processors in order to produce a complete schedule. This two-phase state-space model offers no potential for the production of duplicates. We also describe how the pruning techniques and optimisations developed for the ELS model were adapted or made obsolete by the AO model. An experimental evaluation shows that the use of this new state-space model leads to a significant increase in the number of task graphs able to be scheduled within a feasible time-frame, particularly for task graphs with a high communication-to-computation ratio. Finally, some advanced lower bound heuristics are proposed for the AO model, and evaluation demonstrates that significant gains can be achieved from the consideration of necessary idle time.

具有通信延迟的任务调度的NP难题（$P|p\mathrm{[R}ËC，C_{\mathrm{一世}Ĵ}|C_{\mathrm{最高}}$）通常使用近似方法解决，但是很难保证这些启发式解决方案的质量。因此，最佳时间表对于正确评估这些启发式方法非常宝贵，并且对于时间紧迫的系统中的应用程序非常有用。过去已经证明，使用像A *这样的分支定界算法进行最优求解是有前途的，我们将状态空间模型称为穷举列表调度（ELS）。该模型的明显缺点是，它会导致在搜索过程中产生大量重复状态，因此需要特殊的技术来减轻这种情况，这会花费额外的时间和内存。在本文中，我们定义了一个新的状态空间模型（AO），其中将问题分为两个不同的子问题：首先，我们确定所有任务对处理器的分配，然后我们在分配的处理器上对任务进行排序，以生成完整的计划。这个两阶段的状态空间模型没有潜力产生重复项。我们还描述了为ELS模型开发的修剪技术和优化如何被AO模型改编或作废。实验评估表明，这种新的状态空间模型的使用导致可以在可行的时间范围内调度的任务图的数量显着增加，尤其是对于具有高通信与计算比的任务图而言。最后，针对AO模型提出了一些高级的下界启发式方法，评估表明，通过考虑必要的空闲时间可以实现显着的收益。