最小化空闲能耗的多项式时间调度方法：在工业炉上的应用
A polynomial-time scheduling approach to minimise idle energy consumption: an application to an industrial furnace
摘要：
本文提出了一种新的调度方法，以尽量减少能源消耗的机器在其空闲期间。在调度领域中，通常通过定义一小组机器模式（例如，“开”、“关”和“待机”）来对机器的行为进行建模。然后，模式之间的转换表示的静态转换图。在本文中，我们认为，这种类型的模型可能是过于限制某些类型的机器（如炉）。对于这样的机器，我们建议采用完整的时域动态，并将其集成到一个空闲的能量函数。通过这种方式，调度算法可以利用关于机器动态的全部知识，并将此功能中封装的能耗降至最低。在本文中，我们研究了一个调度问题，其中的任务，其特征在于释放时间和最后期限安排在给定的顺序，使机器的空闲能源消耗最小化。我们表明，这个问题可以在多项式时间内解决的空闲能量函数是凹的。为了突出实用性，我们分析了热密集型系统采用钢淬火炉。我们推导出一个能量最优控制律，和相应的闲置能量函数，双线性系统模型近似的动态炉（和其他可能的热密集型系统）。此外，我们证明，闲置能源功能，确实是凹在这种情况下。因此，可以使用所提出的调度算法。数值实验表明，通过使用我们的方法，结合最优控制和最优调度，可以实现更高的节能，相比国家的最先进的调度方法。
英文摘要：
This article presents a novel scheduling approach to minimise the energy consumption of a machine during its idle periods. In the scheduling domain, it is common to model the behaviour of the machine by defining a small set of machine modes, e.g. "on", "off" and "stand-by". Then the transitions between the modes are represented by a static transition graph. In this paper, we argue that this type of model might be too restrictive for some types of machines (e.g. the furnaces). For such machines, we propose to employ the complete time-domain dynamics and integrate it into an idle energy function. This way, the scheduling algorithm can exploit the full knowledge about the machine dynamics with minimised energy consumption encapsulated in this function. In this paper, we study a scheduling problem, where the tasks characterised by release times and deadlines are scheduled in the given order such that the idle energy consumption of the machine is minimised. We show that this problem can be solved in polynomial time whenever the idle energy function is concave. To highlight the practical applicability, we analyse a heat-intensive system employing a steel-hardening furnace. We derive an energy optimal control law, and the corresponding idle energy function, for the bilinear system model approximating the dynamics of the furnace (and possibly other heat-intensive systems). Further, we prove that the idle energy function is, indeed, concave in this case. Therefore, the proposed scheduling algorithm can be used. Numerical experiments show that by using our approach, combining both the optimal control and optimal scheduling, higher energy savings can be achieved, compared to the state-of-the-art scheduling approaches.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
