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Finding all the Lower Boundary Points in a Multistate Two-Terminal Network

机译:在多状态两端子网络中查找所有下边界点

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System reliability of a multistate flow network can be computed in terms of all the lower boundary points, called d-minimal paths (d-MPs). Although several algorithms have been proposed in the literature for the d-MP problem, there is still room for improvement upon its solution. Here, some new results are presented to improve the solution of the problem. A simple novel algorithm is improved to solve a Diophantine system that appeared in the d-MP problem. Then, an improved algorithm is proposed for the d-MP problem. It is also explained how the proposed algorithm can be used in order to assess the reliability of some smart grid communication networks. We provide the complexity results and show the main algorithm to be more efficient than the existing ones in terms of execution times through some benchmark networks and a general network example. Moreover, we compare the algorithms through one thousand randomly generated test problems using the Dolan and More's performance profile.
机译:可以根据称为d最小路径(d-MP)的所有下边界点来计算多状态流网络的系统可靠性。尽管在文献中已经针对d-MP问题提出了几种算法,但在其解决方案上仍有改进的余地。在这里,提出了一些新的结果来改进问题的解决方案。改进了一种简单的新颖算法,以解决出现在d-MP问题中的Diophantine系统。然后,针对d-MP问题提出了一种改进的算法。还解释了如何使用所提出的算法来评估某些智能电网通信网络的可靠性。我们提供了复杂性结果,并通过一些基准网络和一个通用网络示例显示了在执行时间方面,主要算法比现有算法更有效。此外,我们使用Dolan and More的性能概况通过一千个随机生成的测试问题对算法进行了比较。

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