The reliability evaluation of multistate networks is primarily using minimal path (cut) vectors, namely d-MPs (d-MCs), which are the lower (upper) boundary vectors that satisfy the system demand d. The generation of all d-MPs (d-MCs) is an NP-hard problem. Thus, it is important to develop an efficient algorithm to search for d-MPs (d-MCs). Existing algorithms searching for d-MPs based on MPs all generate duplicate d-MP candidates, and extra steps are required to detect and remove those duplicates. In this article, we propose an improved algorithm to search for d-MPs for all d levels without generating duplicate d-MP candidates for two-terminal multistate networks. First, we discover and prove the mechanism of generating duplicate d-MP candidates based on MPs. Second, a novel method is proposed to prevent generating duplicate d-MP candidates. Third, an improved algorithm is developed by combining the proposed method to search for d-MPs without generating duplicate d-MP candidates for all d levels. Through computational experiments, it is found that the proposed algorithm is more efficient than existing algorithms for finding all d-MPs for all possible d values.

中文翻译：

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在多状态二端网络中搜索所有 d 级的 d-MP，且不重复


多状态网络的可靠性评估主要使用最小路径（割）向量，即d-MP（d-MC），它是满足系统需求d的下（上）边界向量。所有 d-MP (d-MC) 的生成是一个 NP 难题。因此，开发一种有效的算法来搜索 d-MP（d-MC）非常重要。现有的基于 MP 搜索 d-MP 的算法都会生成重复的 d-MP 候选者，并且需要额外的步骤来检测和删除这些重复项。在本文中，我们提出了一种改进的算法来搜索所有 d 级别的 d-MP，而无需为两端多状态网络生成重复的 d-MP 候选。首先，我们发现并证明了基于 MP 生成重复 d-MP 候选的机制。其次，提出了一种新方法来防止生成重复的 d-MP 候选者。第三，通过结合所提出的方法来搜索 d-MP，而不为所有 d 级别生成重复的 d-MP 候选者，开发了一种改进的算法。通过计算实验，发现所提出的算法比现有算法更有效地找到所有可能的 d 值的所有 d-MP。