中文摘要：

最可靠最大流是不确定图中可靠性最高的最大流,它是传统最大流问题在不确定图上的自然延伸.现有的最可靠最大流算法SDBA时间复杂性较高,无法满足实际中不同应用的需求,为此,文中提出一种具有普遍适用性的最可靠最大流解决方案.该方案包含面向不同需求的3种算法：基于负权群落消去的NWCE算法、基于时间约束优先单环消去的SPEA-t算法和基于概率阈值约束优先单环消去的SPEA-p算法.其中,NWCE算法借鉴最小费用最大流的＂流平移＂思想并基于文中提出的负权群落概念,在辅助剩余图中不断地消去可使可靠性增加而流量不变的负权群落,可证当消去所有负权群落时对应的最大流即为最可靠最大流.根据负权群落中由单环组成的群落占很高比例且相对于多环组成的群落更易查找和消去的性质,同时考虑到NWCE算法为了获得最优解,往往为了消去最后少数几个对概率提高贡献很小的负权群落却花费了很长时间的现象,提出SPEA-t和SPEA-p两种快速近似算法,前者是以规定时间内尽可能逼近最优解为目标,后者是以最少时间达到预设的概率阈值为目标,它们都采用了优先消去概率-时间效益较好的单环群落的策略,加快对最优解的逼近速度,减少或放弃时间开销较大的多环群落的消去,以满足那些对算法时间性能要求很高而结果以近似最优即可的应用需求.实验表明,相对于SDBA算法,NWCE算法结合概率剪枝策略在时间性能上有了数量级的提高,而SPEA-t算法和SPEA-p算法则具有更高的性能和更好的适用性.

英文摘要：

This paper presents an effective scheme to solve the problem of the most reliable maximum flow（MRMF）.Three algorithms are studied,called NWCE,SPEA-t and SPEA-p respectively.NWCE starts with an arbitrary maximum flow,and then obtains the next maximum flow with more reliability by eliminating the negative weight communities iteratively.This procedure will get the MRMF when there is no negative weight community.SPEA-t is a quick approximate algorithm with a time constraint and SPEA-pis also a quick approximate algorithm with a probability constraint.The two approximate algorithms prefer eliminating the negative weight communities composed of single-circles,and can achieve an approximate answer quickly for avoiding expensive search for negative weight communities composed of multi-circles.Theseapproximate algorithms can be applied to large-scale network.Finally,experimental results show the effectiveness and efficiency of the proposed algorithms.