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The Shortest Path Problem on a Fuzzy Time-Dependent Network

机译：模糊时变网络上的最短路径问题

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摘要

In this study, we introduce a Fuzzy Time-Dependent Network (FTDN) and analyze its shortest path problem. The FTDN is a network in which travel times are represented as fuzzy sets and are also time-dependent. Under these circumstances, the shortest path problem on the FTDN is far more complex in comparison with the shortest path problem on the existing networks. To highlight the complexity, we show that on the FTDN, "standard" shortest path algorithms (e.g., the well-known Dijkstra algorithm) are not able to come up with solutions. Subsequently, we construct a suitable method which is suitable to deal with the shortest problem. A fuzzy programming model is presented for finding the shortest path on the FTDN. The proposed model is handled through the techniques which combine mechanisms of fuzzy simulation and genetic optimization. In this particular setting, fuzzy simulation is exploited to estimate the value of uncertain functions, which do not exist in the general networks. The proposed model is evaluated with the use of numerical experimentation. A comparative analysis demonstrates that the proposed model leads to the shortest path while standard algorithms are not capable of finding the path when dealing with the shortest path problem on the FTDN.
机译：在这项研究中，我们介绍了模糊时变网络（FTDN），并分析了其最短路径问题。 FTDN是一个网络，其中旅行时间表示为模糊集，并且也与时间有关。在这种情况下，与现有网络上的最短路径问题相比，FTDN上的最短路径问题要复杂得多。为了强调复杂性，我们表明在FTDN上，“标准”最短路径算法（例如著名的Dijkstra算法）无法提出解决方案。随后，我们构建了适合处理最短问题的合适方法。提出了一种模糊规划模型，用于在FTDN上找到最短路径。该模型是通过结合模糊仿真和遗传优化机制的技术来处理的。在这种特定的情况下，利用模糊仿真来估计不确定函数的值，这些不确定函数在一般网络中不存在。使用数值实验对提出的模型进行评估。对比分析表明，提出的模型导致最短路径，而标准算法在处理FTDN上的最短路径问题时却找不到该路径。

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