During the pandemic of COVID-19, the demand of the transportation systems are drastically changed both qualitatively and quantitatively and the network has become obsolete. In this article, we study the problem of finding an optimal subnetwork that guarantee that (i) the minimal access time from any node of the urban network to the new network is not {\em too large} compared to the original transportation network; (ii) for any itinerary, the delay caused by the deletion of nodes of the transportation network is not {\em too big}; and (iii) the number of nodes of the transportation network has been reduced at least by a known factor. A solution is optimal if it induces a minimal global delay. We model this problem as a Mixed Integer Linear Program before applying the model on a real-case application on the Lyon's buses transportation network.

中文翻译：

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扰动网络上的最优子图

在大流行COVID-19的过程中，运输系统的需求在质量和数量上都发生了巨大变化，网络已经过时。在本文中，我们研究了找到一个可确保以下子网络的最佳子网的问题：（i）与原始交通网络相比，从城市网络的任何节点到新网络的最短访问时间不会{\ em太大}；（ii）对于任何行程，由于删除运输网络的节点而引起的延迟不是{\ em too too}；（iii）运输网络的节点数量至少减少了一个已知因素。如果解决方案引起了最小的全局延迟，则它是最佳的。在将模型应用于里昂的公交运输网络的实际案例之前，我们将此问题建模为混合整数线性程序。