Network connectivity

The problem is to determine whether two points on a network where some of the arcs are destroyed. The set of arcs that are destroyed are unknown. So in order to conclude about connectivity, one has to apply costly inspection tests.There is also probabilistic information for the states of the arcs, being operational or not. The goal is to minimize the expected time to find out a connection between the nodes or conclude that they are un reacheble from each other. One particular application is trying to find a reliable route from population centers to safe locations after a major disaster. 
The project requires reviewing some articles, define variations of the problem and develop algorithmic ideas to solve such a problem. The students are expected to be know about basic optimization concepts and be able to develop/update  codes.