An Efficient Method for Selecting a Reliable Path under Uncertainty Conditions

In a network that has the potential to block some paths, choosing a reliable path, so that its survival probability is high, is an important and practical issue. The importance of this issue is very considerable in critical situations such as natural disasters, floods and earthquakes. In the case of the reliable path, survival or blocking of each arc on a network in critical situations is an uncertain parameter that is estimated and among all the paths that connect two distinct points, the route that is most likely to be survived is selected. Since decisions about choosing routes are dependent on other factors, such as distance, cost, or duration of the route, each of these indicators can be added to the problem as some constraints. For modeling the problem, considering the probability of survival of any arc, a reliable path is defined as a path that the product of probability of its arcs is as close as possible to one. Then the logarithm function is used to linearize the probability multiplication and the problem model is converted to the constrained shortest path model form. Finally, an algorithm is provided to solve the proposed model, which in any iteration using logical cuts, eliminates the obtained suboptimal paths and approaches the optimal solution. The results of applying this method on some networks with different structure and size show that the proposed algorithm is able to achieve a path that can be expected with high probability of surviving in critical conditions and its distant does not exceed the specified limit.