Bilevel Model for Adaptive Network Flow Problem

We propose to solve the adaptive network flow problem via a bilevel optimization framework. In this problem, we aim to find a flow that is most robust against any k edges attack. There is an exact algorithm proposed to solve the problem in a specific class of input graphs. However, for some input graphs that are not in that class, a flow obtained from the algorithms is sometimes much less robust than the optimal one. That motivates us to find an efficient exact algorithm based on bilevel optimization framework for the problem in this paper. The framework can give us much better results using reasonable amount of times.