Improved x-space Algorithm for Min-Max Bilevel Integer Programming with an Application to Misinformation Spread in Social Networks

In this work we propose an improvement of the $x$-space algorithm originally introduced by Tang et al. (2016) for min--max bilevel interdiction problems. This algorithm solves upper and lower bound problems until convergence and requires the dualization of the follower's problem in formulating the lower bound problem. We first reformulate the lower bound problem using the properties of an optimal solution to the original formulation, which makes the dualization step unnecessary. The reformulation makes possible to integrate a greedy covering heuristic into the solution scheme, which results in a considerable reduction of the solution time. The new algorithm is implemented and applied to a recent min--max bilevel interdiction problem that arises in the context of reducing the misinformation spread in social networks. It is also assessed on the benchmark instances of two other bilevel problems: zero-one knapsack problem with interdiction and maximum clique problem with interdiction. Numerical results indicate that the performance of the new algorithm is superior to that of the original algorithm.