Shortest path interdiction problem with convex piecewise-linear costs

This paper addresses a special kind of network optimization interdiction problems, called the shortest path interdiction problem. The problem is a natural extension of the well-known shortest path problem in the presence of an adversary. The adversary is capable of increasing arc lengths under budget and bound constraints in a way that the shortest path length between two prescribed nodes becomes large as much as possible. This paper considers the problem in the case that the increment costs are convex piecewise-linear functions. It presents an algorithm which solve the problem in polynomial time. An applicable example and several randomly generated instances are presented to evaluate the performance and validity of the proposed algorithm.