A new model to protect an important node against two threatening agents

One of the main goals of network planners is the protection of important nodes in a network against natural disasters, security threats, attacks, and so on. Given the importance of this issue, a new model is presented in this paper for protecting an important node in a typical network based on a defensive location problem where the two agents threaten this node. The protecting facilities location problem with two agents is formulated as a three-level programming problem. The decision maker in the upper level is a network planner agent. The planner agent wants to find the best possible location of protecting facilities to protect the important node against threatening agents. The second and third levels problems are stated as the shortest path problems in the network in which the edges are weighted with positive values. In this work, the genetic, variable neighborhood search, simulated annealing algorithms are used to solve the problem. The performance of the used metaheuristic algorithms on this class of problems is investigated by a test problem that is generated randomly. Then, t-test are used to compare the performance of these algorithms. The best results are obtained by the variable neighborhood search algorithm.