There are several hard combinatorial optimization problems that, in the context of communication networks, must be solved in short computing times since they are solving real-time critical tasks. This work is focused on the monitor placement problem, whose objective is to locate specific devices, called monitors, in certain nodes of a network with the aim of performing a complete network surveillance. As a consequence of the constant evolution of networks, the problem must be solved in real time if possible. If a solution cannot be found in the allowed computing time, then a penalty is assumed for each link of the network which remains uncovered. A Variable Neighborhood Search algorithm is proposed for solving this problem, comparing it with a hybrid evolutionary algorithm over a set of instances derived from real-life networks to evaluate its efficiency and efficacy.