To ensure robustness in wireless networks, monitoring the network state, performance and functioning of the nodes and links is crucial, especially for critical applications. This paper targets Internet of Things (IoT) networks. In the IoT, devices (things) are vulnerable due to security risks from the Internet. Moreover, they are resource-constrained and connected via lossy links. This paper addresses the optimized scheduling of the monitoring role between the embedded devices in IoT networks. The objective is to minimize energy consumption and communication overhead of monitoring, for each node. Several subsets of the potential monitoring nodes are generated by solving a minimal vertex cover (VC) problem with constraint generation. Assuming periodical functioning, VCs are optimally assigned to time periods in order to distribute the monitoring role throughout the entire network. The assignment of VCs to periods is modeled as a multiobjective generalized assignment problem. To further optimize the energy consumption of the monitors, they are sequenced across time periods to minimize the state transitions of nodes. This part of the problem is modeled as a traveling salesman path problem. The proposed model is tested on randomly generated instances and the experimental results illustrate its effectiveness to optimize the scheduled monitoring for fault tolerance in IoT networks.