A Network-On-Chip (NoC) platform is an emerging topology for large-scale applications. It provides a required number of resources for critical and excessive computations. However, the computations may be interrupted by faults occurring at run-time. Hence, reliability of computations as well as efficient resource management at run-time are crucial for such many-core NoC systems. To achieve this, we utilize an agent-based management system where agents are organized in a three-level hierarchy. We propose to incorporate reallocation and reconfiguration procedures into agents hierarchy such that fault-tolerance mechanisms can be executed at run-time. Task reallocation enables local reconfiguration of a core allowing it to be eventually reused in order to restore the original performance of communication and computations. The contributions of this paper are: (i) an algorithm for initial application mapping with spare cores, (ii) a multi-objective algorithm for efficient utilization of spare cores at run-time in order to enhance fault-tolerance while maintaining efficiency of communication and computations at an adequate level, (iii) an algorithm integrating the local reconfiguration procedure and (iv) formal modeling and verification of the dynamic agent-based NoC management architecture incorporating these algorithms within the Event-B framework.