The aim of Traffic Engineering is to provide routing configurations in networks such that the used resources are minimized while maintaining a high level of quality of service (QoS). Among the optimization problems arising in this domain, we address in this paper the one related to setting weights in networks that are based on shortest path routing protocols (OSPF, IS-IS). Finding weights that induce efficient routing paths (e.g that minimize the maximum congested link) is a computationally hard problem. We propose to use Monte Carlo Search for the first time for this problem. More specifically we apply Nested Rollout Policy Adaptation (NRPA). We also extend NRPA with the force_exploration algorithm to improve the results. In comparison to other algorithms NRPA scales better with the size of the instance and can be easily extended to take into account additional constraints (cost utilization, delay,. . .) or linear/non-linear optimization criteria. For difficult instances the optimum is not known but a lower bound can be computed. NRPA gives results close to the lower bound on a standard dataset of telecommunication networks.