In Software Defined Networks (SDN), intensive traffic monitoring is used to optimize the Quality-of-Service (QoS) of the network paths which are selected. Thus, we introduce the use of the Cognitive Packet Network (CPN) algorithm to SDN in order to optimize the search for new high-QoS paths. We install the CPN algorithm in the Cognitive Routing Engine (CRE), a new application software for SDN, and show that with limited monitoring overhead we are able to determine the near-optimal paths for given QoS metrics that may be proposed by the end users. Measurements that we have conducted on an experimental replica of the GEANT network that our approach uses close to 10 times less monitoring data than conventional SDN, but that we are able to approach the optimal paths within 2%.