This paper presents a new routing protocol for Delay Tolerant Networks (DTNs), based on a distributed swarm intelligence approach. The protocol is called Cultural Greedy Ant (CGrAnt), as it uses a Cultural Algorithm (CA) and a greedy version of the Ant Colony Optimization (ACO) metaheuristic. The term greedy implies the use of a deterministic transition rule to exploit previously found good paths or explore new paths by selecting, from among a set of candidates, the most promising message forwarders. CGrAnt chooses each next node toward the message destination based on pheromone concentration (i.e., global information) whenever it is available. However, as the pheromone is not always available due to connectivity partitions, local information (i.e., heuristic function) captured from DTN nodes also supports a routing decision. Specific metrics and information gathered from the evolution are stored in Situational, Domain, and Historical Knowledge. The knowledge composes the CA's belief space, which is used to guide and improve the search. CGrAnt is compared with two DTN routing protocols (Epidemic and PROPHET) in an activity-based scenario. The results show that CGrAnt achieves a higher delivery ratio and lower byte redundancy than Epidemic and PROPHET.