This paper presents a new prediction-based forwarding protocol for the complex and dynamic Delay Tolerant Networks (DTN). The proposed protocol is called GrAnt (Greedy Ant) as it uses a greedy transition rule for the Ant Colony Optimization (ACO) metaheuristic to select the most promising forwarder nodes or to provide the exploitation of good paths previously found. The main motivation for the use of ACO is to take advantage of its population-based search and of the rapid adaptation of its learning framework. Considering data from heuristic functions and pheromone concentration, the GrAnt protocol includes three modules: routing, scheduling, and buffer management. To the best of our knowledge, this is the first unicast protocol that employs a greedy ACO which: (1) infers best promising forwarders from nodes' social connectivity, (2) determines the best paths to be followed to a message reach its destination, while limiting the message replications and droppings, (3) performs message transmission scheduling and buffer space management. GrAnt is compared to Epidemic and PROPHET protocols in two different scenarios: a working day and a community mobility model. Simulation results obtained by ONE simulator show that in both environments, GrAnt achieves higher delivery ratio, lower messages redundancy, and fewer dropped messages than Epidemic and PROPHET.