In this paper we introduce Ant-Q, a family of algorithms which present many similarities with Q-learning (Watkins, 1989), and which we apply to the solution of symmetric and asymmetric instances of the traveling salesman problem (TSP). Ant-Q algorithms were inspired by work on the ant system (AS), a distributed algorithm for combinatorial optimization based on the metaphor of ant colonies which was recently proposed in (Dorigo, 1992; Dorigo, Maniezzo and Colorni, 1996). We show that AS is a...