Ant-Q: A Reinforcement Learning approach to the traveling salesman problem

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 particular instance of the Ant-Q family, and that there are instances of this family which perform better than AS. We experimentally investigate the functioning of Ant-Q and we show that the results obtained by Ant-Q on symmetric TSP's are competitive with those obtained by other heuristic approaches based on neural networks or local search. Finally, we apply Ant-Q to some difficult asymmetric TSP's obtaining very good results: Ant-Q was able to find solutions of a quality which usually can be found..