Ant System is a general purpose algorithm inspired by the study of the behavior of Ant Colonies. It is based on a cooperative search paradigm that is applicable to the solution of combinatorial optimization problems. In this paper we introduce MAX --MIN Ant System, an improved version of basic Ant System, and report our results for its application to symmetric and asymmetric instances of the well known Traveling Salesman Problem. We show how MAX --MIN Ant System can be significantly improved extending it with local search heuristics. Our results clearly show that MAX --MIN Ant System has the property of effectively guiding the local search heuristics towards promising regions of the search space by generating good initial tours. I. Introduction The Ant System algorithm, originally introduced in [3], [4], is a new cooperative search algorithm inspired by the behavior of real ants. Ants are able to find good solutions to shortest path problems between a food source and their home colony...