Ant Colony Optimization (ACO) has been applied successfully in solving the Traveling Salesman Problem. Marco Dorigo et al. used Ant System (AS) to explore the Symmetric Traveling Salesman Problem and found that the use of a small number of elitist ants can improve algorithm performance. The elitist ants take advantage of global knowledge of the best tour found to date and reinforce this tour with pheromone in order to focus future searches more effectively. This paper discusses an alternative approach where only local information is used to reinforce good tours thereby enhancing the ability of the algorithm for multiprocessor or actual network implementation. In the model proposed, the ants are endowed with a memory of their best tour to date. The ants then reinforce this “local best tour” with pheromone during an iteration to mimic the search focusing of the elitist ants. The environment used to simulate this model is described and compared with Ant System.