Using ant colony systems with pheromone dispersion in the traveling salesman problem

Here we investigate the use of Ant Colony Systems (ACS) for the Traveling Salesman Problem (TSP). We propose the use of a modified ACS for graph problems in which we allow an artificial ant to lay down pheromone, not only on the edges in its path, but also on edges close to it: the closer a given edge is to one of those in the ant's path, the more pheromone it receives. The notion of edge closeness in the TSP takes into account not only the closeness among the nodes composing the edges but also the edges orientation.