The Small World of Pheromone Trails

In this paper we consider $\cal M\!AX\!$---$\cal MI\!N\!$ Ant System and Ant Colony System. They are generally recognized to be the best performing algorithms of the Ant Colony Optimization family. They are characterized by a quite different way for dealing with the pheromone trail. We propose an experimental analysis for observing whether this difference impacts significantly on the characteristics of the pheromone distributions produced during the runs. The results obtained are analyzed by using some concepts derived by the literature on small-world networks. It comes out that ants actually build small-world pheromone graphs during their runs. This behavior is interpreted here as a sort of decomposition of the instances tackled.

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