Abstract
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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References
Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)
Pool, I., Kochen, M.: Contacts and influence. Social Networks 1, 1–48 (1978)
Milgram, S.: The small world problem. Psychology Today 2, 60–67 (1967)
Newman, M.E.J., Barabasi, A.L., WattsD., J.: The Structure and Dynamics of Complex Networks. Princeton University Press, Princeton (2006)
Stützle, T., Hoos, H.H.: Improving the Ant System: A detailed report on the MAX–MIN Ant System. Technical Report AIDA-96-12, FG Intellektik, FB Informatik, Technische Universität Darmstadt, Darmstadt, Germany (1996)
Dorigo, M., Gambardella, L.M.: Ant Colony System: A cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation 1(1), 53–66 (1997)
Watts, D.: Networks, dyanmics, and the small-world phenomenon. The American Journal of Sociology 105(2), 493–527 (1999)
Bollobas, B.: Random Graphs. Academic Press, London (1985)
Watts, D., Strogatz, S.: Collective dynamics of ’small-world’ networks. Nature 393, 440–442 (1998)
Abe, S., Suzuki, N.: Small-world structure of earthquake network. Physica A 337, 357–362 (2004)
Montoya, J.M., Solé, R.V.: Small wolrd patterns in food webs. Journal of theoretical biology 214(3), 405–412 (2002)
Stam, C.J.: Functional connectivity patterns of human magnetoencephalographic recordings: a small-world network? Neuroscience Letters 355, 25–28 (2004)
Birattari, M.: The Problem of Tuning Metaheuristics as Seen from a Machine Learning Perspective. PhD thesis, Université Libre de Bruxelles, Brussels, Belgium (2004)
Pellegrini, P.: ACO: parameters, exploration and quality of solutions. PhD thesis, Department of Applied Mathematics, Università Ca’ Foscari, Venice, Italy (2007)
Friedman, J.H.: A variable span smoother. Technical Report 5, Department of Statistics, Stanford University, Stanford, CA, USA (1984)
Halton, J.H., Terada, R.: A fast algorithm for the euclidean traveling salesman problem, optimal with probability one. SIAM J. Comput. 11(1), 28–46 (1982)
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Pellegrini, P., Ellero, A. (2008). The Small World of Pheromone Trails. In: Dorigo, M., Birattari, M., Blum, C., Clerc, M., Stützle, T., Winfield, A.F.T. (eds) Ant Colony Optimization and Swarm Intelligence. ANTS 2008. Lecture Notes in Computer Science, vol 5217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87527-7_41
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DOI: https://doi.org/10.1007/978-3-540-87527-7_41
Publisher Name: Springer, Berlin, Heidelberg
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