Model Checking the Ant Colony Optimisation

  • Lucio Mauro Duarte
  • Luciana Foss
  • Flávio Rech Wagner
  • Tales Heimfarth
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 329)


We present a model for the travelling salesman problem (TSP) solved using the ant colony optimisation (ACO), a bio-inspired mechanism that helps speed up the search for a solution and that can be applied to many other problems. The natural complexity of the TSP combined with the self-organisation and emergent behaviours that result from the application of the ACO make model-checking this system a hard task. We discuss our approach for modelling the ACO in a well-known probabilistic model checker and describe results of verifications carried out using our model and a couple of probabilistic temporal properties. These results demonstrate not only the effectiveness of the ACO applied to the TSP, but also that our modelling approach for the ACO produces the expected behaviour. It also indicates that the same modelling could be used in other scenarios.


ant colony optimisation self-organisation emergent behaviour probabilistic model checking 


  1. 1.
    Olariu, S., Zomaya, A.: Handbook of Bioinspired Algorithms and Applications. Oxford University Press, Oxford (2007)Google Scholar
  2. 2.
    Heimfarth, T., Danne, K., Rammig, F.: An OS for Mobile Ad hoc Networks Using Ant Based Hueristic to Distribute Mobile Services. In: ICAS-ICNS, p. 77 (2005)Google Scholar
  3. 3.
    Janacik, P., Heimfarth, T., Rammig, F.: Emergent Topology Control Based on Division of Labour in Ants. In: AINA 2006, vol. 1, pp. 733–740 (2006)Google Scholar
  4. 4.
    Camazine, S., Deneubourg, J., Franks, N., et al.: Self-Organization in Biological Systems. Princeton University Press, Princeton (2001)Google Scholar
  5. 5.
    Lewes, G.: Problems of Life and Mind. Kessinger Publishing (2004)Google Scholar
  6. 6.
    De Wolf, T., Holvoet, T.: Emergence Versus Self-Organisation: Different Concepts But Promising When Combined Engineering. In: Brueckner, S.A., Di Marzo Serugendo, G., Karageorgos, A., Nagpal, R. (eds.) ESOA 2005. LNCS (LNAI), vol. 3464, pp. 1–15. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Vardi, M.: Automatic Verification of Probabilistic Concurrent Finite State Programs. In: 26th Annual Symp. on Found. of Comp. Sci., pp. 327–338 (1985)Google Scholar
  8. 8.
    Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. The MIT Press, Cambridge (1999)Google Scholar
  9. 9.
    Applegate, D.L., Bixby, R.E., Chvátal, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study. Princeton University Press, Princeton (2006)MATHGoogle Scholar
  10. 10.
    Dorigo, M., Gambardella, L.: Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem. IEEE Trans. on Evol. Comp. 1, 53–66 (1997)CrossRefGoogle Scholar
  11. 11.
    Kwiatkowska, M., Norman, G., Parker, D.: PRISM: Probabilistic Symbolic Model Checker. In: Field, T., Harrison, P.G., Bradley, J., Harder, U. (eds.) TOOLS 2002. LNCS, vol. 2324, pp. 200–204. Springer, Heidelberg (2002)Google Scholar
  12. 12.
    Hansson, H., Jonsson, B.: A Logic for Reasoning About Time and Reliability. Formal Aspects of Computing 6, 512–535 (1994)MATHCrossRefGoogle Scholar
  13. 13.
    Ben-Ari, M., Manna, Z., Pnueli, A.: The Temporal Logic of Branching Time. Acta Informatica 20, 207–226 (1983)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Balasubramaniam, S., Botvich, D., Donnelly, et al.: Biologically Inspired Self-Governance and Self-Organisation for Autonomic Networks. In: 1st Intl. Conf. on Bio-Inspired Mod. of Net., Inform. and Comp. Sys., pp. 1–30 (2006)Google Scholar
  15. 15.
    Stauffer, A., Mange, D., Rossier, J., Vannel, F.: Bio-inspired Self-Organizing Cellular Systems. BioSystems 94, 164–169 (2008)CrossRefGoogle Scholar
  16. 16.
    Cardelli, L.: Brane Calculi. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 257–278. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Păun, G.: Computing with Membranes. Journal of Computing and System Sciences 61(1), 108–143 (2000)MATHCrossRefGoogle Scholar
  18. 18.
    Shang, G., Lei, Z., Fengting, Z., et al.: Solving Traveling Salesman Problem by Ant Colony Optimization Algorithm with Association Rule. In: 3rd Int. Conf. on Natural Computation, pp. 693–698 (2007)Google Scholar
  19. 19.
    Li, Y., Gong, S.: Dynamic Ant Colony Optimization for TSP. Int. J. Adv. Manuf. Technol. 22, 528–533 (2003)CrossRefGoogle Scholar
  20. 20.
    Ugur, A., Aydin, D.: An Interactive Simulation and Analysis Software for Solving TSP using Ant Colony Optimization Algorithms. Adv. in Eng. Soft. 40, 341–349 (2009)MATHCrossRefGoogle Scholar

Copyright information

© IFIP 2010

Authors and Affiliations

  • Lucio Mauro Duarte
    • 1
  • Luciana Foss
    • 2
  • Flávio Rech Wagner
    • 1
  • Tales Heimfarth
    • 3
  1. 1.Institute of InformaticsFederal University of Rio Grande do SulBrazil
  2. 2.Institute of Physics and Mathematics, DINFOFederal University of PelotasBrazil
  3. 3.Dep. of Computer ScienceFederal University of LavrasBrazil

Personalised recommendations