Second Order Swarm Intelligence

  • Vitorino Ramos
  • David M. S. Rodrigues
  • Jorge Louçã
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8073)


An artificial Ant Colony System (ACS) algorithm to solve general-purpose combinatorial Optimization Problems (COP) that extends previous AC models [21] by the inclusion of a negative pheromone, is here described. Several Traveling Salesman Problem (TSP) were used as benchmark. We show that by using two different sets of pheromones, a second-order coevolved compromise between positive and negative feedbacks achieves better results than single positive feedback systems. The algorithm was tested against known NP-complete combinatorial Optimization Problems, running on symmetrical TSPs. We show that the new algorithm compares favorably against these benchmarks, accordingly to recent biological findings by Robinson [26,27], and Grüter [28] where “No entry” signals and negative feedback allows a colony to quickly reallocate the majority of its foragers to superior food patches. This is the first time an extended ACS algorithm is implemented with these successful characteristics.


Self-Organization Stigmergy Co-Evolution Swarm Intelligence Dynamic Optimization Foraging Cooperative Learning Combinatorial Optimization problems Symmetrical Traveling Salesman Problems (TSP) 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, MI (1975)Google Scholar
  2. 2.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, USA (1989)zbMATHGoogle Scholar
  3. 3.
    Fogel, D.B.: Evolutionary Computation. IEEE Press, Piscataway (1995)Google Scholar
  4. 4.
    Siarry, P., Michalewicz, Z.: Advances in Metaheuristics for Hard Optimization. Springer (2008) Google Scholar
  5. 5.
    Gonzalez, T.F. (ed.): Approximation Algorithms and Metaheuristics. CRC Press (2007)Google Scholar
  6. 6.
    Alba, E.: Parallel Metaheuristics. A New Class of Algorithms. Wiley, Cambridge (2005)zbMATHCrossRefGoogle Scholar
  7. 7.
    Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: From Natural to Artificial Systems. Santa Fe Institute series in the Sciences of Complexity. Oxford Univ. Press, New York (1999)zbMATHGoogle Scholar
  8. 8.
    Blum, C., Merkle, D. (eds.): Swarm Intelligence: Introduction and Applications. Natural Computing Series. Springer, Heidelberg (2008)Google Scholar
  9. 9.
    Camazine, S., Deneubourg, J.-L., Franks, N., Sneyd, J., Theraulaz, G., Bonabeau, E.: Self-Organization in Biological Systems. Princeton University Press, Princeton (2003)zbMATHGoogle Scholar
  10. 10.
    Chialvo, D.R., Millonas, M.M.: How Swarms build Cognitive Maps. In: Steels, L. (ed.) The Biology and Technology of Intelligent Autonomous Agents. NATO ASI Series, vol. 144, pp. 439–450 (1995)Google Scholar
  11. 11.
    Millonas, M.M.: A Connectionist-type model of Self-Organized Foraging and Emergent Behavior in Ant Swarms. J. Theor. Biol. 159, 529 (1992)CrossRefGoogle Scholar
  12. 12.
    Ramos, V., Fernandes, C., Rosa, A.C.: On Self-Regulated Swarms, Societal Memory, Speed and Dynamics. In: Rocha, L.M., Yaeger, L.S., Bedau, M.A., Floreano, D., Goldstone, R.L., Vespignani, A. (eds.) Artificial Life X - Proc. of the Tenth Int. Conf. on the Simulation and Synthesis of Living Systems, Bloomington, Indiana, USA, pp. 393–399. MIT Press (2006)Google Scholar
  13. 13.
    Dorigo, M., Maniezzo, V., Colorni, A.: Positive Feedback as a Search Strategy, Technical report 91-016, Dipartimento di Elettronica, Politecnico di Milano, Italy (1991)Google Scholar
  14. 14.
    Dorigo, M., Di Caro, G.: The Ant Colony Optimization Metaheuristic. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, p. 11. McGraw-Hill, New York (1999)Google Scholar
  15. 15.
    Dorigo, M., Di Caro, G., Gambardella, L.M.: Ant algorithms for Discrete Optimization. Artificial Life 5(2), 137 (1999)CrossRefGoogle Scholar
  16. 16.
    Grassé, P.P.: La reconstruction du nid et les coordinations interindividuelles chez Bellicositermes natalensis et Cubitermes sp. La théorie de la Stigmergie: Essai d’interpretation des termites constructeurs. Insect Sociaux 6, 41–83 (1959)CrossRefGoogle Scholar
  17. 17.
    Theraulaz, G., Bonabeau, E.: A Brief History of Stigmergy. Artificial Life, Special Issue Dedicated to Stigmergy 5(2), 97–116 (1999)CrossRefGoogle Scholar
  18. 18.
    Abraham, A., Grosan, C., Ramos, V.: Stigmergic Optimization. SCI, vol. 31. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  19. 19.
    Diaf, M., Hammouche, K., Siarry, P.: From the Real Ant to the Artificial Ant. In: Nature-Inspired Informatics for Intelligent Applications and Knowledge Discovery, pp. 298–322 (2010)Google Scholar
  20. 20.
    Dorigo, M., Maniezzo, V., Colorni, A.: Ant System: Optimization by a Colony of Cooperating Agents. IEEE Trans. Syst., Man, and Cybern. - Part B 26(1), 29 (1996)CrossRefGoogle Scholar
  21. 21.
    Dorigo, M., Gambardella, L.M.: Ant Colony System: A Cooperative Learning approach to the Travelling Salesman Problem. IEEE Trans. Evol. Computation 1(1), 53 (1997)CrossRefGoogle Scholar
  22. 22.
    Stützle, T., Hoos, H.H.: MAX-MIN Ant System. Future Generation Comput. Syst. 16(8), 889 (2000)CrossRefGoogle Scholar
  23. 23.
    Gambardella, L.M., Dorigo, M.: Ant-Q: A Reinforcement Learning Approach to the Traveling Salesman Problem. In: Prieditis, A., Russell, S. (eds.) Proceedings of the Twelfth International Conference on Machine Learning, ML 1995, Tahoe City, CA, pp. 252–260. Morgan Kaufmann (1995)Google Scholar
  24. 24.
    Lawler, E.L., Lenstra, J.K., Rinnooy-Kan, A.H.G., Shmoys, D.B.: The Travelling Salesman Problem. Wiley, New York (1985)Google Scholar
  25. 25.
    Ramos, V., Almeida, F.: Artificial Ant Colonies in Digital Image Habitats: A Mass Behavior Effect Study on Pattern Recognition. In: Dorigo, M., Middendorf, M., Stützle, T. (eds.) From Ant Colonies to Artificial Ants – ANTS 2000 - 2nd Int. Wkshp on Ant Algorithms, pp. 113–116 (2000)Google Scholar
  26. 26.
    Robinson, E.J.H., et al.: Insect communication - ‘No entry’ signal in ant foraging. Nature 438(7067), 442 (2005)CrossRefGoogle Scholar
  27. 27.
    Robinson, E.J.H., Jackson, D., Hocombe, M., Ratnieks, F.L.W.: No entry signal in ant foraging (Hymenoptera: Formicidae): new insights from an agent-based model. Myrmecological News 10, 120 (2007)Google Scholar
  28. 28.
    Grüter, C., Schürch, R., Czaczkes, T.J., Taylor, K., Durance, T., et al.: Negative Feedback Enables Fast and Flexible Collective Decision-Making in Ants. PLoS ONE 7(9), e44501 (2012), doi:10.1371/journal.pone.0044501 Google Scholar
  29. 29.
    Rodrigues, D.M.S., Louçã, J., Ramos, V.: From Standard to Second-Order Swarm Intelligence Phase-space Maps. In: Thurner, S. (ed.) 8th European Conference on Complex Systems, poster, Vienna, Austria (September 2011)Google Scholar
  30. 30.
    Ramos, V., Rodrigues, D.M.S., Louçã, J.: Spatio-Temporal Dynamics on Co-Evolved Stigmergy. In: Thurner, S. (ed.) 8th European Conference on Complex Systems, poster, Vienna, Austria (September 2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Vitorino Ramos
    • 1
  • David M. S. Rodrigues
    • 2
    • 3
  • Jorge Louçã
    • 3
  1. 1.LaSEEB – Evolutionary Systems and Biomedical Eng. Lab., ISR – Robotic and Systems InstituteTechnical University of Lisbon (IST)LisbonPortugal
  2. 2.The Open UniversityMilton KeynesUnited Kingdom
  3. 3.The Observatorium - ISCTE-IULLisbon University Institute (IUL)LisbonPortugal

Personalised recommendations