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Local Termination Criteria for Swarm Intelligence: A Comparison Between Local Stochastic Diffusion Search and Ant Nest-Site Selection

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Transactions on Computational Collective Intelligence XXXII

Part of the book series: Lecture Notes in Computer Science ((TCCI,volume 11370))

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Abstract

Stochastic diffusion search (SDS) is a global Swarm Intelligence optimisation technique based on the behaviour of ants, rooted in the partial evaluation of an objective function and direct communication between agents. Although population based decision mechanisms employed by many Swarm Intelligence methods can suffer poor convergence resulting in ill-defined halting criteria and loss of the best solution, as a result of its resource allocation mechanism, the solutions found by Stochastic Diffusion Search enjoy excellent stability.

Previous implementations of SDS have deployed stopping criteria derived from global properties of the agent population; this paper examines new local SDS halting criteria and compares their performance with ‘quorum sensing’ (a termination criterion naturally deployed by some species of tandem-running ants). In this chapter we discuss two experiments investigating the robustness and efficiency of the new local termination criteria; our results demonstrate these to be (a) effectively as robust as the classical SDS termination criteria and (b) almost three times faster.

This paper offers extended discussion of results first presented at ICCCI 2016 (Halkidiki) and published in the conference proceedings [11].

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Notes

  1. 1.

    The simplifying assumption is that, by considering only the mean transition of agents between different clusters of agents, rather than the full probability distribution (as investigated in [51]), a sufficiently accurate model of SDS may be obtained.

  2. 2.

    It should be emphasised that this analogy is provided simply to illustrate the communication and feedback mechanisms at the heart of a stochastic diffusion search, and not as a heuristic to be employed by a group of hungry conference delegates.

  3. 3.

    The material in Sect. 6 was included at the suggestion of one of the reviewers of this manuscript; it forms a much extended and adapted version of the ‘practical’ analysis of SDS behaviour first presented by Myatt et al. in [48].

  4. 4.

    Thus multiple testing is very similar to the repeated metrics strategy deployed by real scouts in nest selection, albeit in the latter case scouts assess potential nest sites across a number of metrics using a weighted additive strategy [27].

  5. 5.

    Standard SDS has previously been shown to be a global search algorithm [51] - it will eventually converge to the global best solution in a given search space; by removing agents form the swarm, relative to standard SDS the number of potential agents remaining available for explore-exploit behaviour is reduced.

  6. 6.

    To facilitate the use of homogenous performance metrics, we assume that in a population of k agents, k single asynchronous updates corresponds to one standard synchronous iteration cycle.

  7. 7.

    \(\beta \) defines a “uniform random noise” hypothesis; an aggregate of all the possible hypotheses an agent could have other than the putative solution hypothesis.

  8. 8.

    These parameters define a problem analogous to the search space being infinitely large, wherein the only way an agent can adopt the ‘best’ solution is to receive it via diffusion from an active agent.

References

  1. Aleksander, I., Stonham, T.J.: Guide to pattern recognition using random access memories. Comput. Digit. Tech. 2(1), 29–40 (1979)

    Article  Google Scholar 

  2. Al-Rifaie, M.M., Bishop, J.M.: Stochastic diffusion search review. J. Behav. Robot. 4(3), 155–173 (2013)

    Google Scholar 

  3. Anoop, K., Sumana, A.: Response to a change in the target nest during ant relocation. J. Exp. Biol. 218(6), 887–92 (2015)

    Article  Google Scholar 

  4. Arthur, W.B.: Inductive reasoning and bounded rationality (The El Farol Problem). Amer. Econ. Rev. 84, 406–411 (1994)

    Google Scholar 

  5. Back, T.: Evolutionary Algorithms in Theory and Practice. Oxford University Press, Oxford (1996)

    MATH  Google Scholar 

  6. Beattie, P.D., Bishop, J.M.: Self-localisation in the ‘SENARIO’ autonomous wheelchair. J. Intell. Robot. Syst. 22, 255–267 (1998)

    Article  Google Scholar 

  7. Bishop, J.M.: Stochastic Searching Networks. In: Proceedings of 1st IEE International Conference on Artificial Neural Networks. IEE Conference Publication (313), pp. 329–331. IEE, London (1989)

    Google Scholar 

  8. Bishop, J.M.: Anarchic techniques for pattern classification. Ph.D. thesis, Reading University, UK (1989)

    Google Scholar 

  9. Bishop, J.M., Torr, P.H.S.: The stochastic search network. In: Linggard, R., Myers, D.J., Nightingale, C. (eds.) Neural Networks for Images, Speech and Natural Language. Chapman Hall, New York (1992)

    Google Scholar 

  10. Bishop, J.M., Nasuto, S.J., De Meyer, K.: Dynamic knowledge representation in connectionist systems. In: Dorronsoro, J.R. (ed.) Artificial Neural Networks ICANN. LNCS, vol. 2415, pp. 308–313. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46084-5_51

    Chapter  Google Scholar 

  11. Bishop, J.M., Andrew, O.M., Robinson, E.J.H.: Local termination criteria for stochastic diffusion search: a comparison with the behaviour of ant nest-site selection. In: Nguyen, N., Iliadis, L., Yannis, M., Bogdan, T. (eds.) Computational Collective Intelligence. Lecture Notes in Computer Science, vol. 9875, pp. 474–486. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-319-45243-2_44

    Chapter  Google Scholar 

  12. Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: From Natural to Artificial Systems. Oxford University Press, Oxford (1999)

    MATH  Google Scholar 

  13. Bonabeau, E., Dorigo, M., Theraulaz, G.: Inspiration for optimisation from social insect behaviour. Nature 406, 3942 (2000)

    Article  Google Scholar 

  14. Cao, T.T.: High social density increases foraging and scouting rates and induces polydomy in Temnothorax ants. Behav. Ecol. Sociobiol. 67(11), 1799–1807 (2013)

    Article  Google Scholar 

  15. Carroll, C.R., Janzen, D.H.: Ecology of foraging by ants. Annu. Rev. Ecol. Syst. 4, 231–257 (1973)

    Article  Google Scholar 

  16. Chadab, R., Rettenmeyer, C.: Mass recruitment by army ants. Science 188, 1124–1125 (1975)

    Article  Google Scholar 

  17. Deneubourg, J.L., Pasteels, J.M., Verhaeghe, J.C.: Probabilistic behaviour in ants: a strategy of errors? J. Theor. Biol. 105(2), 259–271 (1983)

    Article  Google Scholar 

  18. Dornhaus, A., Franks, N.R., Hawkins, R.M., Shere, H.N.S.: Ants move to improve: colonies of Leptothorax albipennis emigrate whenever they find a superior nest site. Anim. Behav. 67(5), 959–963 (2004)

    Article  Google Scholar 

  19. Dornhaus, A., Holley, J.A., Pook, V.G., Worswick, G., Franks, N.R.: Why do not all workers work? Colony size and workload during emigrations in the ant Temnothorax albipennis. Behav. Ecol. Sociobiol. 63(1), 43–51 (2008)

    Article  Google Scholar 

  20. Dorigo, M., Maniezzo, V., Colorni, A.: Positive feedback as a search strategy, Dipartimento di Elettronica e Informatica, Politecnico di (1991)

    Google Scholar 

  21. Dorigo, M.: Optimisation, learning and natural algorithms. Politecnico di Italy, Milano (1992)

    Google Scholar 

  22. Dorigo, M., Caro, G.D., Gambardella, L.M.: Ant algorithms for discrete optimisation. Artif. Life 5(2), 137–172 (1999)

    Article  Google Scholar 

  23. Franklin, E.L.: The journey of tandem running: the twists, turns and what we have learned. Insectes Sociaux 61, 1–8 (2014)

    Article  Google Scholar 

  24. Franks, N.R., Dornhaus, A., Metherell, B., Nelson, T., Lanfear, S.A., Symes, W.: Not everything that counts can be counted: ants use multiple metrics for a single nest trait. Proc. R. Soc. Lond. Ser. B 273, 165–169 (2006)

    Google Scholar 

  25. Franks, N.R., Hooper, J.W., Dornhaus, A., Aukett, P.J., Hayward, A.L., Berghoff, S.M.: Reconnaissance and latent learning in ants. Proc. R. Soc. Lond. Ser. B 274(1617), 1505–1509 (2007)

    Google Scholar 

  26. Franks, N.R., et al.: Moving targets: collective decisions and flexible choices in house-hunting ants. Swarm Intell. 1(2), 81–94 (2007)

    Article  Google Scholar 

  27. Franks, N.R., Mallon, E.B., Bray, H.E., Hamilton, M.J., Mischler, T.C.: Strategies for choosing between alternatives with different attributes: exemplified by house-hunting ants. Anim. Behav. 65, 215–223 (2003)

    Article  Google Scholar 

  28. Frank, N.R., et al.: How ants use quorum sensing to estimate the average quality of a fluctuating resource. Sci. Rep. 5, 11890 (2015)

    Article  Google Scholar 

  29. Goldberg, D.: Genetic Algorithms in Search, Optimisation and Machine Learning. Addison Wesley, Reading (1989)

    MATH  Google Scholar 

  30. Goodman, L.J., Fisher, R.C.: The Behaviour and Physiology of Bees. CAB International, Oxon (1991)

    Google Scholar 

  31. Grech-Cini, E.: Locating facial features. Ph.D. dissertation, University of Reading, Reading UK (1995)

    Google Scholar 

  32. Holldobler, B., Wilson, E.O.: The Ants. Springer, Heidelberg (1990)

    Book  Google Scholar 

  33. Holland, J.H.: Adaptation in Natural and Artificial Systems. The University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  34. Fan, H., Hua, Z., Li, J.J., Yuan, D.: Solving a shortest path problem by ant algorithm. In: Proceedings of 2004 International Conference on Machine Learning and Cybernetics, vol. 5, pp. 3174–3177 (2004)

    Google Scholar 

  35. Krieger, M.J., Billeter, J.B., Keller, L.: Ant-like task allocation and recruitment in cooperative robots. Nature 406(6799), 992–995 (2000)

    Article  Google Scholar 

  36. Iosifescu, M.: Finite Markov Processes and Their Applications. Wiley, Chichester (1980)

    MATH  Google Scholar 

  37. Kennedy, J., Eberhart, R.C., Shi, Y.: Swarm Intelligence. Morgan Kauffman, San Francisco (2001)

    Google Scholar 

  38. Kennedy, J., Eberhart, R.C.: Particle swarm optimisation. In: Proceedings of the IEEE International Conference on Neural Networks IV, pp. 1942–1948 (1995)

    Google Scholar 

  39. Kramer, B.H., Scharf, I., Foitzik, S.: The role of per-capita productivity in the evolution of small colony sizes in ants. Behav. Ecol. Sociobiol. 68(1), 41–53 (2013)

    Article  Google Scholar 

  40. De Meyer, K.: Explorations in stochastic diffusion search: soft and hardware implementations of biologically inspired spiking neuron stochastic diffusion networks. Technical report KDM/JMB/2000-1. University of Reading, Reading UK (2000)

    Google Scholar 

  41. De Meyer, K., Bishop, J.M., Nasuto, S.J.: Small world network behaviour of stochastic diffusion search. In: Dorronsoro, J.R. (ed.) Artificial Neural Networks, ICANN, Madrid. LNCS, vol. 2415, pp. 147–152. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46084-5_25

    Chapter  Google Scholar 

  42. De Meyer, K., Nasuto, S.J., Bishop, J.M.: Stochastic diffusion optimisation: the application of partial function evaluation and stochastic recruitment. In: Abraham, A., Grosam, C., Ramos, V. (eds.) Stigmergic Optimisation. SCI, vol. 31, pp. 185–207. Springer, Heidelberg (2006). https://doi.org/10.1007/978-3-540-34690-6_8

    Chapter  Google Scholar 

  43. Kurvers, R.H.J.M., Wolf, M., Krause, J.: Humans use social information to adjust their quorum thresholds adaptively in a simulated predator detection experiment. Behav. Ecol. Sociobiol. 68(3), 449–456 (2014)

    Article  Google Scholar 

  44. Miller, M.B., Bassler, B.L.: Quorum sensing in bacteria. Annu. Rev. Microbiol. 55(1), 165–199 (2001)

    Article  Google Scholar 

  45. Mitrus, S.: The cavity-nest ant Temnothorax crassispinus prefers larger nests. Insectes Sociaux 62(1), 43–49 (2015)

    Article  Google Scholar 

  46. Moglich, M., Maschwitz, U., Holldobler, B.: Tandem calling: a new kind of signal in ant communication. Science 186(4168), 1046–1047 (1974)

    Article  Google Scholar 

  47. Mugford, S.T., Mallon, E.B., Franks, N.R.: The accuracy of Buffon’s needle: a rule of thumb used by ants to estimate area. Behav. Ecol. 12, 655–658 (2001)

    Article  Google Scholar 

  48. Myatt, D.M., Bishop, J.M., Nasuto, S.J.: Minimum stable convergence criteria for stochastic diffusion search. Electron. Lett. 22(40), 112–113 (2004)

    Article  Google Scholar 

  49. Myatt, D., M., Nasuto, S.J., Bishop J.M., : Alternative recruitment strategies for SDS. In: Proceedings of AISB06: Symposium on Exploration vs. Exploitation in Naturally Inspired Search, Bristol, UK, pp. 181–187 (2006)

    Google Scholar 

  50. Nasuto, S.J.: Analysis of resource allocation of stochastic diffusion search. Ph.D. dissertation. University of Reading, Reading UK (1999)

    Google Scholar 

  51. Nasuto, S.J., Bishop, J.M.: Convergence of the stochastic diffusion search. Parallel Algorithms Appl. 14, 89–107 (1999)

    Article  Google Scholar 

  52. Nasuto, S.J., Bishop, J.M., Lauria, S.: Time complexity of stochastic diffusion search. In: Heiss, M. (ed) Proceedings of International ICSC/IFAC Symposium on Neural Computation, Vienna (1998)

    Google Scholar 

  53. Nasuto, S.J., Dautenhahn, K., Bishop, J.M.: Communication as an emergent metaphor for neuronal operation. In: Nehaniv, C. (ed.) Computation for Metaphors, Analogy, and Agents. LNCS, vol. 1562, pp. 365–379. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48834-0_19

    Chapter  Google Scholar 

  54. Nasuto, S.J., Bishop, J.M., De Meyer, K.: Communicating neurons: a connectionist spiking neuron implementation of stochastic diffusion search. Neurocomputing 72(4–6), 704–712 (2008)

    Google Scholar 

  55. Nasuto, S.J., Bishop, J.M.: Steady state resource allocation analysis of the stochastic diffusion search. Biol. Inspired Cogn. Arch. 12, 65–76 (2015)

    Google Scholar 

  56. Neumaier, A.: Complete search in continuous global optimisation and constraint satisfaction. In: Isereles, A. (ed.) Acta Numerica 2004. Cambridge University Press, Cambridge UK (2004)

    Google Scholar 

  57. Pratt, S.C.: Behavioural mechanisms of collective nest-site choice by the ant Temnothorax curvispinosus. Insectes Sociaux 52, 383–392 (2005)

    Article  Google Scholar 

  58. Pratt, S.C.: Quorum sensing by encounter rates in the ant Temnothorax albipennis. Behav. Ecol. 16, 488–496 (2005)

    Article  Google Scholar 

  59. Pratt, S.C., Mallon, E.B., Sumpter, D.J.T., Franks, N.R.: Quorum sensing, recruitment, and collective decision-making during colony emigration by the ant Leptothorax albipennis. Behav. Ecol. Sociobiol. 52(2), 117–127 (2002)

    Article  Google Scholar 

  60. Pratt, S.C., Pierce, N.E.: The cavity-dwelling ant Leptothorax curvispinosus uses nest geometry to discriminate among potential homes. Anim. Behav. 62, 281–287 (2001)

    Article  Google Scholar 

  61. Pratt, S.C., Sumpter, D.J.T., Mallon, E.B., Franks, N.R.: An agent-based model of collective nest site choice by the ant Temnothorax albipennis. Anim. Behav. 70, 1023–1036 (2005)

    Article  Google Scholar 

  62. Robinson, E.J.H., Feinerman, O., Franks, N.R.: How collective comparisons emerge without individual comparisons of the options. Proc. Royal Soc. B 281, 20140737 (2014). https://doi.org/10.1098/rspb.2014.0737

    Article  Google Scholar 

  63. Robinson, E.J.H., Franks, N.R., Ellis, S., Okuda, S., Marshall, J.A.R.: A simple threshold rule is sufficient to explain sophisticated collective decision-making. PLoS One 6, e19981 (2011)

    Article  Google Scholar 

  64. Robinson, E.J.H., Smith, F.D., Sullivan, K.M.E., Franks, N.R.: Do ants make direct comparisons? Proc. Royal Soc. B 276, 2635–2641 (2009)

    Article  Google Scholar 

  65. Sasaki, T., Colling, B., Sonnenschein, A., Boggess, M.M., Pratt, S.C.: Flexibility of collective decision making during house hunting in Temnothorax ants. Behav. Ecol. Sociobiol. 69, 707–714 (2015)

    Article  Google Scholar 

  66. Sasaki, T., Pratt, S.C.: Emergence of group rationality from irrational individuals. Behav. Ecol. 22(2), 276–281 (2011)

    Article  Google Scholar 

  67. Seeley, T.D.: The Wisdom of the Hive. Harvard University Press, Cambridge (1995)

    Google Scholar 

  68. Seeley, T.D., Visscher, P.K.: Quorum sensing during nest-site selection by honeybee swarms. Behav. Ecol. Sociobiol. 56, 594–601 (2004)

    Article  Google Scholar 

  69. Seeley, T.D., Visscher, P.K., Schlegel, T., Hogan, P.M., Franks, N.R., Marshall, J.A.R.: Stop signals provide cross inhibition in collective decision-making by honey bee swarms. Science 335, 108–111 (2012)

    Article  Google Scholar 

  70. Stroeymeyt, N., Robinson, E.J.H., Hogan, P.M., Marshall, J.A.R., Giurfa, M., Franks, N.R.: Experience-dependent flexibility in collective decision-making by house-hunting ants. Behav. Ecol. 22(3), 535–542 (2011)

    Article  Google Scholar 

  71. Sueur, C., Deneubourg, J.L., Petit, O.: Sequence of quorums during collective decision making in macaques. Behav. Ecol. Sociobiol. 64, 1875–1885 (2010)

    Article  Google Scholar 

  72. Sumpter, D.J.T., Pratt, S.C.: Quorum responses and consensus decision making. Proc. R. Soc. B 364(1518), 743–753 (2009)

    Google Scholar 

  73. Ward, A.J.W., Sumpter, D.J.T., Couzin, I.D., Hart, P.J.B., Krause, J.: Quorum decision-making facilitates information transfer in fish shoals. Proc. Nat. Acad. Sci. 105(19), 6948–6953 (2008)

    Article  Google Scholar 

  74. Whitaker, R.M., Hurley, S.: An agent based approach to site selection for wireless networks. In: Proceedings of 2002 ACM Symposium on Applied Computing (Madrid), pp. 574–577. ACM, New York (2002)

    Google Scholar 

  75. Wilson, E.O.: Communication by tandem running in the ant genus Cardiocondyla. Psyche 66(3), 29–34 (1959)

    Article  Google Scholar 

  76. Wilson, E.O.: Chemical communication among workers of the fire ant Solenopsis saevissima (Fr. Smith) 1. The organisation of mass-foraging. Anim. Behav. 10, 134–147 (1962)

    Article  Google Scholar 

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Authors and Affiliations

  1. TCIDA, Goldsmiths, University of London, New Cross, London, UK

    Andrew O. Martin & J. Mark Bishop

  2. York Centre for Complex Systems Analysis and Department of Biology, University of York, York, UK

    Elva J. H. Robinson

  3. Acrefield House, Belle Vue Estate, London, UK

    Darren R. Myatt

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  1. Institute of Informatics, Wrocław University of Technology, Wrocław, Poland

    Ngoc Thanh Nguyen

  2. Swinburne University of Technology, Hawthorn, VIC, Australia

    Ryszard Kowalczyk

  3. Wrocław University of Economics, Wrocław, Poland

    Marcin Hernes

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Martin, A.O., Bishop, J.M., Robinson, E.J.H., Myatt, D.R. (2019). Local Termination Criteria for Swarm Intelligence: A Comparison Between Local Stochastic Diffusion Search and Ant Nest-Site Selection. In: Nguyen, N., Kowalczyk, R., Hernes, M. (eds) Transactions on Computational Collective Intelligence XXXII. Lecture Notes in Computer Science(), vol 11370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-58611-2_3

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