Towards swarm calculus: Urn models of collective decisions and universal properties of swarm performance

Swarm Intelligence

Volumn 7, Issue 2-3, 2013, Pages 145-172

  Hamann, Heiko ^a  

^a UNIVERSITY OF PADERBORN   (Germany)

Author keywords

Collective decision making; Positive feedback; Swarm performance; Urn model

Indexed keywords

CALCULATIONS; DECISION MAKING; MARKOV PROCESSES;

COLLECTIVE DECISION; COLLECTIVE DECISION MAKING; DECISION-MAKING SYSTEMS; DESIGN METHODOLOGY; MEAN FIRST PASSAGE TIME; SWARM PERFORMANCE; UNIVERSAL PROPERTIES; URN MODELS;

FEEDBACK;

EID: 84880763810     PISSN: 19353812     EISSN: 19353820     Source Type: Journal    
DOI: 10.1007/s11721-013-0080-0     Document Type: Article

References (56)

1. Arkin, R. C., Balch, T., & Nitz, E. (1993). Communication of behavioral state in multi-agent retrieval tasks. In W. Book & J. Luh (Eds.), IEEE conference on robotics and automation (Vol. 3, pp. 588-594). Los Alamitos: IEEE Press.
2. Berman, S., Kumar, V., & Nagpal, R. (2011). Design of control policies for spatially inhomogeneous robot swarms with application to commercial pollination. In S. LaValle, H. Arai, O. Brock, H. Ding, C. Laugier, A. M. Okamura, S. S. Reveliotis, G. S. Sukhatme, & Y. Yagi (Eds.), IEEE international conference on robotics and automation (ICRA'11) (pp. 378-385). Los Alamitos: IEEE Press.
3. Bjerknes, J. D., & Winfield, A. (2013). On fault-tolerance and scalability of swarm robotic systems. In A. Martinoli, F. Mondada, N. Correll, G. Mermoud, M. Egerstedt, M. A. Hsieh, L. E. Parker, & K. Støy (Eds.), Springer tracts in advanced robotics: Vol. 83. Distributed autonomous robotic systems (DARS 2010) (pp. 431-444). Berlin: Springer.
4. Bjerknes, J. D., Winfield, A., & Melhuish, C. (2007). An analysis of emergent taxis in a wireless connected swarm of mobile robots. In Y. Shi & M. Dorigo (Eds.), IEEE swarm intelligence symposium (pp. 45-52). Los Alamitos: IEEE Press.
5. Breder, C. M. (1954). Equations descriptive of fish schools and other animal aggregations. Ecology, 35(3), 361-370.
6. Camazine, S., Deneubourg, J.-L., Franks, N. R., Sneyd, J., Theraulaz, G., & Bonabeau, E. (2001). Self-organizing biological systems. Princeton: Princeton University Press.
7. Deneubourg, J.-L., Aron, S., Goss, S., & Pasteels, J. M. (1990). The self-organizing exploratory pattern of the Argentine ant. Journal of Insect Behavior, 3(2), 159-168.
8. Dussutour, A., Fourcassié, V., Helbing, D., & Deneubourg, J.-L. (2004). Optimal traffic organization in ants under crowded conditions. Nature, 428, 70-73.
9. Dussutour, A., Beekman, M., Nicolis, S. C., & Meyer, B. (2009). Noise improves collective decision-making by ants in dynamic environments. Proceedings of the Royal Society of London, Series B, 276, 4353-4361.
10. Edelstein-Keshet, L. (2006). Mathematical models of swarming and social aggregation. Robotica, 24(3), 315-324.
11. Ehrenfest, P., & Ehrenfest, T. (1907). Über zwei bekannte Einwände gegen das Boltzmannsche H-Theorem. Physikalische Zeitschrift, 8, 311-314.
12. Eigen, M., & Winkler, R. (1993). Laws of the game: how the principles of nature govern chance. Princeton: Princeton University Press.
13. Galam, S. (2004). Contrarian deterministic effect on opinion dynamics: the "hung elections scenario". Physica A, 333(1), 453-460.
14. Gardiner, C. W. (1985). Handbook of stochastic methods for physics, chemistry and the natural sciences. Berlin: Springer.
15. Gautrais, J., Theraulaz, G., Deneubourg, J.-L., & Anderson, C. (2002). Emergent polyethism as a consequence of increased colony size in insect societies. Journal of Theoretical Biology, 215(3), 363-373.
16. Goldberg, D., & Matarić, M. J. (1997). Interference as a tool for designing and evaluating multi-robot controllers. In B. J. Kuipers & B. Webber (Eds.), Proc. of the fourteenth national conference on artificial intelligence (AAAI'97) (pp. 637-642). Cambridge: MIT Press.
17. Graham, R., Knuth, D., & Patashnik, O. (1998). Concrete mathematics: a foundation for computer science. Reading: Addison-Wesley.
18. Grinstead, C. M., & Snell, J. L. (1997). Introduction to probability. Providence: American Mathematical Society.
19. Hamann, H. (2006). Modeling and investigation of robot swarms. Master's thesis, University of Stuttgart, Germany.
20. Hamann, H. (2010). Space-time continuous models of swarm robotics systems: supporting global-to-local programming. Berlin: Springer.
21. Hamann, H. (2012). Towards swarm calculus: universal properties of swarm performance and collective decisions. In M. Dorigo, M. Birattari, C. Blum, A. L. Christensen, A. P. Engelbrecht, R. Groß, & T. Stützle (Eds.), Lecture notes in computer science: Vol. 7461. Swarm intelligence: 8th international conference, ANTS 2012 (pp. 168-179). Berlin: Springer.
22. Hamann, H., & Wörn, H. (2007). Embodied computation. Parallel Processing Letters, 17(3), 287-298.
23. Hamann, H., & Wörn, H. (2008). Aggregating robots compute: an adaptive heuristic for the Euclidean Steiner tree problem. In M. Asada, J. C. Hallam, J.-A. Meyer, & J. Tani (Eds.), Lecture notes in artificial intelligence: Vol. 5040. The tenth international conference on simulation of adaptive behavior (SAB'08) (pp. 447-456). Berlin: Springer.
24. Hamann, H., Meyer, B., Schmickl, T., & Crailsheim, K. (2010). A model of symmetry breaking in collective decision-making. In S. Doncieux, B. Girard, A. Guillot, J. Hallam, J.-A. Meyer, & J.-B. Mouret (Eds.), Lecture notes in artificial intelligence: Vol. 6226. From animals to animats 11 (pp. 639-648). Berlin: Springer.
25. Hamann, H., Schmickl, T., Wörn, H., & Crailsheim, K. (2012). Analysis of emergent symmetry breaking in collective decision making. Neural Computing & Applications, 21(2), 207-218.
26. Ingham, A. G., Levinger, G., Graves, J., & Peckham, V. (1974). The Ringelmann effect: studies of group size and group performance. Journal of Experimental Social Psychology, 10(4), 371-384.
27. Jeanne, R. L., & Nordheim, E. V. (1996). Productivity in a social wasp: per capita output increases with swarm size. Behavioral Ecology, 7(1), 43-48.
28. Jeanson, R., Fewell, J. H., Gorelick, R., & Bertram, S. M. (2007). Emergence of increased division of labor as a function of group size. Behavioral Ecology and Sociobiology, 62, 289-298.
29. Karsai, I., & Wenzel, J. W. (1998). Productivity, individual-level and colony-level flexibility, and organization of work as consequences of colony size. Proceedings of the National Academy of Sciences of the United States of America, 95, 8665-8669.
30. Kennedy, J., & Eberhart, R. C. (2001). Swarm intelligence. San Mateo: Morgan Kaufmann.
31. Klein, M. J. (1956). Generalization of the Ehrenfest urn model. Physical Review, 103(1), 17-20.
32. Krafft, O., & Schaefer, M. (1993). Mean passage times for triangular transition matrices and a two parameter Ehrenfest urn model. Journal of Applied Probability, 30(4), 964-970.
33. Lerman, K., & Galstyan, A. (2002). Mathematical model of foraging in a group of robots: effect of interference. Autonomous Robots, 13, 127-141.
34. Lerman, K., Martinoli, A., & Galstyan, A. (2005). A review of probabilistic macroscopic models for swarm robotic systems. In E. Şahin & W. M. Spears (Eds.), Lecture notes in computer science: Vol. 3342. Swarm robotics-SAB 2004 international workshop (pp. 143-152). Berlin: Springer.
35. Levenberg, K. (1944). A method for the solution of certain non-linear problems in least squares. Quarterly of Applied Mathematics, 2, 164-168.
36. Lighthill, M. J., & Whitham, G. B. (1955). On kinematic waves. II. A theory of traffic flow on long crowded roads. Proceedings of the Royal Society of London, Series A, 229(1178), 317-345.
37. Mahmassani, H. S., Dong, J., Kim, J., Chen, R. B., & Park, B. (2009). Incorporating weather impacts in traffic estimation and prediction systems. Technical Report FHWA-JPO-09-065, U. S. Department of Transportation.
38. Mallon, E. B., Pratt, S. C., & Franks, N. R. (2001). Individual and collective decision-making during nest site selection by the ant leptothorax albipennis. Behavioral Ecology and Sociobiology, 50, 352-359.
39. Marquardt, D. (1963). An algorithm for least-squares estimation of nonlinear parameters. SIAM Journal on Applied Mathematics, 11(2), 431-441.
40. Milutinovic, D., & Lima, P. (2007). Cells and robots: modeling and control of large-size agent populations. Berlin: Springer.
41. Miramontes, O. (1995). Order-disorder transitions in the behavior of ant societies. Complexity, 1(1), 56-60.
42. Mondada, F., Bonani, M., Guignard, A., Magnenat, S., Studer, C., & Floreano, D. (2005). Superlinear physical performances in a SWARM-BOT. In M. S. Capcarrere (Ed.), Lecture notes in computer science: Vol. 3630. Proc. of the 8th European conference on artificial life (ECAL) (pp. 282-291). Berlin: Springer.
43. Nembrini, J., Winfield, A. F. T., & Melhuish, C. (2002). Minimalist coherent swarming of wireless networked autonomous mobile robots. In B. Hallam, D. Floreano, J. Hallam, G. Hayes, & J.-A. Meyer (Eds.), Proceedings of the seventh international conference on simulation of adaptive behavior on from animals to animats (pp. 373-382). Cambridge: MIT Press.
44. Nicolis, S. C., Zabzina, N., Latty, T., & Sumpter, D. J. T. (2011). Collective irrationality and positive feedback. PLoS ONE, 6, e18901.
45. Okubo, A. (1986). Dynamical aspects of animal grouping: swarms, schools, flocks, and herds. Advances in Biophysics, 22, 1-94.
46. Okubo, A., & Levin, S. A. (2001). Diffusion and ecological problems: modern perspectives. Berlin: Springer.
47. Østergaard, E. H., Sukhatme, G. S., & Matarić, M. J. (2001). Emergent bucket brigading: a simple mechanisms for improving performance in multi-robot constrained-space foraging tasks. In E. André, S. Sen, C. Frasson, & J. P. Müller (Eds.), Proceedings of the fifth international conference on autonomous agents (AGENTS'01) (pp. 29-35). New York: ACM.
48. Prorok, A., Correll, N., & Martinoli, A. (2011). Multi-level spatial models for swarm-robotic systems. The International Journal of Robotics Research, 30(5), 574-589.
49. Saffre, F., Furey, R., Krafft, B., & Deneubourg, J.-L. (1999). Collective decision-making in social spiders: dragline-mediated amplification process acts as a recruitment mechanism. Journal of Theoretical Biology, 198, 507-517.
50. Schmickl, T., & Hamann, H. (2011). BEECLUST: a swarm algorithm derived from honeybees. In Y. Xiao (Ed.), Bio-inspired computing and communication networks. Boca Raton: CRC Press.
51. Schneider-Fontán, M., & Matarić, M. J. (1996). A study of territoriality: the role of critical mass in adaptive task division. In P. Maes, S. W. Wilson, & M. J. Matarić (Eds.), From animals to animats IV (pp. 553-561). Cambridge: MIT Press.
52. Seeley, T. D., Camazine, S., & Sneyd, J. (1991). Collective decision-making in honey bees: how colonies choose among nectar sources. Behavioral Ecology and Sociobiology, 28(4), 277-290.
53. Strogatz, S. H. (2001). Exploring complex networks. Nature, 410(6825), 268-276.
54. Vicsek, T., & Zafeiris, A. (2012). Collective motion. Physics Reports, 517(3-4), 71-140.
55. Wong, G., & Wong, S. (2002). A multi-class traffic flow model-an extension of LWR model with heterogeneous drivers. Transportation Research. Part A, Policy and Practice, 36(9), 827-841.
56. Yates, C. A., Erban, R., Escudero, C., Couzin, I. D., Buhl, J., Kevrekidis, I. G., Maini, P. K., & Sumpter, D. J. T. (2009). Inherent noise can facilitate coherence in collective swarm motion. Proceedings of the National Academy of Sciences of the United States of America, 106(14), 5464-5469.