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Continuous Approximation of a Discrete Situated and Reactive Multi-agent System: Contribution to Agent Parameterization

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8861))

Abstract

We propose a formal model for situated and reactive multi-agent systems based on correlated discrete random walks. In order to study this model, we construct a continuous approximation ending up on the Fokker-Planck equation. This result allows us to determine an optimal parameterization for the agents, with respect to the system’s objective. Numerical simulations confirm the approach from two points of view, the validity of the continuous model and the optimality of the agents’ parameterization.

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References

  1. Benaim, M., Le Boudec, J.Y.: A class of mean field interaction models for computer and communication systems. Performance Evaluation 65 (2008)

    Google Scholar 

  2. Benaouda, A., Zerhouni, N., Varnier, C.: Une approche multi-agents coopératifs pour la gestion des ressources matérielles dans un contexte multi-sites de e-manufacturing

    Google Scholar 

  3. Bernstein, D.S., Zilberstein, S., Immerman, N.: The complexity of decentralized control of markov decision processes. In: Proc. of the Sixteenth Conference on Uncertainty in Artificial Intelligence (2000)

    Google Scholar 

  4. Boes, J., Migeon, F., Gatto, F.: Self-Organizing Agents for an Adaptive Control of Heat Engines (short paper). In: International Conference on Informatics in Control, Automation and Robotics (ICINCO) (2013)

    Google Scholar 

  5. Bordenave, C., Anantharam, V.: Optimal control of interacting particle systems (June 2007), http://hal.archives-ouvertes.fr/hal-00397327

  6. Bresciani, P., Perini, A., Giorgini, P., Giunchiglia, F., Mylopoulos, J.: Tropos: An agent-oriented software development methodology. JAAMAS 8(3) (2004)

    Google Scholar 

  7. Chen, X., Hambrock, R., Lou, Y.: Evolution of conditional dispersal: a reaction–diffusion–advection model. Journal of Mathematical Biology 57 (2008)

    Google Scholar 

  8. Fadugba, S.E., Edogbanya, O.H., Zelibe, S.C.: Crank Nicolson method for solving parabolic PDEs. Int. Journal of Applied Math. and Modeling IJA2M (2013)

    Google Scholar 

  9. Fechner, G.: Elemente der Psychophysik. No. Bd. 1 in Elemente der Psychophysik, Breitkopf und Härtel (1860)

    Google Scholar 

  10. Gast, N., Gaujal, B.: A mean field approach for optimization in particle systems and applications. ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering) (2009)

    Google Scholar 

  11. Gast, N., Gaujal, B., Le Boudec, J.Y.: Mean field for markov decision processes: from discrete to continuous optimization. IEEE Transactions on Automatic Control (2012)

    Google Scholar 

  12. Guéant, O., Lasry, J.-M., Lions, P.-L.: Mean field games and applications. In: Paris-Princeton Lectures on Mathematical Finance (2011)

    Google Scholar 

  13. Guestrin, C., Koller, D., Parr, R.: Multiagent planning with factored MDPs. In: Neural Information Processing Systems (NIPS) (2001)

    Google Scholar 

  14. Ijspeert, A.J., Martinoli, A., Billard, A., Gambardella, L.M.: Collaboration through the exploitation of local interactions in autonomous collective robotics: The stick pulling experiment. Autonomous Robots 11 (2001)

    Google Scholar 

  15. Jorquera, T., Georgé, J.P., Gleizes, M.P., Régis, C.: A Natural Formalism and a MultiAgent Algorithm for Integrative Multidisciplinary Design Optimization. In: International Conference on Intelligent Agent Technology (IAT) (2013)

    Google Scholar 

  16. Jüngel, A.: Diffusive and nondiffusive population models. In: Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences (2010)

    Google Scholar 

  17. Le Boudec, J.Y., McDonald, D., Mundinger, J.: A generic mean field convergence result for systems of interacting objects. In: Quantitative Evaluation of Systems (QEST). IEEE (2007)

    Google Scholar 

  18. Lepagnot, J., Nakib, A., Oulhadj, H., Siarry, P.: A new multiagent algorithm for dynamic continuous optimization. International Journal of Applied Metaheuristic Computing (IJAMC) (2010)

    Google Scholar 

  19. Lerman, K., Galstyan, A.: A general methodology for mathematical analysis of multi-agent systems. ISI-TR-529, USC Information Sciences Institute, Marina del Rey, CA (2001)

    Google Scholar 

  20. Liggett, T.M.: Particle Systems. Springer (1985)

    Google Scholar 

  21. Liu, J., Jing, H., Tang, Y.: Multi-agent oriented constraint satisfaction. Artificial Intelligence (2002)

    Google Scholar 

  22. Munkres, J.R.: Topology: a first course, vol. 23. Prentice-Hall, Englewood Cliffs (1975)

    MATH  Google Scholar 

  23. Puterman, M.L.: Markov decision processes: discrete stochastic dynamic programming. John Wiley & Sons (2009)

    Google Scholar 

  24. Risken, H.: Fokker-Planck Equation. Springer (1984)

    Google Scholar 

  25. Rougemaille, S., Arcangeli, J.-P., Gleizes, M.-P., Migeon, F.: ADELFE design, AMAS-ML in action. In: Artikis, A., Picard, G., Vercouter, L. (eds.) ESAW 2008. LNCS, vol. 5485, pp. 105–120. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  26. Shigesada, N., Kawasaki, K., Teramoto, E.: Spatial segregation of interacting species. Journal of Theoretical Biology 79 (1979)

    Google Scholar 

  27. Shoham, Y., Leyton-Brown, K.: Multiagent systems: Algorithmic, game-theoretic, and logical foundations. Cambridge University Press (2009)

    Google Scholar 

  28. Spaan, M.T., Melo, F.S.: Interaction-driven markov games for decentralized multiagent planning under uncertainty. In: Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems, vol. 1 (2008)

    Google Scholar 

  29. Spicher, A., Fatès, N.A., Simonin, O., et al.: From reactive multi-agent models to cellular automata-illustration on a diffusion-limited aggregation model. In: Proceedings of ICAART 2009 (2009)

    Google Scholar 

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Stuker, S., Adreit, F., Couveignes, JM., Gleizes, MP. (2014). Continuous Approximation of a Discrete Situated and Reactive Multi-agent System: Contribution to Agent Parameterization. In: Dam, H.K., Pitt, J., Xu, Y., Governatori, G., Ito, T. (eds) PRIMA 2014: Principles and Practice of Multi-Agent Systems. PRIMA 2014. Lecture Notes in Computer Science(), vol 8861. Springer, Cham. https://doi.org/10.1007/978-3-319-13191-7_30

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  • DOI: https://doi.org/10.1007/978-3-319-13191-7_30

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13190-0

  • Online ISBN: 978-3-319-13191-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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