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Hierarchical Population-Based Learning for Optimal Large-Scale Coalition Structure Generation in Smart Grids

  • Sean Hsin-Shyuan Lee
  • Jeremiah D.  Deng
  • Martin K. Purvis
  • Maryam Purvis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11320)

Abstract

Large-scale Coalition Structure Generation poses a key challenge in the Cooperative Game Theory and Multi-Agent Systems in regards to its NP-hardness computation complexity. State-of-the-art algorithms, such as Optimal Dynamic Programming, could only solve the problem on a small scale, e.g. 20 agents, with an excessive running time. Our previous study, using population-based learning to deal with the same scale outperforms others and revels an immense potential of efficiency and accuracy. In this study we further advance the problem to large scales, e.g. 80 agents. Firstly, we show that our PBIL-MW algorithm could obtain an approximate optimal solution. Furthermore, we propose an approach of Hierarchical PBIL-MW with a termination scheme that achieves significant efficiency with only small losses in terms of accuracy. It provides an alternative solution, while time restriction is essential in some applications.

Keywords

Coalition Structure Generation Optimisation Dynamic Programming Population-Based Incremental Learning Smart Grids Hierarchical Structure 

References

  1. 1.
    Baluja, S.: Population-based incremental learning. a method for integrating genetic search based function optimization and competitive learning. Technical report No. CMU-CS-94-163, Carnegie-Mellon University Pittsburgh Pa Department Of Computer Science (1994)Google Scholar
  2. 2.
    Baluja, S., Caruana, R.: Removing the genetics from the standard genetic algorithm. In: Machine Learning: Proceedings of the Twelfth International Conference, pp. 38–46 (1995)CrossRefGoogle Scholar
  3. 3.
    Bell, E.T.: Exponential numbers. Am. Math. Mon. 41(7), 411–419 (1934). www.jstor.org/stable/2300300MathSciNetCrossRefGoogle Scholar
  4. 4.
    Björklund, A., Husfeldt, T., Koivisto, M.: Set partitioning via inclusion-exclusion. SIAM J. Comput. 39(2), 546–563 (2009)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Chalkiadakis, G., Elkind, E., Wooldridge, M.: Computational aspects of cooperative game theory. Synth. Lect. Artif. Intell. Mach. Learn. 5(6), 1–168 (2011)CrossRefGoogle Scholar
  6. 6.
    Changder, N., Dutta, A., Ghose, A.K.: Coalition structure formation using anytime dynamic programming. In: Baldoni, M., Chopra, A.K., Son, T.C., Hirayama, K., Torroni, P. (eds.) PRIMA 2016. LNCS (LNAI), vol. 9862, pp. 295–309. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-44832-9_18CrossRefGoogle Scholar
  7. 7.
    Lee, S.H.S., Deng, J.D., Peng, L., Purvis, M.K., Purvis, M.: Top-k merit weighting PBIL for optimal coalition structure generation of smart grids. In: Liu, D., Xie, S., Li, Y., Zhao, D., El-Alfy, E.S. (eds.) Neural Information Processing, ICONIP 2017. LNCS, vol. 10637, pp. 171–181. Springer, Heidelberg (2017).  https://doi.org/10.1007/978-3-319-70093-9_18CrossRefGoogle Scholar
  8. 8.
    Lee, S.H.S., Deng, J.D., Purvis, M.K., Purvis, M., Peng, L.: An improved PBIL algorithm for optimal coalition structure generation of smart grids. In: Workshop on Data Ming for Energy Modelling and Optimization (DaMEMO), The 22nd Pacific-Asia Conference on Knowledge Discovery and Data Mining. Springer (2018)Google Scholar
  9. 9.
    Michalak, T., Rahwan, T., Elkind, E., Wooldridge, M., Jennings, N.R.: A hybrid exact algorithm for complete set partitioning. Artif. Intell. 230(C), 14–50 (2016).  https://doi.org/10.1016/j.artint.2015.09.006MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Rahwan, T., Michalak, T.P., Wooldridge, M., Jennings, N.R.: Coalition structure generation: a survey. Artif. Intell. 229, 139–174 (2015)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Sandholm, T., Larson, K., Andersson, M., Shehory, O., Tohmé, F.: Coalition structure generation with worst case guarantees. Artif. Intell. 111(1–2), 209–238 (1999)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Sen, S., Dutta, P.S.: Searching for optimal coalition structures. In: 2000 Proceedings Fourth International Conference on Multiagent Systems, pp. 287–292. IEEE (2000)Google Scholar
  13. 13.
    Shoham, Y., Leyton-Brown, K.: Multiagent Systems: Algorithmic, Game-theoretic, and Logical Foundations. Cambridge University Press, Cambridge (2008)CrossRefGoogle Scholar
  14. 14.
    Yeh, D.Y.: A dynamic programming approach to the complete set partitioning problem. BIT Numer. Math. 26(4), 467–474 (1986)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Sean Hsin-Shyuan Lee
    • 1
  • Jeremiah D.  Deng
    • 1
  • Martin K. Purvis
    • 1
  • Maryam Purvis
    • 1
  1. 1.Department of Information ScienceUniversity of OtagoDunedinNew Zealand

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