Advertisement

An Anytime Algorithm for Simultaneous Coalition Structure Generation and Assignment

  • Fredrik Präntare
  • Fredrik Heintz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11224)

Abstract

A fundamental problem in artificial intelligence is how to organize and coordinate agents to improve their performance and skills. In this paper, we consider simultaneously generating coalitions of agents and assigning the coalitions to independent tasks, and present an anytime algorithm for the simultaneous coalition structure generation and assignment problem. This optimization problem has many real-world applications, including forming goal-oriented teams of agents. To evaluate the algorithm’s performance, we extend established methods for synthetic problem set generation, and benchmark the algorithm against CPLEX using randomized data sets of varying distribution and complexity. We also apply the algorithm to solve the problem of assigning agents to regions in a major commercial strategy game, and show that the algorithm can be utilized in game-playing to coordinate smaller sets of agents in real-time.

Keywords

Coalition structure generation Assignment problem 

Notes

Acknowledgements

This work was partially supported by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation.

References

  1. 1.
    Andrews, G., Eriksson, K.: Integer Partitions. Cambridge University Press, Cambridge (2004)CrossRefGoogle Scholar
  2. 2.
    Buro, M.: Real-time strategy games: a new AI research challenge. In: International Joint Conference on Artificial Intelligence, pp. 1534–1535 (2003)Google Scholar
  3. 3.
    Chalkiadakis, G., Elkind, E., Markakis, E., Polukarov, M., Jennings, N.R.: Cooperative games with overlapping coalitions. J. Artif. Intell. Res. 39, 179–216 (2010)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Chu, P.C., Beasley, J.E.: A genetic algorithm for the generalised assignment problem. Comput. Oper. Res. 24(1), 17–23 (1997)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Dang, V.D., Dash, R.K., Rogers, A., Jennings, N.R.: Overlapping coalition formation for efficient data fusion in multi-sensor networks. In: AAAI, vol. 6, pp. 635–640 (2006)Google Scholar
  6. 6.
    Dukeman, A., Adams, J.A.: Hybrid mission planning with coalition formation. Auton. Agents Multi-Agent Syst. 31(6), 1424–1466 (2017)CrossRefGoogle Scholar
  7. 7.
    Gerkey, B.P., Matarić, M.J.: A formal analysis and taxonomy of task allocation in multi-robot systems. Int. J. Robot. Res. 23(9), 939–954 (2004)CrossRefGoogle Scholar
  8. 8.
    Habib, F.R., Polukarov, M., Gerding, E.H.: Optimising social welfare in multi-resource threshold task games. In: An, B., Bazzan, A., Leite, J., Villata, S., van der Torre, L. (eds.) PRIMA 2017. LNCS (LNAI), vol. 10621, pp. 110–126. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-69131-2_7 CrossRefGoogle Scholar
  9. 9.
    Han, Z., Poor, H.V.: Coalition games with cooperative transmission: a cure for the curse of boundary nodes in selfish packet-forwarding wireless networks. IEEE Trans. Commun. 57(1), 203–213 (2009)CrossRefGoogle Scholar
  10. 10.
    Horling, B., Lesser, V.: A survey of multi-agent organizational paradigms. Knowl. Eng. Rev. 19(4), 281–316 (2004)CrossRefGoogle Scholar
  11. 11.
    Kelso, A.S., Crawford, V.P.: Job matching, coalition formation, and gross substitutes. Econometrica: J. Econ. Soc. 1483–1504 (1982)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kuhn, H.W.: The hungarian method for the assignment problem. Nav. Res. Logist. (NRL) 2(1–2), 83–97 (1955)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Larson, K.S., Sandholm, T.W.: Anytime coalition structure generation: an average case study. J. Exp. Theor. Artif. Intell. 12(1), 23–42 (2000)CrossRefGoogle Scholar
  14. 14.
    Leibo, J.Z., Zambaldi, V., Lanctot, M., Marecki, J., Graepel, T.: Multi-agent reinforcement learning in sequential social dilemmas. In: Proceedings of the 16th Conference on Autonomous Agents and MultiAgent Systems, pp. 464–473. International Foundation for Autonomous Agents and Multiagent Systems (2017)Google Scholar
  15. 15.
    Munkres, J.: Algorithms for the assignment and transportation problems. J. Soc. Ind. Appl. Math. 5(1), 32–38 (1957)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Pentico, D.W.: Assignment problems: a golden anniversary survey. Eur. J. Oper. Res. 176(2), 774–793 (2007)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Präntare, F., Ragnemalm, I., Heintz, F.: An algorithm for simultaneous coalition structure generation and task assignment. In: An, B., Bazzan, A., Leite, J., Villata, S., van der Torre, L. (eds.) PRIMA 2017. LNCS (LNAI), vol. 10621, pp. 514–522. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-69131-2_34 CrossRefGoogle Scholar
  18. 18.
    Rahwan, T., Jennings, N.R.: An improved dynamic programming algorithm for coalition structure generation. In: Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems, vol. 3, pp. 1417–1420. International Foundation for Autonomous Agents and Multiagent Systems (2008)Google Scholar
  19. 19.
    Rahwan, T., Michalak, T.P., Jennings, N.R.: A hybrid algorithm for coalition structure generation. In: AAAI, pp. 1443–1449 (2012)Google Scholar
  20. 20.
    Rahwan, T., Michalak, T.P., Wooldridge, M., Jennings, N.R.: Coalition structure generation: a survey. Artif. Intell. 229, 139–174 (2015)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Rahwan, T., Ramchurn, S.D., Jennings, N.R., Giovannucci, A.: An anytime algorithm for optimal coalition structure generation. J. Artif. Intell. Res. 34, 521–567 (2009)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Ray, D., Vohra, R.: Coalition formation. In: Handbook of Game Theory with Economic Applications, vol. 4, pp. 239–326. Elsevier (2015)Google Scholar
  23. 23.
    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
  24. 24.
    Shehory, O., Kraus, S.: Methods for task allocation via agent coalition formation. Artif. Intell. 101(1–2), 165–200 (1998)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Stojmenović, I., Zoghbi, A.: Fast algorithms for genegrating integer partitions. Int. J. Comput. Math. 70(2), 319–332 (1998)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Takaoka, T.: An O(1) time algorithm for generating multiset permutations. ISAAC 1999. LNCS, vol. 1741, pp. 237–246. Springer, Heidelberg (1999).  https://doi.org/10.1007/3-540-46632-0_25 CrossRefGoogle Scholar
  27. 27.
    Ueda, S., Iwasaki, A., Yokoo, M., Silaghi, M.C., Hirayama, K., Matsui, T.: Coalition structure generation based on distributed constraint optimization. In: AAAI, vol. 10, pp. 197–203 (2010)Google Scholar
  28. 28.
    Williams, A.: Loopless generation of multiset permutations using a constant number of variables by prefix shifts. In: Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 987–996. Society for Industrial and Applied Mathematics (2009)Google Scholar
  29. 29.
    Yamada, T., Nasu, Y.: Heuristic and exact algorithms for the simultaneous assignment problem. Eur. J. Oper. Res. 123(3), 531–542 (2000)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Yamamoto, J., Sycara, K.: A stable and efficient buyer coalition formation scheme for e-marketplaces. In: Proceedings of the Fifth International Conference on Autonomous Agents, pp. 576–583. ACM (2001)Google Scholar
  31. 31.
    Yeh, D.Y.: A dynamic programming approach to the complete set partitioning problem. BIT Numer. Math. 26(4), 467–474 (1986)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Zhang, Z., Song, L., Han, Z., Saad, W.: Coalitional games with overlapping coalitions for interference management in small cell networks. IEEE Trans. Wireless Commun. 13(5), 2659–2669 (2014)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Linköping UniversityLinköpingSweden

Personalised recommendations