A Distributed Branch-and-Bound Algorithm for Computing Optimal Coalition Structures

  • Chattrakul Sombattheera
  • Aditya Ghose
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3955)


Coalition formation is an important area of research in multi-agent systems. Computing optimal coalition structures for a large number of agents is an important problem in coalition formation but has received little attention in the literature. Previous studies assume that each coalition value is known a priori. This assumption is impractical in real world settings. Furthermore, the problem of finding coalition values become intractable for even a relatively small number of agents. This work proposes a distributed branch-and-bound algorithm for computing optimal coalition structures in linear production domain, where each coalition value is not known a priori. The common goal of the agents is to maximize the system’s profit. In our algorithm, agents perform two tasks: i) deliberate profitable coalitions, and ii) cooperatively compute optimal coalition structures. We show that our algorithm outperforms exhaustive search in generating optimal coalition structure in terms of elapses time and number of coalition structures generated.


Exhaustive Search Multiagent System Coalition Formation Coalition Structure Ranking Tree 


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  1. 1.
    Neumann, J.V., Morgenstern, O.: Theory of Games and Economic Behaviour. Princeton University Press, Princeton, New Jersey (1953) (printing, 1963)Google Scholar
  2. 2.
    Kahan, J.P., Rapoport, A.: Theories of Coalition Formation. Lawrence Erlbaum Associates, Hillsdale, New Jersey (1984)MATHGoogle Scholar
  3. 3.
    Sandholm, T., Larson, K., Andersson, M., Shehory, O., Tohm, F.: Worst-case-optimal anytime coalition structure generation. In: Proceedings of AAAI 1998, pp. 46–53 (1998)Google Scholar
  4. 4.
    Sandholm, T., Larson, K., Andersson, M., Shehory, O., Tohm, F.: Coalition structure generation with worst case guarantees. Artif. Intell. 111, 209–238 (1999)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Dang, V.D., Jennings, N.R.: Generating coalition structures with finite bound from the optimal guarantees. In: Third International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS 2004, vol. 2, pp. 564–571 (2004) Google Scholar
  6. 6.
    Shehory, O., Kraus, S.: Feasible formation of coalitions among autonomous agents in non-super-additive environments. Computational Intelligence 15, 218–251 (1999)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Owen, G.: On the core of linear production games. Mathematical Programming 9(1975), 358–370 (1975)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Sombattheera, C., Ghose, A.: A distributed algorithm for coalition formation in linear production domain. In: Proceedings of ICEIS 2006(2006)Google Scholar
  9. 9.
    Shehory, O., Kraus, S.: Task allocation via coalition formation among autonomous agents. In: Proc. of IJCAI, pp. 655–661 (1995)Google Scholar
  10. 10.
    Shehory, O., Kraus, S.: Formation of overlapping coalitions for precedence-ordered task-execution among autonomous agents. In: ICMAS 1996, pp. 330–337 (1996)Google Scholar
  11. 11.
    Sandholm, T., Lesser, V.: Coalition Formation among Bounded Rational Agents. In: 14th International Joint Conference on Artificial Intelligence, pp. 662–669 (1995)Google Scholar
  12. 12.
    Soh, L.K., Tsatsoulis, C.: Satisficing coalition formation among agents. In: Proceedings of the first international joint conference on Autonomous agents and multiagent systems, pp. 1062–1063. ACM Press, New York (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Chattrakul Sombattheera
    • 1
  • Aditya Ghose
    • 1
  1. 1.Decision Systems Lab, School of IT and Computer Science, Faculty of InformaticsUniversity of WollongongAustralia

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