An Algorithm for Simultaneous Coalition Structure Generation and Task Assignment

  • Fredrik Präntare
  • Ingemar Ragnemalm
  • Fredrik Heintz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10621)


Groups of agents in multi-agent systems may have to cooperate to solve tasks efficiently, and coordinating such groups is an important problem in the field of artificial intelligence. In this paper, we consider the problem of forming disjoint coalitions and assigning them to independent tasks simultaneously, and present an anytime algorithm that efficiently solves the simultaneous coalition structure generation and task assignment problem. This NP-complete combinatorial optimization problem has many real-world applications, including forming cross-functional teams aimed at solving tasks. To evaluate the algorithm’s performance, we extend established methods for synthetic problem set generation, and benchmark the algorithm using randomized data sets of varying distribution and complexity. Our results show that the presented algorithm efficiently finds optimal solutions, and generates high quality solutions when interrupted prior to finishing an exhaustive search. Additionally, we apply the algorithm to solve the problem of assigning agents to regions in a commercial computer-based strategy game, and empirically show that our algorithm can significantly improve the coordination and computational efficiency of agents in a real-time multi-agent system.


Coalition formation Task allocation Multi-agent system Artificial intelligence Optimal assignment 


  1. 1.
    Bryan, H., Lesser, V.: A survey of multi-agent organizational paradigms. Knowl. Eng. Rev. (2004)Google Scholar
  2. 2.
    Gerkey, B.P., Matar, M.J.: A formal analysis and taxonomy of task allocation in multi-robot systems. Int. J. Robot. Res. 23(9), 943 (2004)Google Scholar
  3. 3.
    Kuhn, H.W.: The Hungarian method for the assignment problem. Naval Res. Logist. Q. 2(1–2), 83–97 (1955)Google Scholar
  4. 4.
    Larson, K.S., Sandholm, T.W.: Anytime coalition structure generation: an average case study. J. Exp. Theoret. Artif. Intell. 12(1), 23–42 (2000)Google Scholar
  5. 5.
    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. International Foundation for Autonomous Agents and Multiagent Systems (2008)Google Scholar
  6. 6.
    Rahwan, T., Michalak, T.P., Wooldridge, M., Jennings, N.R.: Coalition structure generation: a survey. Artif. Intell. 229, 139–174 (2015)Google Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    Shehory, O., Kraus, S.: Methods for task allocation via agent coalition formation. Artif. Intell. 101(1–2), 165–200 (1998)Google Scholar
  9. 9.
    Takaoka, T.: An O(1) time algorithm for generating multiset permutations. In: International Symposium on Algorithms and Computation. Springer (1999)Google Scholar
  10. 10.
    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. Society for Industrial and Applied Mathematics (2009)Google Scholar
  11. 11.
    Yamada, T., Nasu, Y.: Heuristic and exact algorithms for the simultaneous assignment problem. Eur. J. Oper. Res. 123(3), 531–542 (2000)Google Scholar
  12. 12.
    Yang, J., Luo, Z.: Coalition formation mechanism in multi-agent systems based on genetic algorithms. Appl. Soft Comput. 7(2), 561–568 (2007)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Fredrik Präntare
    • 1
  • Ingemar Ragnemalm
    • 1
  • Fredrik Heintz
    • 1
  1. 1.Linköping UniversityLinköpingSweden

Personalised recommendations