### Abstract

We consider the problem of dynamic coalition formation among a set of agents where the value function of the agents is constrained by the size of a coalition - larger coalitions are able to get higher value but only up to a certain fixed coalition size, denoted by n_{max}. The objective of the coalition formation problem is to determine a partition of the agent set that gives the highest utility to the agents. This problem is non-trivial as the set of partitions that needs to be explored grows exponentially with the number of agents and an exhaustive search in the space of partitions makes the problem intractable. To address this problem, we first provide a formal framework to model the coalition formation problem using a coalition structure graph (CSG). We then propose a branch and bound-based algorithm called bottom Up CSG Search that searches for the optimal partitions or coalition structures among the nodes of CSG while pruning nodes that are not going to lead to the optimal coalition structure. We have provided analytical results related to the completeness, anytime-nature and time complexity of our algorithm. We have also verified the performance of our algorithm for a dynamic reformation problem where a set of physical e-puck robots starting from arbitrary positions form sub-teams that maximize their utility. Our experimental results show that our proposed algorithm performs better in terms of number of nodes generated and the time required to find the optimal coalition structure or partition than existing CSG-search algorithms.

Original language | English (US) |
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Title of host publication | Proceedings - 2013 IEEE/WIC/ACM International Conference on Intelligent Agent Technology, IAT 2013 |

Publisher | IEEE Computer Society |

Pages | 329-336 |

Number of pages | 8 |

ISBN (Print) | 9781479929023 |

DOIs | |

State | Published - Jan 1 2013 |

Event | 2013 12th IEEE/WIC/ACM International Conference on Intelligent Agent Technology, IAT 2013 - Atlanta, GA, United States Duration: Nov 17 2013 → Nov 20 2013 |

### Publication series

Name | Proceedings - 2013 IEEE/WIC/ACM International Conference on Intelligent Agent Technology, IAT 2013 |
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Volume | 2 |

### Conference

Conference | 2013 12th IEEE/WIC/ACM International Conference on Intelligent Agent Technology, IAT 2013 |
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Country | United States |

City | Atlanta, GA |

Period | 11/17/13 → 11/20/13 |

### Fingerprint

### ASJC Scopus subject areas

- Artificial Intelligence

### Cite this

*Proceedings - 2013 IEEE/WIC/ACM International Conference on Intelligent Agent Technology, IAT 2013*(pp. 329-336). [6690808] (Proceedings - 2013 IEEE/WIC/ACM International Conference on Intelligent Agent Technology, IAT 2013; Vol. 2). IEEE Computer Society. https://doi.org/10.1109/WI-IAT.2013.128

**A bottom-up search algorithm for dynamic reformation of agent coalitions under coalition size constraints.** / Dutta, Ayan; Dasgupta, Prithviraj; Baca, José; Nelson, Carl A.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - 2013 IEEE/WIC/ACM International Conference on Intelligent Agent Technology, IAT 2013.*, 6690808, Proceedings - 2013 IEEE/WIC/ACM International Conference on Intelligent Agent Technology, IAT 2013, vol. 2, IEEE Computer Society, pp. 329-336, 2013 12th IEEE/WIC/ACM International Conference on Intelligent Agent Technology, IAT 2013, Atlanta, GA, United States, 11/17/13. https://doi.org/10.1109/WI-IAT.2013.128

}

TY - GEN

T1 - A bottom-up search algorithm for dynamic reformation of agent coalitions under coalition size constraints

AU - Dutta, Ayan

AU - Dasgupta, Prithviraj

AU - Baca, José

AU - Nelson, Carl A

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We consider the problem of dynamic coalition formation among a set of agents where the value function of the agents is constrained by the size of a coalition - larger coalitions are able to get higher value but only up to a certain fixed coalition size, denoted by nmax. The objective of the coalition formation problem is to determine a partition of the agent set that gives the highest utility to the agents. This problem is non-trivial as the set of partitions that needs to be explored grows exponentially with the number of agents and an exhaustive search in the space of partitions makes the problem intractable. To address this problem, we first provide a formal framework to model the coalition formation problem using a coalition structure graph (CSG). We then propose a branch and bound-based algorithm called bottom Up CSG Search that searches for the optimal partitions or coalition structures among the nodes of CSG while pruning nodes that are not going to lead to the optimal coalition structure. We have provided analytical results related to the completeness, anytime-nature and time complexity of our algorithm. We have also verified the performance of our algorithm for a dynamic reformation problem where a set of physical e-puck robots starting from arbitrary positions form sub-teams that maximize their utility. Our experimental results show that our proposed algorithm performs better in terms of number of nodes generated and the time required to find the optimal coalition structure or partition than existing CSG-search algorithms.

AB - We consider the problem of dynamic coalition formation among a set of agents where the value function of the agents is constrained by the size of a coalition - larger coalitions are able to get higher value but only up to a certain fixed coalition size, denoted by nmax. The objective of the coalition formation problem is to determine a partition of the agent set that gives the highest utility to the agents. This problem is non-trivial as the set of partitions that needs to be explored grows exponentially with the number of agents and an exhaustive search in the space of partitions makes the problem intractable. To address this problem, we first provide a formal framework to model the coalition formation problem using a coalition structure graph (CSG). We then propose a branch and bound-based algorithm called bottom Up CSG Search that searches for the optimal partitions or coalition structures among the nodes of CSG while pruning nodes that are not going to lead to the optimal coalition structure. We have provided analytical results related to the completeness, anytime-nature and time complexity of our algorithm. We have also verified the performance of our algorithm for a dynamic reformation problem where a set of physical e-puck robots starting from arbitrary positions form sub-teams that maximize their utility. Our experimental results show that our proposed algorithm performs better in terms of number of nodes generated and the time required to find the optimal coalition structure or partition than existing CSG-search algorithms.

UR - http://www.scopus.com/inward/record.url?scp=84893312431&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893312431&partnerID=8YFLogxK

U2 - 10.1109/WI-IAT.2013.128

DO - 10.1109/WI-IAT.2013.128

M3 - Conference contribution

SN - 9781479929023

T3 - Proceedings - 2013 IEEE/WIC/ACM International Conference on Intelligent Agent Technology, IAT 2013

SP - 329

EP - 336

BT - Proceedings - 2013 IEEE/WIC/ACM International Conference on Intelligent Agent Technology, IAT 2013

PB - IEEE Computer Society

ER -