### Abstract

In this paper, we propose a Quantifie Distributed Constraint Optimization problem (QDCOP) that extends the framework of Distributed Constraint Optimization problems (DCOPs). DCOPs have been studied as a fundamental model of multi-agent cooperation. In traditional DCOPs, all agents cooperate to optimize the sum of their cost functions. However, in practical systems some agents may desire to select the value of their variables without cooperation. In special cases, such agents may take the values with the worst impact on the quality of the result reachable by the optimization process. We apply existential/universal quantifier to distinct uncooperative variables. A universally quantifie variable is left unassigned by the optimization as the result has to hold when it takes any value from its domain, while an existentially quantifie variable takes exactly one of its values for each context. Similar classes of problems have recently been studied as (Distributed) Quantifie Constraint Problems, where the variables of the CSP have quantifiers All constraints should be satisfie independently of the value taken by universal variables. We propose a QDCOP that applies the concept of game tree search to DCOP. If the original problem is a minimization problem, agents that own universally quantifie variables may intend to maximize the cost value in the worst case. Other agents normally intend to optimize the minimizing problems. Therefore, only the bounds, especially the upper bounds, of the optimal value are guaranteed. The purpose of the new class of problems is to compute such bounds, as well as to compute sub-optimal solutions. For the QDCOP, we also propose several methods that are based on min-max/alpha-beta and ADOPT algorithms.

Original language | English |
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Title of host publication | 9th International Joint Conference on Autonomous Agents and Multiagent Systems 2010, AAMAS 2010 |

Publisher | International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS) |

Pages | 1023-1030 |

Number of pages | 8 |

ISBN (Print) | 9781617387715 |

Publication status | Published - Jan 1 2010 |

Event | 9th International Joint Conference on Autonomous Agents and Multiagent Systems 2010, AAMAS 2010 - Toronto, ON, Canada Duration: May 10 2010 → … |

### Publication series

Name | Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS |
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Volume | 2 |

ISSN (Print) | 1548-8403 |

ISSN (Electronic) | 1558-2914 |

### Other

Other | 9th International Joint Conference on Autonomous Agents and Multiagent Systems 2010, AAMAS 2010 |
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Country | Canada |

City | Toronto, ON |

Period | 5/10/10 → … |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Artificial Intelligence

### Cite this

*9th International Joint Conference on Autonomous Agents and Multiagent Systems 2010, AAMAS 2010*(pp. 1023-1030). (Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS; Vol. 2). International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).

**A quantified distributed constraint optimization problem.** / Matsui, Toshihiro; Matsuo, Hirohsi; Hirayama, Katsutoshi; Silaghi, Marius Cǎlin; Yokoo, Makoto; Baba, Satomi.

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

*9th International Joint Conference on Autonomous Agents and Multiagent Systems 2010, AAMAS 2010.*Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS, vol. 2, International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS), pp. 1023-1030, 9th International Joint Conference on Autonomous Agents and Multiagent Systems 2010, AAMAS 2010, Toronto, ON, Canada, 5/10/10.

}

TY - GEN

T1 - A quantified distributed constraint optimization problem

AU - Matsui, Toshihiro

AU - Matsuo, Hirohsi

AU - Hirayama, Katsutoshi

AU - Silaghi, Marius Cǎlin

AU - Yokoo, Makoto

AU - Baba, Satomi

PY - 2010/1/1

Y1 - 2010/1/1

N2 - In this paper, we propose a Quantifie Distributed Constraint Optimization problem (QDCOP) that extends the framework of Distributed Constraint Optimization problems (DCOPs). DCOPs have been studied as a fundamental model of multi-agent cooperation. In traditional DCOPs, all agents cooperate to optimize the sum of their cost functions. However, in practical systems some agents may desire to select the value of their variables without cooperation. In special cases, such agents may take the values with the worst impact on the quality of the result reachable by the optimization process. We apply existential/universal quantifier to distinct uncooperative variables. A universally quantifie variable is left unassigned by the optimization as the result has to hold when it takes any value from its domain, while an existentially quantifie variable takes exactly one of its values for each context. Similar classes of problems have recently been studied as (Distributed) Quantifie Constraint Problems, where the variables of the CSP have quantifiers All constraints should be satisfie independently of the value taken by universal variables. We propose a QDCOP that applies the concept of game tree search to DCOP. If the original problem is a minimization problem, agents that own universally quantifie variables may intend to maximize the cost value in the worst case. Other agents normally intend to optimize the minimizing problems. Therefore, only the bounds, especially the upper bounds, of the optimal value are guaranteed. The purpose of the new class of problems is to compute such bounds, as well as to compute sub-optimal solutions. For the QDCOP, we also propose several methods that are based on min-max/alpha-beta and ADOPT algorithms.

AB - In this paper, we propose a Quantifie Distributed Constraint Optimization problem (QDCOP) that extends the framework of Distributed Constraint Optimization problems (DCOPs). DCOPs have been studied as a fundamental model of multi-agent cooperation. In traditional DCOPs, all agents cooperate to optimize the sum of their cost functions. However, in practical systems some agents may desire to select the value of their variables without cooperation. In special cases, such agents may take the values with the worst impact on the quality of the result reachable by the optimization process. We apply existential/universal quantifier to distinct uncooperative variables. A universally quantifie variable is left unassigned by the optimization as the result has to hold when it takes any value from its domain, while an existentially quantifie variable takes exactly one of its values for each context. Similar classes of problems have recently been studied as (Distributed) Quantifie Constraint Problems, where the variables of the CSP have quantifiers All constraints should be satisfie independently of the value taken by universal variables. We propose a QDCOP that applies the concept of game tree search to DCOP. If the original problem is a minimization problem, agents that own universally quantifie variables may intend to maximize the cost value in the worst case. Other agents normally intend to optimize the minimizing problems. Therefore, only the bounds, especially the upper bounds, of the optimal value are guaranteed. The purpose of the new class of problems is to compute such bounds, as well as to compute sub-optimal solutions. For the QDCOP, we also propose several methods that are based on min-max/alpha-beta and ADOPT algorithms.

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M3 - Conference contribution

AN - SCOPUS:80055060848

SN - 9781617387715

T3 - Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS

SP - 1023

EP - 1030

BT - 9th International Joint Conference on Autonomous Agents and Multiagent Systems 2010, AAMAS 2010

PB - International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)

ER -