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Extending MaxSAT to Solve the Coalition Structure Generation Problem with Externalities Based on Agent Relations
Xiaojuan LIAO Miyuki KOSHIMURA Hiroshi FUJITA Ryuzo HASEGAWA
Publication
IEICE TRANSACTIONS on Information and Systems
Vol.E97D
No.7
pp.18121821 Publication Date: 2014/07/01 Online ISSN: 17451361
DOI: 10.1587/transinf.E97.D.1812 Type of Manuscript: PAPER Category: Information Network Keyword: weighted partial MaxSAT, coalition structure generation, externality, cooperative games,
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Summary:
Coalition Structure Generation (CSG) means partitioning agents into exhaustive and disjoint coalitions so that the sum of values of all the coalitions is maximized. Solving this problem could be facilitated by employing some compact representation schemes, such as marginal contribution network (MCnet). In MCnet, the CSG problem is represented by a set of rules where each rule is associated with a realvalued weights, and the goal is to maximize the sum of weights of rules under some constraints. This naturally leads to a combinatorial optimization problem that could be solved with weighted partial MaxSAT (WPM). In general, WPM deals with only positive weights while the weights involved in a CSG problem could be either positive or negative. With this in mind, in this paper, we propose an extension of WPM to handle negative weights and take advantage of the extended WPM to solve the MCnetbased CSG problem. Specifically, we encode the relations between each pair of agents and reform the MCnet as a set of Boolean formulas. Thus, the CSG problem is encoded as an optimization problem for WPM solvers. Furthermore, we apply this agent relationbased WPM with minor revision to solve the extended CSG problem where the value of a coalition is affected by the formation of other coalitions, a coalition known as externality. Experiments demonstrate that, compared to the previous encoding, our proposed method speeds up the process of solving the CSG problem significantly, as it generates fewer number of Boolean variables and clauses that need to be examined by WPM solver.

