Solving the Coalition Structure Generation Problem with MaxSAT

Abstract

Coalition Structure Generation (CSG), a main research issue in the domain of coalition games, involves partitioning agents into exhaustive and disjoint coalitions so that the social welfare is optimized. The advent of compact representation schemes, such as marginal contribution networks (MC-nets), promotes the efficiency of solving the CSG problem. In this paper, inspired by the dramatic speed-up of Boolean Satisfiability Problem (SAT) solvers, we make the first step towards a study of applying MaxSAT solvers to the CSG problem. We set out to encode the MC-nets into propositional Boolean logic and utilize an off-the-shelf MaxSAT solver as an optimization tool for solving the CSG problem. Specifically, based on the previous works, we encode rule relations and their constraints into weighted partial MaxSAT formulas and show that MaxSAT solvers are useful in solving the CSG problem. Furthermore, we put forward a brand-new method based on agent relations which specify whether two agents of a rule are in the same coalition. Experimental evaluations show that our methods outperform other state-of-the-art algorithms.