Coalition Structure Generation based on Distributed Constraint Optimization

Abstract

Forming effective coalitions is a major research challenge in AI and multi-agent systems (MAS). Coalition Structure generation (CSG) involves partitioning a set of agents into coalitions so that social surplus (the sum of the rewards of all coalitions) is maximized. A partition is called a Coalition Structure (CS). In traditional works, the value of a coalition is given by a black box function called a characteristic function. In this paper, we propose a novel formalization of CSG, i.e., we assume the value of a characteristic function is given by an optimal solution of a distributed constraint optimization problem (DCOP) among the agents of a coalition. A DCOP is a popular approach for modeling cooperative agents, since it is quite general and can formalize various application problems in MAS. At first glance, one might assume that the computational costs required in this approach would be too expensive, since we need to solve an NP-hard problem just to obtain the value of a single coalition. To optimally solve a CSG, we might need to solve n-th power of 2 DCOP problem instances, where n is the number of agents. However, quite surprisingly, we show that an approximation algorithm, whose computational cost is about the same as solving just one DCOP, can find a CS with quality guarantees. More specifically, we develop an algorithm with parameter k that can find a CS whose social surplus is at least max(k/(w*+1), 2k/n) of the optimal CS, where w* is the tree width of a constraint graph. When k=1, the complexity of this algorithm is about the same as solving just one DCOP. These results illustrate that the locality of interactions among agents, which is explicitly modeled in the DCOP formalization, is quite useful in developing an efficient CSG algorithm with quality guarantees.