Coalition Structure Generation Utilizing Compact Characteristic Function Representations

This paper presents a new way of formalizing the Coalition Structure Generation problem (CSG), so that we can apply constraint optimization techniques to it. Forming effective coalitions is a major research challenge in AI and multi-agent systems. CSG involves partitioning a set of agents into coalitions so that social surplus is maximized. Traditionally, the input of the CSG problem is a black-box function called a characteristic function, which takes a coalition as an input and returns the value of the coalition. As a result, applying constraint optimization techniques to this problem has been infeasible. However, characteristic functions that appear in practice often can be represented concisely by a set of rules, rather than a single black-box function. Then, we can solve the CSG problem more efficiently by applying constraint optimization techniques to the compact representation directly. We present new formalizations of the CSG problem by utilizing recently developed compact representation schemes for characteristic functions. We first characterize the complexity of the CSG under these representation schemes. In this context, the complexity is driven more by the number of rules rather than by the number of agents. Furthermore, as an initial step towards developing efficient constraint optimization algorithms for solving the CSG problem, we develop mixed integer programming formulations and show that an off-the-shelf optimization package can perform reasonably well, i.e., it can solve instances with a few hundred agents, while the state-of-the-art algorithm (which does not make use of compact representations) can solve instances with up to 27 agents.