Anytime Optimal Coalition Structure Generation

Forming effective coalitions is a major research challenge in the field of multi-agent systems. Central to this endeavour is the problem of determining the best groups of agents to select to achieve some goal. To this end, in this paper, we present a novel, optimal anytime algorithm for this coalition structure generation problem that is significantly faster than previous algorithms designed for this purpose. Specifically, our algorithm can generate solutions by partitioning the space of all potential coalitions into sub-spaces that contain coalition structures that are similar, according to some criterion, such that these sub-spaces can be pruned by identifying their bounds. Using this representation, the algorithm then searches through only valid and unique coalition structures and selects the best among them using a branch-and-bound technique. We empirically show that we are able to find solutions that are optimal in 0.082% of the time taken by the state of the art dynamic programming algorithm (for 27 agents) using much less memory O(2n) instead of O(3n) for the set of n agents). Moreover, our algorithm is the first to be able to solve the coalition structure generation problem for numbers of agents bigger than 27 in reasonable time (less than 90 minutes for 27 agents as opposed to around 2 months for the best previous solution)