An anytime algorithm for optimal simultaneous coalition structure generation and assignment

An important research problem in artificial intelligence is how to organize multiple agents, and coordinate them, so that they can work together to solve problems. Coordinating agents in a multi-agent system can significantly affect the system’s performance—the agents can, in many instances, be organized so that they can solve tasks more efficiently, and consequently benefit collectively and individually. Central to this endeavor is coalition formation—the process by which heterogeneous agents organize and form disjoint groups (coalitions). Coalition formation often involves finding a coalition structure (an exhaustive set of disjoint coalitions) that maximizes the system’s potential performance (e.g., social welfare) through coalition structure generation. However, coalition structure generation typically has no notion of goals. In cooperative settings, where coordination of multiple coalitions is important, this may generate suboptimal teams for achieving and accomplishing the tasks and goals at hand. With this in mind, we consider simultaneously generating coalitions of agents and assigning the coalitions to independent alternatives (e.g., tasks/goals), and present an anytime algorithm for the simultaneous coalition structure generation and assignment problem. This combinatorial optimization problem has many real-world applications, including forming goal-oriented teams. To evaluate the presented algorithm’s performance, we present five methods for synthetic problem set generation, and benchmark the algorithm against the industry-grade solver CPLEX using randomized data sets of varying distribution and complexity. To test its anytime-performance, we compare the quality of its interim solutions against those generated by a greedy algorithm and pure random search. Finally, we also apply the algorithm to solve the problem of assigning agents to regions in a major commercial strategy game, and show that it can be used in game-playing to coordinate smaller sets of agents in real-time.