The coalition structure formation problem represents an active research area in multi-agent systems. A coalition structure is defined as a partition of the agents involved in a system into disjoint coalitions. The problem of finding the optimal coalition structure is NP-complete. In order to find the optimal solution in a combinatorial optimization problem it is theoretically possible to enumerate the solutions and evaluate each. But this approach is infeasible since the number of solutions often grows exponentially with the size of the problem. In this paper we present a greedy adaptive search procedure (GRASP) to efficiently search the space of coalition structures in order to find an optimal one. Experiments and comparisons to other algorithms prove the validity of the proposed method in solving this hard combinatorial problem.
We present a simulated annealing algorithm for coalition formation represented as characteristic function games. We provide a detailed analysis of various neighbourhoods for the algorithm, and of their effects to the algorithm's performance. Our practical experiments and comparisons with other methods demonstrate that simulated annealing provides a useful tool to tackle the combinatorics involved in multi-agent coalition formation. Coalition formation has been a very active area of research in multiagent systems. Most of this research has concentrated on decentralized procedures that allow self-interested agents to negotiate the formation of coalitions and division of coalition payoffs. A different line of research has addressed the problem of finding the optimal division of agents into coalitions such that the sum total of the the payoffs to all the coalitions is maximized (Larson and Sandholm, 1999). This is the optimal coalition structure identification problem. Deterministic search algorithms have been proposed and evaluated under the assumption that the performance of a coalition is independent of other coalitions. We use an order-based genetic algorithm (OBGA) as a stochastic search process to identify the optimal coalition structure. We compare the performance of the OBGA with a representative deterministic algorithm presented in the literature. Though the OBGA has no performance guarantees, it is found to dominate the deterministic algorithm in a significant number of problem settings. An additional advantage of the OBGA is its scalability to larger problem sizes and to problems where performance of a coalition depends on other coalitions in the environment.