In Artificial Intelligence with Coalition Structure Generation (CSG) one refers to those cooperative complex problems that require to find an optimal partition, maximising a social welfare, of a set of entities involved in a system into exhaustive and disjoint coalitions. The solution of the CSG problem finds applications in many fields such as Machine Learning (covering machines, clustering), Data Mining (decision tree, discretization), Graph Theory, Natural Language Processing (aggregation), Semantic Web (service composition), and Bioinformatics. The problem of finding the optimal coalition structure is NP-complete. In this paper we present a greedy adaptive search procedure (GRASP) with path-relinking to efficiently search the space of coalition structures. Experiments and comparisons to other algorithms prove the validity of the proposed method in solving this hard combinatorial problem.
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.  There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.