Optimal Coalition Structure Generation Algorithm with Branch and Bound Technique

This paper is concerned with optimal coalition structure generation in multi-agent systems. For characteristic function game representations, we propose a branch and bound technique presented in the form of possible bipartite partitions and upper bound of coalition structure value, these techniques can be incorporated into many potential coalition structure generation algorithms. In order to test the effectiveness of our approach, we compare the sequential application of DP (Dynamic Programming) algorithm of Rothkopf with and without the branch and bound technique. Following the multi agent system, we show that for uniform distributions of coalition values, BBDP (Branch and Bound Dynamic Programming) can reduce the number of bipartite partition need to be evaluated. For example, in a system of 21 agents, fewer than 58.2% of bipartite partitions need not to be evaluated in BBDP algorithm than in DP algorithm. Because anytime algorithm is to evaluate all the k part partition, so branch and bound technique, which we proposed will be applied in any kind of anytime in future.