On the Online Coalition Structure Generation Problem

We consider the online version of the coalition structure generation problem, in which agents, corresponding to the vertices of a graph, appear in an online fashion and have to be partitioned into coalitions by an authority (i.e., an online algorithm). When an agent appears, the algorithm has to decide whether to put the agent into an existing coalition or to create a new one containing, at this moment, only her. The decision is irrevocable. The objective is partitioning agents into coalitions so as to maximize the resulting social welfare that is the sum of all coalition values. We consider two cases for the value of a coalition: (1) the sum of the weights of its edges, and (2) the sum of the weights of its edges divided by its size. Coalition structures appear in a variety of application in AI, multi-agent systems, networks, as well as in social networks, data analysis, computational biology, game theory, and scheduling. For each of the coalition value functions we consider the bounded and unbounded cases depending on whether or not the size of a coalition can exceed a given value α. Furthermore, we consider the case of a limited number of coalitions and various weight functions for the edges, i.e., unrestricted, positive and constant weights. We show tight or nearly tight bounds for the competitive ratio in each case.

Monte-Carlo Tree Search for Scalable Coalition Formation

We propose a novel algorithm based on Monte-Carlo tree search for the problem of coalition structure generation (CSG). Specifically, we find the optimal solution by sampling the coalition structure graph and incrementally expanding a search tree, which represents the partial space that has been searched. We prove that our algorithm is complete and converges to the optimal given sufficient number of iterations. Moreover, it is anytime and can scale to large CSG problems with many agents. Experimental results on six common CSG benchmark problems and a disaster response domain confirm the advantages of our approach comparing to the state-of-the-art methods.

A New Genetic Algorithm Encoding for Coalition Structure Generation Problems

Genetic algorithms have proved to be a useful improvement heuristic for tackling several combinatorial problems, including the coalition structure generation problem. In this case, the focus lies on selecting the best partition from a discrete set. A relevant issue when designing a Genetic algorithm for coalition structure generation problems is to choose a proper genetic encoding that enables an efficient computational implementation. In this paper, we present a novel hybrid encoding, and we compare its performance against several genetic encoding proposed in the literature. We show that even in difficult instances of the coalition structure generation problem, the proposed approach is a competitive alternative to obtaining good quality solutions in reasonable computing times. Furthermore, we also show that the encoding relevance increases as the number of players increases.

ODSS: Efficient Hybridization for Optimal Coalition Structure Generation

Coalition Structure Generation (CSG) is an NP-complete problem that remains difficult to solve on account of its complexity. In this paper, we propose an efficient hybrid algorithm for optimal coalition structure generation called ODSS. ODSS is a hybrid version of two previously established algorithms IDP (Rahwan and Jennings 2008) and IP (Rahwan et al. 2009). ODSS minimizes the overlapping between IDP and IP by dividing the whole search space of CSG into two disjoint sets of subspaces and proposes a novel subspace shrinking technique to reduce the size of the subspace searched by IP with the help of IDP. When compared to the state-of-the-art against a wide variety of value distributions, ODSS is shown to perform better by up to 54.15% on benchmark inputs.