Coalition Structure Generation based on Distributed Constraint Optimization

Abstract

Forming effective coalitions is a major research challenge in AI and multi-agent systems. Coalition Structure Generation (CSG) involves partitioning a set of agents into coalitions so that social surplus (the sum of the rewards of all coalitions) is maximized. A partition is called a coalition structure (CS). In traditional works, the value of a coalition is given by a black box function called a characteristic function. In this paper, we propose a novel formalization of CSG, i.e., we assume that the value of a characteristic function is given by an optimal solution of a distributed constraint optimization problem (DCOP) among the agents of a coalition. A DCOP is a popular approach for modeling cooperative agents, since it is quite general and can formalize various application problems in MAS. At first glance, this approach sounds like a very bad idea considering the computational costs, since we need to solve an NP-hard problem just to obtain the value of a single coalition. To optimally solve a CSG, we might need to solve O(2 n ) DCOP problem instances, where n is the number of agents. However, quite surprisingly, we show that an approximation algorithm, whose computational cost is about the same as solving just one DCOP, can find a CS whose social surplus is at least max(1/ n/2 , 1/(w * + 1)) of the optimal CS, where w * is the tree width of a constraint graph. Furthermore, we can generalize this approximation algorithm with a parameter k, i.e., the generalized algorithm can find a CS whose social surplus is at least max(k/ n/2 , k/(w * + 1)) of the optimal CS by exploring more search space. These results illustrate that the locality of interactions among agents, which is explicitly modeled in the DCOP formalization, is quite useful in developing efficient CSG algorithms with quality guarantees.

Nash Stable Outcomes in Fractional Hedonic Games: Existence, Efficiency and Computation

“…Aziz and de Keijzer (2011) show that when the number of agent types is bounded by a constant (two agents have the same type if they are strategically equivalent) or in many cases in which the game is represented compactly on combinatorial domains, the problem becomes polynomially solvable. Alternative approaches to deal with specific valuations consist in defining a set of rules modeling in a concise way a value function, in order to efficiently solve the CSG problem by applying constraint optimization techniques (Ohta et al, 2009), or assuming that the value of a coalition is given by an optimal solution of a distributed constraint optimization problem among the agents of a coalition (Ueda et al, 2010). The online version of the CSG problem has been recently considered by Flammini, Monaco, Moscardelli, Shalom, and Zaks (2018).…”

“…Not surprisingly, the optimization problem of partitioning agents into coalitions so as to maximize the social welfare is a major research challenge in AI and it has been extensively investigated in the field of multi-agent systems under the name of Coalition Structure Generation (CSG). Several works characterize the computational complexity of finding optimal solutions, providing efficient algorithms, hardness results and suitable approximations under different assumptions or variants of the problem (Aziz & de Keijzer, 2011;Bachrach, Kohli, Kolmogorov, & Zadimoghaddam, 2013;Bansal, Blum, & Chawla, 2004;Deng & Papadimitriou, 1994;Ohta, Conitzer, Ichimura, Sakurai, Iwasaki, & Yokoo, 2009;Rahwan, Michalak, Wooldridge, & Jennings, 2012;Ueda, Iwasaki, Yokoo, Silaghi, Hirayama, & Matsui, 2010;Voice, Polukarov, & Jennings, 2012). A recent survey of the different approaches in this setting is also available (Rahwan, Michalak, Wooldridge, & Jennings, 2015).…”

Dynamic constrained coalition formation among electric vehicles

“…Nonetheless, their work is much more concerned with payoff division than CSG itself. Ueda et al [17] proposed the use of distributed constraint optimization (DCOP) instances to solve the CSG problem. However, the focus of their work is not to find optimal CSG solutions (the best CS), but optimal DCOP solutions (the correct value of the coalitions).…”

A Tutorial on Optimization for Multi-Agent Systems

“…In several situations, the computation of these coordinated actions may be a necessary step to address more general problems. For example, as discussed in section 2, one critical aspect of coalition formation is how to assess the value of a coalition which may go from a very simple computation to a hard optimization problem involving the coordination of agents actions [33]. Similarly, in the auction mechanisms presented in section 4 bidders may need to coordinate internally to assess the value for which they bid for a service (e.g.…”