5,196 research outputs found
A hybrid algorithm for coalition structure generation
The current state-of-the-art algorithm for optimal coalition structure generation is IDP-IPâan algorithm that combines IDP (a dynamic programming algorithm due to Rahwan and Jennings, 2008b) with IP (a tree-search algorithm due to Rahwan et al., 2009). In this paper we analyse IDP-IP, highlight its limitations, and then develop a new approach for combining IDP with IP that overcomes these limitations
Algorithms for Graph-Constrained Coalition Formation in the Real World
Coalition formation typically involves the coming together of multiple,
heterogeneous, agents to achieve both their individual and collective goals. In
this paper, we focus on a special case of coalition formation known as
Graph-Constrained Coalition Formation (GCCF) whereby a network connecting the
agents constrains the formation of coalitions. We focus on this type of problem
given that in many real-world applications, agents may be connected by a
communication network or only trust certain peers in their social network. We
propose a novel representation of this problem based on the concept of edge
contraction, which allows us to model the search space induced by the GCCF
problem as a rooted tree. Then, we propose an anytime solution algorithm
(CFSS), which is particularly efficient when applied to a general class of
characteristic functions called functions. Moreover, we show how CFSS can
be efficiently parallelised to solve GCCF using a non-redundant partition of
the search space. We benchmark CFSS on both synthetic and realistic scenarios,
using a real-world dataset consisting of the energy consumption of a large
number of households in the UK. Our results show that, in the best case, the
serial version of CFSS is 4 orders of magnitude faster than the state of the
art, while the parallel version is 9.44 times faster than the serial version on
a 12-core machine. Moreover, CFSS is the first approach to provide anytime
approximate solutions with quality guarantees for very large systems of agents
(i.e., with more than 2700 agents).Comment: Accepted for publication, cite as "in press
Correlation Clustering Based Coalition Formation For Multi-Robot Task Allocation
In this paper, we study the multi-robot task allocation problem where a group
of robots needs to be allocated to a set of tasks so that the tasks can be
finished optimally. One task may need more than one robot to finish it.
Therefore the robots need to form coalitions to complete these tasks.
Multi-robot coalition formation for task allocation is a well-known NP-hard
problem. To solve this problem, we use a linear-programming based graph
partitioning approach along with a region growing strategy which allocates
(near) optimal robot coalitions to tasks in a negligible amount of time. Our
proposed algorithm is fast (only taking 230 secs. for 100 robots and 10 tasks)
and it also finds a near-optimal solution (up to 97.66% of the optimal). We
have empirically demonstrated that the proposed approach in this paper always
finds a solution which is closer (up to 9.1 times) to the optimal solution than
a theoretical worst-case bound proved in an earlier work
Coalition structure generation in cooperative games with compact representations
This paper presents a new way of formalizing the coalition structure generation problem (CSG) so that we can apply constraint optimization techniques to it. Forming effective coalitions is a major research challenge in AI and multi-agent systems. CSG involves partitioning a set of agents into coalitions to maximize social surplus. Traditionally, the input of the CSG problem is a black-box function called a characteristic function, which takes a coalition as input and returns the value of the coalition. As a result, applying constraint optimization techniques to this problem has been infeasible. However, characteristic functions that appear in practice often can be represented concisely by a set of rules, rather than treating the function as a black box. Then we can solve the CSG problem more efficiently by directly applying constraint optimization techniques to this compact representation. We present new formalizations of the CSG problem by utilizing recently developed compact representation schemes for characteristic functions. We first characterize the complexity of CSG under these representation schemes. In this context, the complexity is driven more by the number of rules than by the number of agents. As an initial step toward developing efficient constraint optimization algorithms for solving the CSG problem, we also develop mixed integer programming formulations and show that an off-the-shelf optimization package can perform reasonably well
Anytime coalition structure generation on synergy graphs
We consider the coalition structure generation (CSG) problem on synergy graphs, which arises in many practical applications where communication constraints, social or trust relationships must be taken into account when forming coalitions. We propose a novel representation of this problem based on the concept of edge contraction, and an innovative branch and bound approach (CFSS), which is particularly efficient when applied to a general class of characteristic functions. This new model provides a non-redundant partition of the search space, hence allowing an effective parallelisation. We evaluate CFSS on two benchmark functions, the edge sum with coordination cost and the collective energy purchasing functions, comparing its performance with the best algorithm for CSG on synergy graphs: DyCE. The latter approach is centralised and cannot be efficiently parallelised due to the exponential memory requirements in the number of agents, which limits its scalability (while CFSS memory requirements are only polynomial). Our results show that, when the graphs are very sparse, CFSS is 4 orders of magnitude faster than DyCE. Moreover, CFSS is the first approach to provide anytime approximate solutions with quality guarantees for very large systems (i.e., with more than 2700 agents
Coalition structure generation over graphs
We give the analysis of the computational complexity of coalition structure generation over graphs. Given an undirected graph G = (N,E) and a valuation function v : P(N) â R over the subsets of nodes, the problem is to find a partition of N into connected subsets, that maximises the sum of the components values. This problem is generally NP-complete; in particular, it is hard for a defined class of valuation functions which are independent of disconnected members â that is, two nodes have no effect on each others marginal contribution to their vertex separator. Nonetheless, for all such functions we provide bounds on the complexity of coalition structure generation over general and minor free graphs. Our proof is constructive and yields algorithms for solving corresponding instances of the problem. Furthermore, we derive linear time bounds for graphs of bounded treewidth. However, as we show, the problem remains NP-complete for planar graphs, and hence, for any Kk minor free graphs where k â„ 5. Moreover, a 3-SAT problem with m clauses can be represented by a coalition structure generation problem over a planar graph with O(m2) nodes. Importantly, our hardness result holds for a particular subclass of valuation functions, termed edge sum, where the value of each subset of nodes is simply determined by the sum of given weights of the edges in the induced subgraph
Complexity of coalition structure generation
We revisit the coalition structure generation problem in which the goal is to
partition the players into exhaustive and disjoint coalitions so as to maximize
the social welfare. One of our key results is a general polynomial-time
algorithm to solve the problem for all coalitional games provided that player
types are known and the number of player types is bounded by a constant. As a
corollary, we obtain a polynomial-time algorithm to compute an optimal
partition for weighted voting games with a constant number of weight values and
for coalitional skill games with a constant number of skills. We also consider
well-studied and well-motivated coalitional games defined compactly on
combinatorial domains. For these games, we characterize the complexity of
computing an optimal coalition structure by presenting polynomial-time
algorithms, approximation algorithms, or NP-hardness and inapproximability
lower bounds.Comment: 17 page
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