Coalition Structure Generation with GRASP

Abstract

The coalition structure generation problem represents an active research area in multi-agent systems. A coalition structure is defined as a partition of the agents involved in a system into disjoint coalitions. The problem of finding the optimal coalition structure is NP-complete. In order to find the optimal solution in a combinatorial optimization problem it is theoretically possible to enumerate the solutions and evaluate each. But this approach is infeasible since the number of solutions often grows exponentially with the size of the problem. In this paper we present a greedy adaptive search procedure (GRASP) to efficiently search the space of coalition structures in order to find an optimal one

A hierarchical clustering approach to large-scale near-optimal coalition formation with quality guarantees

“…For example, Sen and Dutta in [31] propose a solution based on genetic algorithms while Dos Santos and Bazzan in [12] propose an approach based on swarm intelligence (the bee clustering algorithm) for task allocation in the RoboCup Rescue domain. Metaheuristic approaches to CSG have also been investigated, for example Di Mauro et al in [11] use a stochastic local search approach (GRASP) to iteratively build a coalition structure of high quality. Similar to what our approach does, such GRASP-based method tries to build a coalition structure of good quality by merging coalitions.…”

“…Then, at every iteration, we compute the most suitable pair of coalitions (see lines 6,7 and 18,19); if merging a coalition pair is convenient for the system (line 9), namely if there is a pair of coalitions for which the linkage function is positive, such coalitions are removed from the current partition and replaced with their union, in order to define the next level of the hierarchy (lines [11][12][13]. Otherwise the algorithm stops, and the current partition is returned.…”

“…In particular, our algorithm has been evaluated on four data sets: i) a synthetic benchmark data-set where the values of coalitions follow a uniform distribution [11], ii) a synthetic data-set where the values of coalition structures are normally distributed [22], iii) a collective energy purchasing scenario [36] and iv) a ride-sharing scenario [5]. Crucially, our evaluation of CSG algorithms on two real-world large scale datasets is the first of its kind, and hence is our main focus 9 .…”

“…Along this line, previous approaches include Genetic Algorithms [31], swarm intelligence [12] and Meta-heuristics [11], but these typically do not provide guarantees on convergence and solution quality for generic CSG problems and depend on several domain specific parameters to be tuned by the system designers.…”

“…Third, we validate the C-Link approach in different data-sets: i) two synthetic benchmarks, one employing uniform distribution for coalition values [11] and the other with Normally Distributed Coalition Structures (NDCS) [22]; ii) a coalition formation problem where users can form groups to buy energy at discounted prices [36]; and iii) a ride-sharing scenario where commuters arrange one-time rides, forming groups to minimize transportation costs [4]. We compare the quality of solutions generated by the different variants of our approach against the optimal solution (computed using standard Integer Programming) when this is computationally feasible: C-Link is shown to provide high quality solutions.…”