Anytime coalition structure generation: an average case study

Abstract

Abstract.Coalition formation is a key topic in multiagent systems. One would prefer a coalition structure that maxim izes the sum of the values of the coalitions, but often the number of coalition structures is too larg e to allow for exhaustive search for the optimal one. We present exp erimental results for three anytim e algorithms that search the space of coalition structures. We show that, in the ave rag e case, all three algorithms do much better than the recently established theoretical worst case results in Sandholm et al. (1999a ). We also show that no one algorithm is dom inant. Each algorithm's performance is in¯uenced by the particular instance distribution, with each algorithm outperforming the others for diOE erent instances. We present a possible explanation for the behaviour of the algorithms and support our hypothesis with data collected from a controlled experimental run.K eywords: coalition structure, algorithm, multiagent systems IntroductionMultiagent system s with self-interested ag ents are becoming increasingly im portant. One reason for this is the technology push of a growing standardized communication infrastructureÐ Internet, W W W, EDI, KQM L, FIPA, Concordia, Voyager, Odyssey, Telescript, Java, etc.Ð over which separately designed ag ents belonging to diOE erent organizations can interact in an open environment in real-time and safely carry out transactions. The second reason is strong application pull for computer support for negotiation at the operative decision making level. For exam ple, we are witnessing the advent of small transaction commerce on the Internet for purchasing goods, information and communication bandwidth. In many multiagent settings, self-interested ag ents representing real world parties can operate more eOE ectively by forming coalitions and coordinating their activities and pooling resources within each coalition. This may allow tasks to be completed that otherwise would not have been possible. For exam ple, there is an industrial trend toward virtual enterprises: dynam ic alliances of small, agile enterprises which together can take advantage of economies of scale when availab le (e.g., respond to more diverse orders than individual age nts can ), but do not suOE er from diseconomies of scale.Multiagent technology facilitates the automated formation of such dynam ic coalitions. This automation can save labour time of human negotiators, but in addition, other savings are possible because computational ag ents can be more eOE ective at ® nding bene® cial short-term coalitions than humans are in strategically and combinatorially complex settings.

Constant factor approximation algorithms for coalition structure generation

“…Two of the problem distributions are similar to distributions used in previous empirical coalition structure generation studies [3,7]. The three problem distributions are 1. uniform distribution, the value of each coalition C was drawn from a uniform distribution between 0 and 10 · |C|, 2. normal distribution, the value of each coalition C was drawn from a normal distribution with mean 15 4 and variance 1 16 , and 3. uniform with bonus distribution, the base value of each coalition C is drawn from a uniform distribution between 0 and 10 · |C|; however, each coalition's utility is increased by a random number drawn uniformly between 0 and 50 with 20% probability.…”

“…We show that our algorithms always return the optimal solution in superadditive domains and present empirical results of our algorithms on three different types of problem distributions, two of which are similar to those previously used in related average case coalition structure generation analysis [3,7].…”

Performance of software agents in non-transferable payoff group buying

“…Research in coalition formation in MASs , Shehory and Kraus 1999, Larson and Sandholm 2000, Sen and Dutta 2000, Dang and Jennings 2004) (the list of references is not exhaustive) has mainly focused on transferable payoff; like Osborne and Rubinstein (1994), we consider the term 'payoff' to be synonymous with the term 'utility' when we analyse the process from the game theory point of view. This case, which is specific, is defined by a payoff attributed to each possible coalition.…”

Grasp and Path-Relinking for Coalition Structure Generation

“…Instances of the CSG problem have been defined using the following distributions, as proposed in [14,20], for the values of the characteristic function v: Each graph plots on the x-axis the value of the coalition structures whose cardinality is represented by a point on the y-axis. As we can see, it seems easy to find optimal solutions in the case of normal and uniform distributions, while it becomes more complicated for the case of scaled distributions.…”