Coalition Structure Generation for Partition Function Games Utilizing a Concise Graphical Representation

Zha, Aolong; Nomoto, Kazuki; Ueda, Suguru; Koshimura, Miyuki; Sakurai, Yuko; Yokoo, Makoto

doi:10.1007/978-3-319-69131-2_9

Cited by 5 publications

(5 citation statements)

References 10 publications

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“…Such externalities is a crucial aspect in many social and economic interactions. For instance, in environmental economics, the value of a resource to one party can be heavily impacted by the usage of a resource by another party [36,225,203].…”

Section: Social Welfare Functions Preferences and Valuementioning

confidence: 99%

“…A final welfare function that we investigate from a computational perspective is cross-bundle dependent welfare, which has applications that have attracted considerable interest in the multi-agent systems and game theory literature, see e.g., [153,36,60,135,193,203,124,225]. We refer to the corresponding optimization problem as cross-bundle combinatorial assignment (XCA).…”

Section: Externalities and Cross-bundle Welfarementioning

confidence: 99%

“…Related to our work on interdependency effects between bundles is CSG with externalities, which adds cross-coalitional effects to the corresponding value function [152] and models the problem as a partition function game [203]. For this problem, only a few concise representations have so far been presented, such as a tree-based one [225]. Our work on externalities can also be applied to such problems.…”

Section: Examples Of Combinatorial Assignment Problems and Related Workmentioning

confidence: 99%

See 2 more Smart Citations

Dividing the Indivisible : Algorithms, Empirical Advances, and Complexity Results for Value-Maximizing Combinatorial Assignment Problems

Präntare

2024

Linköping Studies in Science and Technology. Dissertations

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Denna avhandling tar sig an en av de mest grundläggande utmaningarna vid skärningspunkten mellan datavetenskap, politik, artificiell intelligens och ekonomi:Hur kan vi på bästa sätt fördela en mängd odelbara enheter?Föreställ dig exempelvis ett scenario där en internationell hjälporganisation måste fördela personal samt begränsade medicinska resurser till sjukhus under en global hälsokris. Dessa enheter-exempelvis läkare, sjuksköterskor, respiratorer och vaccin, som inte kan fragmenteras-kräver en fördelningsprocess som maximerar både nytta och rättvisa.

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Section: Social Welfare Functions Preferences and Valuementioning

confidence: 99%

Section: Externalities and Cross-bundle Welfarementioning

confidence: 99%

Section: Examples Of Combinatorial Assignment Problems and Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Dividing the Indivisible : Algorithms, Empirical Advances, and Complexity Results for Value-Maximizing Combinatorial Assignment Problems

Präntare

2024

Linköping Studies in Science and Technology. Dissertations

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“…Furthermore, Skibski et al [39] presented a graphical representation based on rooted directed trees called partition decision trees, which Zha et al [53] then used to solve the CSG problem using (1) a depth-first branch-and-bound algorithm, and (2) a maximum satisfiability (MaxSAT) encoding together with an off-the-shelve solver. However, there are many settings and scenarios in which the expected future utility of a team not only depends on its members (as in CFGs), or the way all agents are partitioned (as in PFGs), but also on the its collective goal (e.g., its purpose, or the task/job it is assigned to).…”

Section: Definition 2 Embedded Coalition An Embedded Coalition Over Tmentioning

confidence: 99%

An anytime algorithm for optimal simultaneous coalition structure generation and assignment

Präntare

Heintz

2020

Auton Agent Multi-Agent Syst

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An important research problem in artificial intelligence is how to organize multiple agents, and coordinate them, so that they can work together to solve problems. Coordinating agents in a multi-agent system can significantly affect the system's performance-the agents can, in many instances, be organized so that they can solve tasks more efficiently, and consequently benefit collectively and individually. Central to this endeavor is coalition formation-the process by which heterogeneous agents organize and form disjoint groups (coalitions). Coalition formation often involves finding a coalition structure (an exhaustive set of disjoint coalitions) that maximizes the system's potential performance (e.g., social welfare) through coalition structure generation. However, coalition structure generation typically has no notion of goals. In cooperative settings, where coordination of multiple coalitions is important, this may generate suboptimal teams for achieving and accomplishing the tasks and goals at hand. With this in mind, we consider simultaneously generating coalitions of agents and assigning the coalitions to independent alternatives (e.g., tasks/goals), and present an anytime algorithm for the simultaneous coalition structure generation and assignment problem. This combinatorial optimization problem has many real-world applications, including forming goal-oriented teams. To evaluate the presented algorithm's performance, we present five methods for synthetic problem set generation, and benchmark the algorithm against the industry-grade solver CPLEX using randomized data sets of varying distribution and complexity. To test its anytimeperformance, we compare the quality of its interim solutions against those generated by a greedy algorithm and pure random search. Finally, we also apply the algorithm to solve the problem of assigning agents to regions in a major commercial strategy game, and show that it can be used in game-playing to coordinate smaller sets of agents in real-time.

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“…Examples of algorithms that work with MC-nets and develop mixed-integer linear programming formulations can be found in Ueda et al [35] and Liao et al [39], where an improved version of Weighted Partial MaxSAT (WPM) encoding alongside an off-the-shelf WPM solver were developed. A similar WPM-based technique was proposed in Zha et al [40] but in the context of PDTcompact representation. e basic idea behind compact representations is to define rules which are used to compute the value of each coalition.…”

Section: Related Workmentioning

confidence: 99%

A New Genetic Algorithm Encoding for Coalition Structure Generation Problems

Contreras

Bosch

Varas

et al. 2020

Mathematical Problems in Engineering

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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.

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Coalition Structure Generation for Partition Function Games Utilizing a Concise Graphical Representation

Cited by 5 publications

References 10 publications

Dividing the Indivisible : Algorithms, Empirical Advances, and Complexity Results for Value-Maximizing Combinatorial Assignment Problems

Dividing the Indivisible : Algorithms, Empirical Advances, and Complexity Results for Value-Maximizing Combinatorial Assignment Problems

An anytime algorithm for optimal simultaneous coalition structure generation and assignment

A New Genetic Algorithm Encoding for Coalition Structure Generation Problems

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