How to form effective coalitions is an important issue in multi-agent systems. Coalition Structure Generation (\({{\mathsf {CSG}}}\)) is a fundamental problem whose formalization can encompass various applications related to multi-agent cooperation. \({{\mathsf {CSG}}}\) involves partitioning a set of agents into coalitions such that the social surplus (i.e., the sum of the values of all coalitions) is maximized. In traditional \({\mathsf {CSG}}\), we are guaranteed that all coalitions will be successfully established, that is, the attendance rate of each agent for joining any coalition is assumed to be 1.0. Having the real world in mind, however, it is natural to consider the uncertainty of agents’ availabilities, e.g., an agent might be available only two or three days a week because of his/her own schedule. Probabilistic Coalition Structure Generation (\({{\mathsf {PCSG}}}\)) is an extension of \({\mathsf {CSG}}\) where the attendance type of each agent is considered. The aim of this problem is to find the optimal coalition structure which maximizes the sum of the expected values of all coalitions. In \({\mathsf {PCSG}}\), since finding the optimal coalition structure easily becomes intractable, it is important to consider approximation algorithms, i.e., to consider a trade-off between the quality of the returned solution and tractability. In this paper, a formal framework for \({\mathsf {PCSG}}\) is introduced. Approximation algorithms for \({\mathsf {PCSG}}\) called Bounded Approximation Algorithm based on Attendance Types (\({{\mathsf {BAAAT}}}\)) and Involved \({\mathsf {BAAAT}}\) (\({{\mathsf {IBAAAT}}}\)) are then presented. We prove a priori bounds on the quality of the solution returned by \({\mathsf {BAAAT}}\) and \({\mathsf {IBAAAT}}\) with respect to the optimum and perform experimental evaluations on a number of benchmarks.

中文翻译：

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具有质量限制的概率联盟结构生成的两种近似算法

在多智能体系统中，如何形成有效的联盟是一个重要的问题。联盟结构生成（\（{{\ mathsf {CSG}}} \））是一个基本问题，其形式化可以包含与多代理协作相关的各种应用程序。\（{{\ mathsf {CSG}}} \）涉及将一组特工划分为多个联盟，以使社会剩余（即所有联盟的价值之和）最大化。在传统\（{\ mathsf {CSG}} \）中，我们保证所有联盟都会成功建立，也就是说，假定每个特工参加任何联盟的出席率是1.0。但是，考虑到现实世界，自然要考虑业务代表可用性的不确定性，例如，由于自己的日程安排，业务代表每周可能只有两到三天有空。概率联盟结构生成（\（{{\ mathsf {PCSG}}} \））是\（{\ mathsf {CSG}} \\）的扩展，其中考虑了每个座席的出勤类型。这个问题的目的是找到使所有联盟的期望值之和最大化的最佳联盟结构。在\（{\ mathsf {PCSG}} \）中，因为找到最佳的联合结构很容易变得棘手，因此考虑近似算法很重要，即考虑返回的解决方案的质量和可处理性之间的权衡。本文介绍了\（{\ mathsf {PCSG}} \）的正式框架。逼近算法\（{\ mathsf {PCSG}} \）基于出席类型称为界逼近算法（\（{{\ mathsf {BAAAT}}} \） ）和所涉及\（{\ mathsf {BAAAT}} \）（\（{{\ mathsf {IBAAAT}}} \））然后出现。我们证明\（{\ mathsf {BAAAT}} \）和\（{\ mathsf {IBAAAT}} \）返回的解决方案的质量具有先验界限 关于最佳，并在多个基准上进行实验评估。