This paper develops a stochastic programming framework for multi-agent systems where task decomposition, assignment, and scheduling problems are simultaneously optimized. Due to their inherent flexibility and robustness, multi-agent systems are applied in a growing range of real-world problems that involve heterogeneous tasks and uncertain information. Most previous works assume a unique way to decompose a task into roles that can later be assigned to the agents. This assumption is not valid for a complex task where the roles can vary and multiple decomposition structures exist. Meanwhile, it is unclear how uncertainties in task requirements and agent capabilities can be systematically quantified and optimized under a multi-agent system setting. A representation for complex tasks is proposed to avoid the non-convex task decomposition enumeration: agent capabilities are represented as a vector of random distributions, and task requirements are verified by a generalizable binary function. The conditional value at risk (CVaR) is chosen as a metric in the objective function to generate robust plans. An efficient algorithm is described to solve the model, and the whole framework is evaluated in two different practical test cases: capture-the-flag and robotic service coordination during a pandemic (e.g., COVID-19). Results demonstrate that the framework is scalable, generalizable, and provides low-cost plans that ensure a high probability of success.

翻译：本文为任务分解、任务分配和时间安排问题同时得到优化的多试剂系统制定了一个随机性规划框架。由于多试剂系统的内在灵活性和稳健性,多试剂系统应用于涉及不同任务和不确定信息的日益广泛的现实世界问题中。大多数以前的工作都以独特的方式将任务分解成一个可以随后分配给代理人的角色。这一假设对于任务可能不同的角色和存在多种分解结构的复杂任务来说是无效的。与此同时,还不清楚如何在多试剂系统设置下系统地量化和优化任务要求和代理能力的不确定性。提出了复杂任务的代表性,以避免非混杂的任务分解点计:代理能力是随机分布的矢量,任务要求由可概括的二元功能加以核实。在目标功能中选择了有条件的风险值(CVaR)作为生成稳健计划的衡量标准。描述高效的算法,在两种不同的实际测试案例中对整个框架进行了评估:捕获-旗杆和机器人服务能力的分解点(CO-VI)计划能够保证高概率性、高的C-VI总结果(e.g)能够提供高概率的C-VI。