This paper investigates heterogeneous-cost task allocation with budget constraints (HCTAB), wherein heterogeneity is manifested through the varying capabilities and costs associated with different agents for task execution. Different from the centralized optimization-based method, the HCTAB problem is solved using a fully distributed framework, and a coalition formation game is introduced to provide a theoretical guarantee for this distributed framework. To solve the coalition formation game, a convergence-guaranteed log-linear learning algorithm based on heterogeneous cost is proposed. This algorithm incorporates two improvement strategies, namely, a cooperative exchange strategy and a heterogeneous-cost log-linear learning strategy. These strategies are specifically designed to be compatible with the heterogeneous cost and budget constraints characteristic of the HCTAB problem. Through ablation experiments, we demonstrate the effectiveness of these two improvements. Finally, numerical results show that the proposed algorithm outperforms existing task allocation algorithms and learning algorithms in terms of solving the HCTAB problem.

翻译：本文研究了预算约束下的异构成本任务分配问题（HCTAB），其中异构性体现为不同智能体执行任务时具备差异化的能力与成本。与基于集中式优化的方法不同，本工作采用全分布式框架解决HCTAB问题，并引入联盟形成博弈为该分布式框架提供理论保障。针对该联盟形成博弈，本文提出了一种基于异构成本的收敛保证对数线性学习算法。该算法融合两种改进策略：合作交换策略与异构成本对数线性学习策略，二者专门针对HCTAB问题中异构成本与预算约束特性设计。通过消融实验验证了两种改进策略的有效性。数值结果表明，所提算法在解决HCTAB问题时性能优于现有任务分配算法及学习算法。