Dynamic task assignment involves assigning arriving tasks to a limited number of resources in order to minimize the overall cost of the assignments. To achieve optimal task assignment, it is necessary to model the assignment problem first. While there exist separate formalisms, specifically Markov Decision Processes and (Colored) Petri Nets, to model, execute, and solve different aspects of the problem, there is no integrated modeling technique. To address this gap, this paper proposes Action-Evolution Petri Nets (A-E PN) as a framework for modeling and solving dynamic task assignment problems. A-E PN provides a unified modeling technique that can represent all elements of dynamic task assignment problems. Moreover, A-E PN models are executable, which means they can be used to learn close-to-optimal assignment policies through Reinforcement Learning (RL) without additional modeling effort. To evaluate the framework, we define a taxonomy of archetypical assignment problems. We show for three cases that A-E PN can be used to learn close-to-optimal assignment policies. Our results suggest that A-E PN can be used to model and solve a broad range of dynamic task assignment problems.

翻译：动态任务分配涉及将到达的任务分配给有限的资源，以最小化分配的总成本。为了实现最优任务分配，首先需要对分配问题进行建模。虽然存在独立的建模形式——特别是马尔可夫决策过程和（着色）佩特里网——用于建模、执行和求解问题的不同方面，但目前缺乏一种集成的建模技术。为填补这一空白，本文提出行动-演化佩特里网（A-E PN）作为动态任务分配问题建模与求解的框架。A-E PN提供了一种统一的建模技术，能够表示动态任务分配问题的所有要素。此外，A-E PN模型是可执行的，这意味着无需额外建模工作即可通过强化学习（RL）学习接近最优的分配策略。为评估该框架，我们定义了一组原型分配问题的分类体系。通过三个案例，我们展示了A-E PN可用于学习接近最优的分配策略。结果表明，A-E PN能够建模并求解广泛的动态任务分配问题。