Action-Evolution Petri Nets: a Framework for Modeling and Solving Dynamic Task Assignment Problems

R. Bianco, R. Dijkman, Wim P. M. Nuijten, W. Jaarsveld
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Abstract

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.
动作演化Petri网:建模与解决动态任务分配问题的框架
动态任务分配涉及到将到达的任务分配给有限数量的资源,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。虽然存在独立的形式化方法,特别是马尔可夫决策过程和(有色)Petri网,用于建模、执行和解决问题的不同方面,但没有集成的建模技术。为了解决这一差距,本文提出了行动进化Petri网(a - e PN)作为建模和解决动态任务分配问题的框架。a - e PN提供了一种统一的建模技术,可以表示动态任务分配问题的所有元素。此外,A-E PN模型是可执行的,这意味着它们可以通过强化学习(RL)来学习接近最优的分配策略,而无需额外的建模工作。为了评估这个框架,我们定义了一个典型分配问题的分类。我们展示了三种情况下,A-E PN可以用来学习接近最优的分配策略。我们的研究结果表明,a - e - PN可以用于建模和解决广泛的动态任务分配问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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