Timed Petri nets (TPNs) have been widely used for modeling discrete-event systems of diverse manufacturing and service industries. In this article, we introduce a reachability tree-based optimization algorithm to optimize cyclic schedules of TPNs. In particular, we focus on a special class of cyclic schedules that are referred to as one-cyclic schedules, i.e., the algorithm efficiently finds the optimal one-cyclic transition firing schedule of a TPN. The proposed scheduling method can be robustly applied and extended to a number of different scheduling models since the methodology is not bounded to a specific domain. To enhance the computational performance, we establish a set of transition ordering constraints that can reduce the tree size during the search procedure. We evaluate the computational efficiency of the suggested algorithm by examining robotized manufacturing systems where one-cyclic schedules are popularly being used. It is numerically shown that the proposed algorithm is computationally more efficient than the previously studied Petri net-based optimization methods. Note to Practitioners —Resource scheduling is one of the most important managerial issues in diverse industrial systems. An optimal scheduling method for a certain industrial system is often locally developed by utilizing domain-specific operational properties. Although such domain-dependent knowledge can contribute to enhancing the computational efficiency of an optimization method, such an approach has a weak point that the method might not be applicable to scheduling problems of different industrial fields. Our motivation is to develop an algorithm for optimizing steady-state schedules that can be robustly applied for various types of discrete-event systems. The algorithm is developed on the basis of the Petri net modeling framework as it is widely being used for describing cyclic behaviors of diverse manufacturing systems, service systems, and social systems. It is experimentally shown that the proposed algorithm is computationally efficient compared with the existing cyclic scheduling methods.

中文翻译：

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基于可达树的定时Petri网循环调度优化算法

定时 Petri 网 (TPN) 已广泛用于建模不同制造和服务行业的离散事件系统。在本文中，我们介绍了一种基于可达性树的优化算法来优化 TPN 的循环调度。特别是，我们关注一类特殊的循环调度，称为单循环调度，即该算法有效地找到了 TPN 的最佳单循环转换触发调度。所提出的调度方法可以稳健地应用并扩展到许多不同的调度模型，因为该方法不受特定领域的限制。为了提高计算性能，我们建立了一组过渡排序约束，可以在搜索过程中减少树的大小。我们通过检查普遍使用单循环调度的机器人制造系统来评估建议算法的计算效率。数值结果表明，所提出的算法在计算上比之前研究的基于 Petri 网的优化方法更有效。从业者须知 ——资源调度是各种工业系统中最重要的管理问题之一。特定工业系统的最佳调度方法通常是通过利用特定领域的操作属性在本地开发的。虽然这种领域相关的知识有助于提高优化方法的计算效率，但这种方法有一个弱点，即该方法可能不适用于不同工业领域的调度问题。我们的动机是开发一种优化稳态调度的算法，该算法可以稳健地应用于各种类型的离散事件系统。该算法是在 Petri 网建模框架的基础上开发的，因为它被广泛用于描述不同制造系统、服务系统和社会系统的循环行为。