Abstract This paper deals with the problem of estimating the Minimum Initial Marking (MIM) of Labeled Petri Nets (L-PN). By the observation of a sequence of labels, we determine the set of possible MIMs related to a given L-PN through an approach based on GRASP (Greedy Randomized Adaptive Search Procedure) inspired method – GMIM. The objective is to get the maximum of feasible MIMs by exploring the search space and giving best solutions for real time cyber systems in short time. We consider four basic assumptions during the reasoning: (i) the L-PN structure is known; (ii) for each transition of L-PN, a label is associated, (iii) the label sequence is known, and (iv) all transitions of L-PN are observable. We show the validity and efficiency of our approach by applying the proposed GMIM metaheuristic to two validation examples: Initialization of two parallel machines (example widely cited in literature) and resources allocation in a monitoring problem via mobile robot network.

中文翻译：

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基于GRASP启发方法（GMIM）的标记Petri网的最小初始标记估计

摘要 本文涉及估计标记 Petri 网 (L-PN) 的最小初始标记 (MIM) 的问题。通过对一系列标签的观察，我们通过基于 GRASP（贪婪随机自适应搜索程序）启发的方法 – GMIM 的方法确定与给定 L-PN 相关的可能 MIM 集。目标是通过探索搜索空间并在短时间内为实时网络系统提供最佳解决方案来获得最大的可行 MIM。我们在推理过程中考虑了四个基本假设：（i）L-PN 结构已知；(ii) 对于 L-PN 的每个转换，都关联一个标签，(iii) 标记序列是已知的，以及 (iv) L-PN 的所有转换都是可观察的。我们通过将提议的 GMIM 元启发式应用于两个验证示例来展示我们方法的有效性和效率：