Minimum Initial Marking Estimation of Labeled Petri Nets Based on GRASP Inspired Method (GMIM).

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.