A simulated annealing method for minimum initial marking estimation in labeled Petri nets: Applications and comparative studies

State estimation plays an important role in the field of system supervisory control. With the increase in the scale and complexity of practical systems, problems of state/event estimation for discrete event systems in Petri nets have attracted significant attention. One of the well-studied problems is how to estimate the minimum initial markings (MIMs) in a known labeled Petri net based on the observation of its event sequence. The existing approaches have disadvantages such as (1) much higher computational complexity in order to increase the MIM quantity; and (2) much fewer MIMs in order to decrease the computational complexity. In this paper, a variant of simulated annealing (SA) algorithm is developed to determine the set of MIMs. We take advantage of SA for global search in the problem’s search space to find initial markings that are minimal in their token counts, and then use the selection strategy of SA to determine MIMs from them. Finally, the effectiveness of the proposed method is illustrated through two simulation experiments of industrial applications. Comparisons with existing work are conducted to demonstrate the merits of our method.