Computing the minimum initial marking (MIM) in labeled Petri nets (PN) while considering a sequence of labels constitutes a difficult problem. The existing solutions of such a problem suffer from diverse limitations. In this paper, we proposed a new approach to automatically compute the MIM in labeled PNs in a timely fashion. We adopted a genetic-based algorithm to model the MIM problem. The choice of such an algorithm is justified by the nature of the MIM process which belongs to the NP-hard class. We experimentally showed the effectiveness of our approach and empirically studied the initial marking quality in particular.

In this article, we study the NP-Hard combinatorial optimization problem of the minimum initial marking (MIM) computation in labeled Petri net (L-PN) while considering a sequence of labels to minimize the resource consumption in a flexible manufacturing system (FMS), and we propose an approach based on the ant colony optimization (ACO) precisely the extension Rank-based ACO to optimal resource allocation and scheduling in FMS. The ACO meta-heuristic is inspired by the behavior of ants in foraging based on pheromones deposit. The numerical results show that the proposed algorithm obtained much better results than previous studies.

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