Received December 12, 2019, accepted December 29, 2019, date of publication January 17, 2020, date of current version February 6, 2020. Digital Object Identifier 10.1109/ACCESS.2020.2967342 Genetic-Based Approach for Minimum Initial Marking Estimation in Labeled Petri Nets HICHEM KMIMECH 1 , ACHRAF JABEUR TELMOUDI 2 (Member, IEEE), LAYTH SLIMAN 3 , AND LOTFI NABLI 1 1 Research Laboratory of Automatic Signal and Image Processing, University of Monastir, Monastir 5000, Tunisia 2 National Higher Engineering School of Tunis, University of Tunis, Tunis 1007, Tunisia 3 Ècole d’Ingénieur des Technologies de l’Information et de la Communication, 94800 Villejuif, France Corresponding author: Hichem Kmimech (hichemkmimech@gmail.com) ABSTRACT 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. INDEX TERMS Labeled Petri nets, minimum initial marking, label sequence, genetic algorithms, optimiza- tion. I. INTRODUCTION Labeled Petri Nets (PNs) have been proposed as a funda- mental modeling method for discrete event (states oriented) systems in a wide variety of applications such as manufactur- ing systems, process-based systems, and so on [1], [2]. One of the major studied problems in labeled PNs concerns the minimum Initial Marking (IM) computation while consider- ing a given label sequence [2], [3]. This estimation is carried out by computing the Firing Sequence (FS) of a well-known length, while ensuring a minimum use of resources. The required FS computation process is interesting as it is used in different domains and applications (manufacturing systems, services-based systems, etc.). However, the process of min- imum IM estimation in Labeled PNs is a difficult and an NP-hard problem [2]. The minimum IM problem in (labeled) PNs has been receiving a particular attention in the recent decades. Differ- ent approaches have been proposed [2], [4]–[6]. While being interesting, these approaches have different limitations and do not go further in ensuring a minimal use of resources. The main objective of this paper is to develop a new approach to automatically compute the minimum IM in labeled PNs in a timely fashion. We adopt a Genetic Algorithm (GA) to address the minimum IM problem. In fact, the GA is a The associate editor coordinating the review of this manuscript and approving it for publication was Wei Wei . powerful tool to deal with combinatorial problems, which is successfully applied in many other research domains (services compositions, manufacturing systems, cloud resource allocation, and so on.). This success motivates our choice of GA to solve the minimum IM computation problem, which has similar properties in terms of large scale and problem complexity. The rest of this paper is organized as follows: In Section II, we present a review of the state of the art and the basic concepts of the labeled PN. In Section III describes the mini- mum IM estimation problem in labeled PNs and its modeling process using genetic algorithms. The empirical studies of the proposed approach is provided in Section IV. In particular, we accentuate the benefits of our approach compared to the related work. Section V concludes this paper and presents some future works. II. BACKGROUND AND RELATED WORK In this section, we introduce first an overview of genetic algorithms (GA). Then, we present a summary of the related work. Finally, we describe the basic concept of the LPN that will be used throughout the paper. A. OVERVIEW OF GENETIC ALGORITHMS Genetic algorithms (GA) are adaptive, heuristic-based search methods [7], [8]. They are usually used to solve NP-hard optimization problems like ours. As stated in [8], the imple- mentation of GA basically requires the following elements: 22854 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see http://creativecommons.org/licenses/by/4.0/ VOLUME 8, 2020