A. P. Dimitriev¹, T. A. Lavina¹, R. I. Bazhenov², T. N. Kopysheva¹

¹Chuvash State University (Cheboksary, Russian Federation)

²Sholom-Aleichem Priamursky State University (Birobidzhan, Russian Federation)

Abstract. In Russian universities, the problem of distributing the departmental educational load is annually resolved. This problem belongs to the class of combinatorial discrete optimization problems. To solve some problems of this class, it is effective to use the selection sequence optimization algorithm developed by the authors earlier. This article provides a flowchart of this algorithm for the purpose of its visual presentation, which is aimed at further understanding of the material presented. Modeling the dynamics of the algorithm is carried out using a mathematical model built on the basis of one of the varieties of colored Petri nets - that is, on the J-net. The operating logic of this model is described in detail. A reachability tape has been built for this J-net. It contains 269 markings, some of which, representing the main nuances, are presented in the paper in table form. The reachability tape has a significant size even with a minimal non-trivial amount of simulated data, so unattainable markings are rejected by additional analysis of some inequalities sets. Due to the difficulty of contemplative analysis of inequalities’ systems, а software tool has been developed for solving these systems, whose algorithm has polynomial time complexity. Analysis of the reachability tape shows the correct operation of the optimization algorithm. Scientific novelty of the work is that for the first time, a reachability tape for the J-net has been constructed.

Key Words: reachability tape, selection sequence optimization, discrete optimization, educational load, J-net, Petri net

For citation: A. P. Dimitriev, T. A. Lavina, R. I. Bazhenov, T. N. Kopysheva. Reachability tape of J-net simulating the application of selection sequence optimization algorithm to single problem. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 27:4(2025), 517–538. DOI: https://doi.org/10.15507/2079-6900.27.202504.517-538

Information about the authors:

Alexander P. Dimitriev, Ph.D. (Engineering), Associate professor, Department of Computer Technologies, Chuvash State University (15 Moskovsky av., Cheboksary 428015, Russia), ORCID: http://orcid.org/0000-0002-7345-9790, dimitrie1@yandex.ru

Tatyana A. Lavina, Dr. Sci. (Pedagogy), Head of Department of Computer Technologies, Chuvash State University (15 Moskovsky av., Cheboksary 428015, Russia), ORCID: http://orcid.org/0000-0002-7622-2246, tlavina@mail.ru

Ruslan I. Bazhenov, Ph. D. (Pedagogy), Head Department of Information Systems, Mathematics and Legal Informatics, Sholom-Aleichem Priamursky State University (70a Shirokaya St., Birobidzhan 679015, Russia), ORCID: http://orcid.org/0000-0003-2668-1142, r-i-bazhenov@yandex.ru

Tatyana N. Kopysheva, Ph. D. (Phys.-Math.), Head of Department of Mathematical and Hardware Support for Information Systems, Chuvash State University (15 Moskovsky av., Cheboksary 428015, Russia), ORCID: http://orcid.org/0000-0003-3392-1431, tn_pavlova@mail.ru