Математическая модель и комбинированный квазиоптимальный алгоритм процесса переработки сахарной свеклы

Дмитрий Владимирович Баландин; Олег Анатольевич Кузенков; Альберт Исмаилович Эгамов; Арина Олеговна Гертель

doi:10.17308/sait/1995-5499/2023/2/62-76

Authors

Dmitry V. Balandin Lobachevsky University of Nizhny Novgorod https://orcid.org/0000-0001-7727-5924 (unauthenticated)
Oleg A. Kuzenkov Lobachevsky University of Nizhny Novgorod https://orcid.org/0000-0001-9407-0517 (unauthenticated)
Albert I. Egamov Lobachevsky University of Nizhny Novgorod https://orcid.org/0000-0002-3630-7237 (unauthenticated)
Arina O. Gertel Lobachevsky University of Nizhny Novgorod https://orcid.org/0000-0003-4391-1843 (unauthenticated)

DOI:

https://doi.org/10.17308/sait/1995-5499/2023/2/62-76

Keywords:

mathematical model, sugar beet processing, quasi-optimal schedule, ripening

Abstract

The article presents a mathematical model of sugar beet processing. A set of batches of raw materials is considered, which differ from each other in the initial chemical composition and the rate of its change during storage. A distinctive feature of the study is to take into account the effect of ripening of raw materials at the initial stage of storage. The main optimization task of the study is to build such a sequence of processing of existing batches of raw materials, in which the sugar yield will be maximum. The exact solution of the problem is possible on the basis of a well-known assignment problem in discrete optimization. However, the impossibility of a priori knowledge about the change in all the characteristics of raw materials during storage requires the development of heuristic algorithms that do not use exhaustive information about the composition of raw materials. In this article, two new heuristic processing algorithms are proposed, which are combinations of already known heuristic algorithms – "greedy" and "thrifty". This combination is due to the effect of ripening of raw materials and consists in the alternate application of "greedy" and "thrifty". Algorithms at different stages of storage – during the ripening period and at a subsequent time when beet wilting occurs, accompanied by a decrease in sugar content. In the course of the study, the problem of evaluating the effectiveness of heuristic quasi-optimal algorithms for processing sugar beet in relation to the theoretically calculated maximum possible sugar yield was solved. The evaluation of the effectiveness of the proposed algorithms was carried out taking into account the data of the SergachSugar Factory. As a result of the conducted research, it was found that the quasi-optimal algorithm, regardless of the duration of the ripening stage, is the thrifty /greedy algorithm. It is this algorithm that is recommended to be used in practice in the presence of a ripening process.

Author Biographies

Dmitry V. Balandin, Lobachevsky University of Nizhny Novgorod

DSc in Physics and Mathematics, Professor, Lobachevsky University of Nizhny Novgorod
Oleg A. Kuzenkov, Lobachevsky University of Nizhny Novgorod

PhD in Physics and Mathematics, Associate Professor, Lobachevsky University of Nizhny Novgorod
Albert I. Egamov, Lobachevsky University of Nizhny Novgorod

PhD in Physics and Mathematics, Associate Professor, Lobachevsky University of Nizhny Novgorod
Arina O. Gertel, Lobachevsky University of Nizhny Novgorod

Student of 4 course, Lobachevsky University of Nizhny Novgorod

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