Математическая модель оптимизации рецептуры многокомпонентных пищевых продуктов
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Научный журнал Моделирование, оптимизация и информационные технологииThe scientific journal Modeling, Optimization and Information Technology
Online media
issn 2310-6018

A mathematical model for optimizing the formulation of multicomponent food products

idKalach A.V., idBugaev Y.V., idNikitin B.E., idMatytsina I.A.

UDC 637.045
DOI: 10.26102/2310-6018/2026.61.10.015

  • Abstract
  • List of references
  • About authors

One of the important factors in the design of new food products is the biological value of proteins, which is determined by the balance of amino acid composition. In a number of publications, it has been noted that the required level of balance in the composition of food products can only be achieved through their multi-component nature. In this case, optimization involves selecting components and determining their ratios to ensure that the mass fractions of nutrients are as close as possible to a reference product containing the so-called "ideal protein". In this regard, the purpose of this work is to develop, based on the mathematical apparatus, a unified approach to the design of balanced products, in particular, to choose a universal criterion for the balance of the amino acid composition. The authors formulated the requirements for the desired optimality criterion. Three well-known criteria for assessing the amino acid composition of food products have been analyzed. It has been shown that the amino acid composition balance coefficient fully meets the formulated requirements. Based on the selected criterion, mathematical models have been developed for optimizing the amino acid composition of a multi-component product, which correspond to various target functions and ensure a guaranteed level of amino acid composition balance. Based on the literature data on the amino acid composition of food products, illustrative examples of designing an optimal food additive recipe have been compiled by optimizing the amino acid composition balance coefficient and the index of essential amino acids.

1. Garaeva S.N., Redkozubova G.V., Postolati G.V. Amino acids in a living organism. Chisinau: B. i.; 2009. 552 p. (In Russ.).

2. Krukhmaleva M.V., Kamerbayev A.Yu. Optimization of the biological value of secondary raw materials of the agro industrial complex. Vestnik Innovatsionnogo Evraziiskogo universiteta. 2018;(3):64–68. (In Russ.).

3. Okuskhanova E.K., Asenova B.K., Rebezov M.B., Omargalieva N.K., Yesimbekov Zh.S. Aminoacid composition of pâté based on maral meat and protein enricher. Food Processing: Techniques and Technology. 2015;(4):71–79. (In Russ.).

4. Zverev S.V., Zubtsov V.A., Lobanov V.G., Roslyakov Yu.F., Glukhova E.V. Flaxseed cake in protein food additives. Izvestiya Vuzov. Food Technology. 2020;(5-6):93–97. (In Russ.). https://doi.org/10.26297/0579-3009.2020.5-6.22

5. Zverev S.V., Nikitina M.A. Balance of protein supplements according to the criterion of convertible protein. Food Systems. 2019;2(1):16–19. https://doi.org/10.21323/2618-9771-2019-2-1-16-19

6. Zverev S., Sesikashvili O., Pruidze E. Enrichment of protein barley and triticale groats by adding chickpea. Journal of Food and Nutrition Research. 2020;59(3):202–206.

7. Burlacu R. Mathematical model of optimization energy metabolism and protein quality to swine. Scientific Papers. Series D. Animal Science. 2018;LXI(1):115–120.

8. Stein H. Evaluating protein quality of human foods using the pig as a model. Journal of Animal Science. 2016;94(suppl_2):20–21. https://doi.org/10.2527/msasas2016-045

9. Ouyang J., Huang N., Jiang Y. A single-model quality assessment method for poor quality protein structure. BMC Bioinformatics. 2020;21(1):157. https://doi.org/10.1186/s12859-020-3499-5

10. Wolfe R.R., Rutherfurd Sh.M., Kim I.-Y., Moughan P.J. Protein quality as determined by the Digestible Indispensable Amino Acid Score: Evaluation of factors underlying the calculation. Nutrition Reviews. 2016;74(9):584–599. https://doi.org/10.1093/nutrit/nuw022

11. Liu Sh., Xie J., Fan Zh., Ma X., Yin Y. Effects of low protein diet with a balanced amino acid pattern on growth performance, meat quality and cecal microflora of finishing pigs. Journal of the Science of Food and Agriculture. 2023;103(2):957–967. https://doi.org/10.1002/jsfa.12245

12. Shi Y., Song H., Liu J., Lin J., Fang L. Comprehensive evaluation of clinical application of balanced compound amino acid injection. Frontiers in Nutrition. 2022;9:880256. https://doi.org/10.3389/fnut.2022.880256

13. Zinina O., Merenkova S., Rebezov M., Tazeddinova D., Yessimbekov Z., Vietoris V. Optimization of cattle by-products amino acid composition formula. Agronomy Research. 2019;17(5):2127–2138. https://doi.org/10.15159/AR.19.159

14. Gordynets S., Charniauskaya L., Yakhnovets J. Biological value of edible hen eggs sold on the market of the Republic of Belarus. Topical Issues of Processing of Meat and Milk Raw Materials. 2021;(15):246–256. (In Russ.). https://doi.org/10.47612/2220-8755-2020-15-246-256

15. Zverev S.V., Karpov V.I., Nikitina M.A. Optimization of food compositions according to the ideal protein profile. Food Systems. 2021;4(1):4–11. (In Russ.). https://doi.org/10.21323/2618-9771-2021-4-1-4-11

16. Uziela K., Hurtado D.M., Shu N., Wallner B., Elofsson A. Improved protein model quality assessments by changing the target function. Proteins: Structure, Function, and Bioinformatics. 2018;86(6):654–663. https://doi.org/10.1002/prot.25492

17. Keeney R.L., Raiffa H. Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Moscow: Radio i svyaz; 1981. 560 p. (In Russ.).

18. Dykalo N.Ya., Anisimov S.V., Lodygin A.D., et al. The paradigm of food systems balanceness. Paper 1. Modelling criteria. Modern Science and Innovations. 2019;(3):127–135. (In Russ.).

Kalach Andrey Vladimirovich
Doctor of Chemical Sciences, Professor

ORCID |

Voronezh Institute of the Federal Penitentiary Service of Russia

Voronezh, Russian Federation

Bugaev Yuri Vladimirovich
Doctor of Physical and Mathematical Sciences, Professor

ORCID |

Air Force Academy named after prof. N.E. Zhukovsky and Yu.A. Gagarin

Voronezh, Russian Federation

Nikitin Boris Egorovich
Candidate of Physical and Mathematical Sciences, Docent

ORCID |

Voronezh State University of Engineering Technologies

Voronezh, Russian Federation

Matytsina Irina Aleksandrovna
Candidate of Engineering Sciences

ORCID |

Voronezh Institute of the Federal Penitentiary Service of Russia

Voronezh, Russian Federation

Keywords: mathematical model, optimization, recipe design, balanced amino acid composition, multicomponent food products

For citation: Kalach A.V., Bugaev Y.V., Nikitin B.E., Matytsina I.A. A mathematical model for optimizing the formulation of multicomponent food products. Modeling, Optimization and Information Technology. 2026;14(10). URL: https://moitvivt.ru/ru/journal/article?id=2628 DOI: 10.26102/2310-6018/2026.61.10.015 (In Russ).

© Kalach A.V., Bugaev Y.V., Nikitin B.E., Matytsina I.A. Статья опубликована на условиях лицензии Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NS 4.0)
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Received 31.08.2026

Revised 20.10.2026

Accepted 27.10.2026