Development of Mathematical Apparatus of the Expert System for Modelling Ice Cream Recipes with Specified Quality Parameters

1Breus, NM  https://orcid.org/0000-0002-0213-9159
1Hrybkov, SV  https://orcid.org/0000-0002-2552-2839
1Polischuk, GYe  https://orcid.org/0000-0003-3013-3245
1Seidykh, OL  https://orcid.org/0000-0003-4590-2019
1National University of Food Technologies
Sci. innov. 2019, 15(5):69-77
https://doi.org/10.15407/scine15.05.069
Section: Scientific Basis of Innovation Activity
Language: English
Abstract: 
Introduction. Application of new methods, in particular, expert systems with mathematical apparatus, enables improving the recipe composition of multi-component food products in a wide range of content of components with their full or partial replacement by alternative ones, including natural functional and technological ingredients.
Problem Statement. The creation and use of hybrid expert system of ice cream recipe modelling is impossible without using special mathematical apparatus.
Purpose. To develop mathematical models and methods that enable to calculate the multicomponent ice cream recipes with the standard chemical composition taking into account the raw materials and functional and technological ingredients available at the manufacturer and to get the finished products of guaranteed quality.
Materials and Methods. The methods of analysis and synthesis, generalization and scientific abstraction, as well as the method of mathematical modelling are used. The information base of the research is the results of laboratory studies of the quality of recipe components and ice creams of different chemical composition. Mathematical modelling with the use of tuples, systems of equations and restrictions, is made in MathCad and MathLab software packages.
Results. As a result of the development of the expert system mathematical apparatus, a set-theoretical mathematical model of the finished product quality control at the stage of operative planning of new types of ice cream with increased nutritional value has been obtained; multi-component ice cream recipes have been optimized in terms of composition; and a model for determining the optimal set of control actions in the presence of technological defects in the calculation of recipes has been built.
Conclusions. The created mathematical apparatus for modeling ice cream recipes has a large-scale application due to interchangeability of separate functional and technological components, which has been tested and confirmed during the trials in research laboratories.
Keywords: expert system, ice cream recipe modelling, mathematical apparatus, optimization
References: 
1. Lipatov, N. N., Rogov, I. A. (1987). Metodologiya proyektirovaniya produktov pitaniya s trebuyemym kompleksom pokazateley pishchevoy tsennosti. Izvestiya vuzov. Pishchevaya tekhnologiya, 2, 9–15 [in Ukrainian].
2. Ivashkin, Yu. A. (2000). Informatsionnyye tekhnologii proyektirovaniya i otsenki kachestva pishchevykh produktov napravlennogo deystviya. Myasnaya industriya, 5, 40–41 [in Ukrainian].
3. Olenev, Y. U. A., Tvorogova, A. A., Kazakova, N., V., Solov'yeva, L. N. (2004). Spravochnik po proizvodstvu morozhenogo. Moskva: DeLi print.
4. Goff, H. D., Hartel, W. R. (2012). Ice Cream. Springer US, New York.
https://doi.org/10.1007/978-1-4614-6096-1
5. Polischuk, G. E., Breus, N. M., Vovkodav, N. I., Ramanauskas, R. (2013). Matematicheskoye modelirovaniye aktivatsii funktsional'no-tekhnologicheskikh svoystv yablochnogo pyure. Maisto chemija ir technologija. Mokslo darbai (Food chemistry and technology. Proceedings), 47, 45–52 [in Latvia].
6. Polischuk, G. E., Ivanov, S. V., Breus, N. M. (2014). Features of ice-cream foam structure formation. Food science and technology, 2(27), 57–62 [in Ukrainian].
7. Breus, N. M., Manoha, L. U., Polischuk, G. E. (2015). Obgruntuvannya dotsilʹnosti stvorennya hibrydnoyi ekspertnoyi systemy kontrolyu yakosti zamorozhenykh produktiv desertnoho pryznachennya. Naukovi pratsi Natsionalʹnoho universytetu kharchovykh tekhnolohiy, 6, 109–116 [in Ukrainian].
8. Manoha, L. U., Polischuk, G. E., Breus, N. M., Bass, O. O. (2016). Optymizatsiya skladu morozyva na molochniy osnovi z tsukrystymy rechovynamy. Naukovi pratsi Natsionalʹnoho universytetu kharchovykh tekhnolohiy, 1, 166–172 [in Ukrainian].
9. Ustymenko, I. M., Breus, N. M., Polischuk, G. E. (2016). Naukove obgruntuvannya skladu emulʹsiy, pryznachenykh dlya normalizatsiyi molokovmisnykh produktiv. Naukovi pratsi Natsionalʹnoho universytetu kharchovykh tekhnolohiy, 5, 183–189 [in Ukrainian].
10. Breus, N. M., Hrybkov, S. V., Polischuk, G. E. (2017). Hybrid expert system to model the ice cream recipes. Ukrainian Journal of Food Science, 5(2), 294–305 [in Ukrainian].
https://doi.org/10.24263/2310-1008-2017-5-2-13
11. Krasnov, A. Ye., Krasulya, O. N., Vorob'yova, A. V., Saprykina, I. D. (2007). Informatsionnoye opisaniye tekhnologicheskikh protsessov. Uchebnoprakticheskoye posobiye dlya studentov tekhnologicheskikh, upravlencheskikh i inzhenernykh spetsial'nostey, M.; MGUTU.
12. Portal iskusstvennogo intellekta. Ekspertnyye sistemy.
URL: http://www.aiportal.ru/articles/expert-systems/expert-systems.html
(Last accessed: 19.10.2018).
13. Tokarev, A. V., Krasulia, O. N. (2015). Optimizatsiya upravlyayushchikh vozdeystviy v retsepturakh kolbasnykh izdeliy pri nalichii tekhnologicheskikh defektov. Vestnik VGUIT, 4, 66–71 [in Russia].
14. Sablani, S. S., Rahman, M. Shafiur, Datta, A. K., Mujumdar, A. S. (2007). Handbook of Food and Bioprocess Modeling Techniques. CRC Press Taylor & Francis Group.
https://doi.org/10.1201/9781420015072
15. Sergiyenko, I. V., Gulyanitskiy, L. F., Sirenko, S. I. (2009). Klassifikatsiya prikladnykh metodov kombinatornoy optimizatsii. Kibernetika i sistemnyy analiz, 5, 71-83.
16. Blum, C., Puchinger, J., Raid, G. R., Roli, A. (2011). Hybrid metaheuristics in combinatorial optimization: A survey. Applied Soft Computing, 11(6), 4135-4151.
https://doi.org/10.1016/j.asoc.2011.02.032
17. Hulianytskyi, L. F., Sirenko, S. I. (2010). Cooperative model-based metaheuristics. Electronic Notes in Discrete Mathematics, 36, 33-40 [in Ukrainian].
https://doi.org/10.1016/j.endm.2010.05.005
18. Raidl, G. R. (2006). A unified view on hybrid metaheuristics. Lect. Notes Computer Sci. Berlin: Springer-Verlag, 1-12.
https://doi.org/10.1007/11890584_1
19. MacGregor, R. (2013). Using a description classifier to enhance knowledge representation. IEEE Expert, 6(3), 41-46.
https://doi.org/10.1109/64.87683
20. Cornelius, T. L. (2009). Expert Systems: The Technology of Knowledge Management and Decision Making for the 21st Century. Academic Press.
21. Wong, B. K., Monaco, J. A. (2013). Expert system applications in business: a review and analysis of the literature, Information and Management, 3, 141-152.
https://doi.org/10.1016/0378-7206(95)00023-P