Abstract

The scientific direction of the food product designing with a specified set of indicators of nutritional value is currently topical in the world. The mathematical bases for solving formulation problems are well studied. The problems concerning the multi-objective optimization of formulations for multicomponent products are frequently met. At the same time, only one, the most important, criterion is to be optimized, and the rest criteria act as the additional constraints, since the intersection of sets of the optimal solutions for all single-objective problems usually turns out to be an empty set. As a result, several formulation alternatives are obtained, which are optimized according to any single or several (but not all) criteria. The purpose of the work is to theoretically substantiate a universal approach to choosing out of the set of alternatives of the optimized formulations of food products. The authors suggest reasserting the problem of choice as the problem of assessing the degree of the product’s composition conformance with the recommended physiological standards. When assessing the balanced state of the formulation alternatives, the conclusions are made by comparing the relative degree of conformance of the generalized Harrington´s desirability function value with the reference standard, and not of the absolute value of the generalized desirability function. To select from a variety of the optimized formulation alternatives of the multicomponent food products, it is proposed to use the following 6 criteria: a balanced state index of the product’s macronutrient composition; a balanced state index of the vitamin composition; a balanced state index of the mineral composition; a balanced state index of the amino acid composition; a balanced state index of the fatty acid composition; and a balanced state index of the energy value. Wherein, it is proposed to calculate the generalized Harrington´s desirability function as a geometric mean of the partial balanced state indices. A universal approach is suggested for making a choice out of the variety of the optimized formulation alternatives. At the same time, the subjectivity is eliminated in choosing the nomenclature and numerical values of the physical indicators of quality of the compared variants of multicomponent products.

Keywords

Formulation, food product, multicomponent product, mathematical design of a product composition, optimization of formulation

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