MULTI–CRITERIA OPTIMIZATION OF A PRODUCT RECIPE COMPOSITION

The scientific direction of multicomponent food modeling with a certain set of indicators for nutritional and energy values is still topical in the whole world. At present, the mathematical foundations of solving tasks by a single criterion (single-criterion optimization) are well studied. However, multi-criteria tasks, in which a system is to be optimized by several criteria simultaneously, exist in various fields of engineer solutions, research and management activities. The aim of the work is to theoretically substantiate the methodology of the multi-criteria model of food recipe optimization in different settings for different criteria of nutritional, biological and energy values, as well as amino acid, fatty acid, vitamin and mineral adequacy. It is proposed to use an effective method of multi-criteria optimization — the Pareto method. Since the Pareto-optimal solution can be not the only one, the definition of the Pareto-optimal set of solutions is given as a set of non-dominated alternatives. The authors propose not to select non-dominative options of food products, but slightly extend a subset by choosing a nucleus in the initial set, in which all alternatives are incomparable to each other and any option that is not included in the nucleus is dominated by at least one alternative of the nucleus. The following reduction of the options can be achieved by imposing other tighter constraints, for example, by increasing the threshold value for the index of agreement C and decreasing the threshold value for the index of disagreement. The use of the IT-technologies realized by the methods of multi-criteria structure optimization and mathematical programming allows correcting and optimizing food recipes by different criteria of the non-linear character, structuring the obtained set of alternatives and detecting the optimal food recipe option with the targeted quality, composition and properties or a diet for a particular population category with consideration for the therapeutic and prophylactic direction.