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Simultaneous optimization of response variables in protein mixture formulation: constrained simplex method approach
Author(s) -
Castro I. A.,
Silva R. S. F.,
Tirapegui J.,
Borsato D.,
Bona E.
Publication year - 2003
Publication title -
international journal of food science and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.831
H-Index - 96
eISSN - 1365-2621
pISSN - 0950-5423
DOI - 10.1046/j.1365-2621.2003.00650.x
Subject(s) - mathematics , simplex algorithm , linear programming , simplex , ternary operation , mathematical optimization , centroid , nonlinear programming , computer science , nonlinear system , combinatorics , geometry , programming language , physics , quantum mechanics
Summary The objective of this study was to test a complex constrained simplex, direct search, sequential method for the optimization of a ternary mixture of protein ingredients used in a formulation for the preparation of a milk drink regularly consumed in institutional nutritional programmes. Three proteins [hydrolysed gelatine (HG), wheat gluten (WG) and soybean protein isolate (SPI)] were mixed according to a simplex‐centroid design, in order to explore the possible synergies between the sensory, nutritional and economic attributes. Mixtures containing different proportions of the three ingredients were submitted to sensory, nutritional and economic evaluations. All responses were modelled using Scheffé's canonical equations. A microinformatics application was developed in order to permit optimization to be computed. The optimum solution obtained by this non‐linear programming was HG = 20%, WG = 27% and SPI = 53%, suggesting that the program is efficient and flexible enough for multiresponse optimization. The optimal point behaviour of the entry variables (HG, WG and SPI) can be monitored with graphs of the trace plot type, in which the proportion of two variables is fixed and the third is allowed to vary in relation to the desired response.