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Textile color formulation using linear programming based on Kubelka‐Munk and Duncan theories
Author(s) -
Moussa Ali
Publication year - 2021
Publication title -
color research and application
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.393
H-Index - 62
eISSN - 1520-6378
pISSN - 0361-2317
DOI - 10.1002/col.22626
Subject(s) - linear programming , function (biology) , textile , nonlinear programming , relevance (law) , constant (computer programming) , sample (material) , mathematics , computer science , dyeing , mathematical optimization , algorithm , nonlinear system , materials science , physics , composite material , thermodynamics , quantum mechanics , evolutionary biology , political science , law , biology , programming language
In this article, a new approach based on linear programming optimization is proposed to solve the textile color formulation problem. The principle aims to find the appropriate dyes to mix and their exact concentrations, which, when applied correctly, produce the required color. Two ranges of reactive dyes were used for dyeing cotton fabrics. The objective function and all the constraints of the model are expressed linearly according to the decision variables. The objective function is to minimize the differences between the K / S spectra of the sample dyed with the proposed mixture and the target color. The constraints of the model are formulated based on Kubelka‐Munk and Duncan theories in the same way as those of the single‐constant model. The relevance of the method developed using linear programming optimization was evaluated and proven by calculating errors between the proposed and actual recipes, errors in K / S spectra, and Colour Measurement Committee CMC(2:1) differences between the reproduced and target colors. The proposed program showed very good results with very small values of errors and color differences.