Coloration Technology. 2019;00:1–12. wileyonlinelibrary.com/journal/cote | 1 © 2019 The Authors. Coloration Technology © 2019 Society of Dyers and Colourists 1 | INTRODUCTION For the colour industry, the major problem in the formulation of textile colours is to find the optimal recipe with a minimal number of corrections. This step needs the choice of appro- priate dyes and their corresponding concentrations allowing matching to the target colour. In fact, several dye mixtures (bi- chromatic, trichromatic or greater) at different concentrations can result in the desired shade with certain colour differences. In the literature, several studies were carried out for colour recipe prediction. 1-4 Those based on the Kubelka–Munk the- ory were numerous. In fact, in 1931, Kubelka and Munk de- veloped a system of differential equations from a simplified model of propagation of light in a matt paint layer spread on a surface. 1 Its mathematical form is expressed as: where K, S and R are the absorption coefficient, scattering co- efficient and the reflectance factor at a specific wavelength (λ), respectively. This theory has been much exploited and is largely used in the textiles industry. Because absorption and scattering coefficients of individ- ual pigments in a mixture are additive in proportion to their respective concentrations, different assumptions were made. 5 Consequently, at a specific wavelength, the Kubelka–Munk function (K/S) for a combination of n different dyes D i with concentrations of C i is given by: where mix, sub and i stand for mixture, substrate and dye D i , respectively. In addition, a linear relationship between the (K/S) i of each dye D i and its concentration C i exists and thus allows the determination of the proportion of each dye concentration in any given mixture. 4 Generally, there are two kinds of Kubelka–Munk models, known as single‐constant and two‐constant theories. 6 The single‐constant theory is usually used for colour matching of textiles and papers samples. However, the two‐constant the- ory is applied in paint systems. 7 Different approaches and methods were developed for colour recipe prediction. Some researchers have proposed (1) K() S() = [1 - R()] 2 2 × R() (2) ( K S ) mix = ( K S ) sub + n  i = 1 C i × ( K S ) i Received: 16 February 2018 | Accepted: 13 May 2019 DOI: 10.1111/cote.12409 ORIGINAL ARTICLE Colour recipe prediction using ant colony algorithm: principle of resolution and analysis of performances Sabrine Chaouch 1,2 | Ali Moussa 1,2 | Imed Ben Marzoug 1,3 | Neji Ladhari 1,4 1 Textile Engineering Laboratory (LGTex), University of Monastir, Ksar‐ Hellal, Tunisia 2 National Engineering School of Monastir (ENIM), University of Monastir, Monastir, Tunisia 3 Higher Institute of Technological Studies (ISET) of Ksar‐Hellal, Ksar‐Hellal, Tunisia 4 Higher Institute of Fashion Crafts of Monastir (IS3M), University of Monastir, Monastir, Tunisia Correspondence Ali Moussa, Department of Textile Engineering, National Engineering School of Monastir (ENIM), Rue Ibn El Jazzar, Monastir 5019, Tunisia. Email: ali.moussa76@yahoo.fr Abstract This paper presents a new method for colour recipe prediction using ant colony opti- misation. Three reactive dyes, namely CI Reactive Yellow 145, CI Reactive Red 238 and CI Reactive Blue 235, were used for colour formulation. Samples of 100% cotton fabrics were used for dyeing. The objective was to assure, control and optimise the colour formulation step by determining the dyes to be applied and their respective concentrations to reproduce the desired shades. The criterion of optimisation is to minimise the colour differences [Colour Measurement Committee (2:1)] between the target colour and the colour obtained by the proposed recipe. Errors between the proposed recipe and actual concentrations are also evaluated. The developed algo- rithm showed good performances with small colour differences between the target and reproduced colours (all lower than 0.7).