Table 1 Specific applications of intelligent techniques and optimisation algorithms in the field of colour matching and colour prediction

ANN

This research investigated the ability of three reactive dyes (Levafix Red CA, Levafix Yellow CA, and Levafix Blue CA) to match colours on cotton fabrics

Approximately 80% of the test data had a mean colour difference [CMC(2:1)] of less than 1.5

Almodarresi et al. (2013)

This research focused on modelling the colour properties of denim treated by lasers, and the grey scale (percentage of brightness) was found to have the greatest influence on colour characteristics of the laser-treated denim

ANN method provided more accurate predictions than the LR method

Hung et al. (2014)

This research aimed to predict the colour of leather dyeing using trimodal values (X, Y, Z) for a given dye concentration

The ANN model had the potential to provide a better level of colour prediction than the traditional Kubelka–Munk model, with a lower colour difference of 0.78 compared to 2.65 using the Kubelka–Munk model

Jawahar et al. (2015)

This research focused on solving the colour mismatch between the design display and the actual fabric using ANN. The colour systems used were the standard RGB and CIE colour systems, respectively

This method substantially enhanced the colour matching between the design and its printed version with all decision coefficients greater than 0.9

Hwang et al. (2015)

This research proposed an ANN model to predict colour characteristics of 1005 cotton knitted fabrics engraved by lasers under different process conditions. DPI and pixel time were identified as the two main factors influencing the colour yields

The relative errors in the ANN model mostly ranged between 0 and 5%, which is a reasonable range

Kan and Song (2016)

This research focused on predicting viscose fibre mixture colours using a traditional neural network and a combination of several small neural networks

The average colour difference between the actual and predicted mixture colours of the test set samples was close to 1.0, indicating a high level of accuracy. The study also found that a combination of several small neural networks performed better than a traditional neural network when there were few training examples

Hemingray and Westland (2016)

These researchers designed a mixing method based on Kubelka–Munk + ANN that can model the process of mixing fibres of different colours to match a desired colour and predict the reflectance values of the mixture

The results of the study showed that the predictions made by the Kubelka–Munk + ANN method were found to be valid after a paired t-test

Furferi et al. (2016)

This research focused on predicting concentration of dyes and silver nanoparticles on silk knitwear using an artificial neural network (ANN) approach

The ANN approach resulted in a correlation of 0.994, indicating that the dye and AgNPs concentration predictions were highly accurate

Nateri et al. (2017)

This research aimed to develop a spectrophotometric algorithm for top-dyed melange yarns by predicting the weighted average spectrum using ANNs and making recipe predictions from the weighted average using constrained least squares

The sum of the squared errors in the prediction of weighted average reflectance is just 0.15%, and the average colour difference is 0.79 CMC (2:1) units for the actual samples according to the predictions of nine blind test targets, which demonstrates the ability and usefulness of the algorithm for precise colour prediction

Shen and Zhou (2017)

This research investigated the correlations between the input digital image pixels and the chromaticity parameters of the printed textile samples using a competitive neural network

The best prediction results were obtained with a correlation of 0.9671 and MSE of 0.0091

Hajipour and Shams‐Nateri (2019)

This research aimed to predict the colour of digital textile printing using a spectral representation model of the optimized RBF neural network

In the test colour samples, 90% spectral error was less than 0.04, and the average and maximum spectral error were 0.025 and 0.066 respectively. The 90% colour difference (DE2000) of the test colour samples was less than 2.8, with the maximum and average values being 8.5 and 1.89

Liu and Liang (2018)

This research investigated the use of ANN to predict dyeing parameters for achieving the required colour and fastness of cotton dyeing

The standard deviation and standard error showed a close match of the input–output system and remained within the 95% confidence level, indicating that the ANN model was effective in predicting dyeing parameters

Chakraborty et al. (2019)

This research focused on the development of a shade prediction system using ANNs to predict the colour change of finished samples

The developed model was found to be capable of predicting the colour change with over 90% accuracy, with MAEs of 0.6542, 0.5872, 0.5318, 0.4839 and 0.4707 for the delta colour coordinate value (Delta CIE L*a*b*C*h values) models respectively

Farooq et al. (2020)

This research investigated the use of ANNs to predict the Delta CIE L*a*b*C*h values of finished samples for dyed knitted fabrics after application of softeners

The developed system was able to predict shade changes with greater than 90% accuracy, with mean absolute errors of 0.78, 0.71, 0.54, 0.37 and 0.33 for the Delta CIE L*a*b*C*h values of the finished samples, respectively

Farooq et al. (2021)

This research investigated the use of an ANN method to predict the CIE L*a*b* values of yarns after the dyeing process

The differences between the actual and predicted values were within acceptable limits, with most of the predicted data deviating from the test data by less than 0.5

Şahin et al. (2022)

RNN

This research proposed an intelligent model to predict the dye recipe for cotton fabric dyeing using hyperspectral colour measurements and the RNN approach. The study included 343 uniformly dyed fabrics and 20 unevenly dyed fabrics with three different dyestuffs

The relative prediction errors for the three types of dyeing formulations were 3.40%, 2.70%, and 3.10%, indicating good prediction accuracy using the RNN approach

Zhang et al. (2021)

ANN and RSM

This research aimed to predict the colour intensity of hyperbranched polymers (HBPs) on fabrics after treatment using RSM and ANN models

The ANN model had a lower relative error of 1.67%, indicating greater accuracy than the RSM model, which had a relative error of 1.80%

Hasanzadeh et al. (2013)

This research investigated the modelling and optimization of conditions for blue pigments for reactive cotton dyeing by combining RSM and ANN methods

The R² between the predicted and actual values was 0.942, indicating a high level of correlation between predicted and actual values

Rosa et al. (2021)

ANN and ANFIS

This research investigated how plasma treatment parameters affect dyed samples' colour intensity and tested the effectiveness of ANN and ANFIS methods in predicting colour intensity

The proposed ANN and ANFIS methods provided accurate predictions with R² values of 0.986 and 0.997, respectively, with ANFIS having higher prediction accuracy

Haji and Payvandy (2020)

ANN and FL

This research focused on modelling the colour properties of viscose knitwear

For FL, the R², root mean square error (RMSE), and mean absolute error (MAE) were 0.977, 1.025, and 4.61%, respectively. For ANN, they were 0.992, 0.726, and 3.28%, respectively. Both FL and ANN accurately predicted the fabric colour strength, but ANN showed more accurate predictions than FL

Hossain et al. (2017)

Fuzzy Logic Expert System (FLES)

This research aimed to predict the colour intensity of blended knitwear made of viscose and lycra (95:5) using the FLES, and to identify the key factors that determine the colour intensity

The FLES model showed an average relative error of 3.80%, a correlation coefficient of 0.992, and a fit of 0.986 between the actual and predicted results from the fabric

Hossain et al. (2015)

This research aimed to predict colour fastness of three types of cotton knitwear using an expert system based on fuzzy knowledge

The absolute error between the actual and predicted colour intensity of the knitted fabric was found to be less than 5%

Hossain et al., (2016a, 2016b)

Taguchi method

This research aimed to predict colour fastness of blended knitwear made of viscose and lycra using the Taguchi method. The Taguchi method was effective in optimizing and predicting colour fastness of the fabric

The mean absolute error (MAE) was 3.48%, and the coefficient of determination (R²) was 0.88

Hossain et al., (2016a, 2016b)

ACO

This research aimed to use the ACO method to match the colours of direct dye mixtures for dyeing cotton fabrics and to select appropriate dyes and their concentrations in the dye bath to reproduce the desired shades

The proposed method showed good performance with mean values of theoretical and experimental colour differences being 0.3322 and 0.8075, respectively

Chaouch et al. (2019a)

This research investigated the use of an ACO method for predicting the colour formulation of three reactive dyestuffs (CI Reactive Yellow 145, CI Reactive Red 238, and CI Reactive Blue 235)

The implemented algorithm provided satisfactory results resulting in minor colour differences, below 0.7, between the reference and reproduced colours

Chaouch et al. (2019b)

ACO and GA

This research aimed to predict colour formulations for three different reactive dyes using two optimization techniques: ACO and GA

The ACO was slightly more accurate than the GA, with a mean MSE of 0.0048 for ACO and 0.1299 for GA. The ACO is also more efficient in terms of computation time

Chaouch et al. (2022)

SVM algorithm

This research aimed to classify dyes in coloured fibres using spectral imaging with a sparse logistic regression algorithm and SVM algorithm. First, the sparse logistic regression algorithm was employed to analyse the reflectance data of the dyed fibres so as to identify a number of discriminatory bands. Then, the SVM algorithm was used to classify the reflectance considering a selection of spectral bands

It was found that 9 selected bands in the shortwave infrared region, in the range of 1000–2500 nm, classified dyes approximately 97.4% accurately

Rahaman et al. (2020)

PSO-LSSVM

This research focused on estimating K/S values for cotton fabrics dyed with reactive dyes using PSO-LSSVM, with the inputs to the model consisting of dye concentration and process conditions

The R² between the experimental and predicted values were extremely close to 1, indicating a good fit between dye concentration, process factors, and K/S values for cotton fabrics

Yu et al. (2020)

This research developed a computerized dye formulation prediction method for a single database of reactive dyes using a PSO-LSSVM model and evaluated its performance in predicting the CIE L*a*b* values for dyed fabrics

The predicted CIE L*a*b* values for dyed fabrics at dye concentrations from the PSO-LSSVM model showed a high correlation with the measured values of the cotton fabrics, with a correlation coefficient of 0.9945 for the PSO-LSSVM model

Yu et al. (2021)

GA

This research aimed to solve a new model for predicting colour formulation using mixtures of reactive and direct dyes

The proposed algorithm showed a small CMC colour difference between the target and reproduction colours, with mean values of 0.328 and 0.686, indicating high accuracy

Chaouch et al. (2020)

ANN, GA and FL

This research focused on modelling Madder's harmless dyeing of polyester fabrics using ANNs optimised by GA and FL. The study aimed to assess how each parameter affects colour power and to estimate the actual K/S values using ANN and FL models

Both the ANN and FL models were able to accurately predict the K/S values with mean absolute percentage errors (MAPEs) of 2.52 and 3.01, respectively

Haji and Vadood (2021)

MOGA and MOPSO algorithm

This research aimed to optimize the cotton dyeing process with reactive black 5 dye to achieve the maximum K/S value within a predefined range using MOGA and MOPSO algorithms

The results showed that both algorithms proved to be very useful computational tools

Boukouvalas et al. (2021)

ANN and optimization algorithms such as GA, PSO, GWO, FMINCON, and PSO-FMIN

This research investigated the prediction of colour coordinates of cellulose fabrics in binary dyeing with natural dyes using ANN and optimization algorithms such as GA, PSO, GWO, FMINCON, and PSO-FMIN

The results showed that ANN weighting using the PSO-FMIN algorithm has higher accuracy in predicting colour coordinates. For CIE L*a*b* coordinates, the outputs MSEs' were 2.02, 1.68, and 1.39, respectively

Vadood and Haji (2022a)

using GAs to optimize ANN and NSGAII's multi-objective optimization algorithm

This research aimed to estimate colour properties of polyester fabrics treated with natural dyes using GAs to optimize ANN and NSGAII multi-objective optimization algorithm

MAPEs of the ANN for predicting CIE L*a*b* values were 0.67, 1.29, and 1.27, respectively, indicating relatively high accuracy. The proposed method was also highly efficient in determining the colouration parameters to achieve the desired colours using a multi-objective optimization method

Vadood and Haji (2022b)