Modeling and optimization of reactive cotton dyeing using response surface methodology combined with artificial neural network and particle swarm techniques

This work explores the modeling and optimization of the conditions to obtain blue color intensities in the dyeing cotton process with Reactive Black 5 (RB5), by means of an approach that combines the techniques response surface methodology (RSM), artificial neural network (ANN) and particle swarm optimization (PSO). By means of RSM technique, the interactions and the effects of the main process variables (factors) on the behavior of coloristic intensity (K S −1 ) were investigated. For this, a 2 6 central composite rotational design was carried out considering the factors temperature, NaCl, Na 2 CO 3 , NaOH, processing time and RB5 concentration. The investigation conducted with RSM was used to indicate which process variables would compose the input layer of a multilayer perceptron ANN (MLP-ANN), which was trained with the data produced in the dyeing experiments to predict K S −1 values. Then, the PSO and MLP-ANN techniques were combined to determine the optimized condition for obtaining a desired K S −1 value at the lowest production cost. The results achieved by RSM show that all investigated factors have a considerable effect on the behavior of K S −1 . In addition, the determination coefficient obtained ( R 2 = 0.942) in the predictions made by the MLP-ANN confirms its effectiveness in modeling the nonlinear behavior of dyeing with RB5. Finally, the combination of PSO with MLP-ANN proved to be a very useful computational tool for providing optimized conditions to obtain colors of the blue palette using RB5 dye with the lowest production costs, facilitating the assembly of the dyes in the textile industry and promoting the saving of chemical inputs and the reduction of process time and economic costs. Graphic abstract