Optimization of cotton dyeing with reactive dyestuff using multiobjective evolutionary algorithms

Abstract

This work explores the optimization of the conditions for obtaining blue coloristic intensities (expressed by K/S values) in the cotton dyeing process with Reactive Black 5 (RB5), which involves two conflicting objectives: maximize the coloristic intensity and minimize the production cost. To this end, an approach that combines response surface methodology (RSM) and multiobjective evolutionary algorithms (MOEA) was developed. First, the RSM with a central composite rotatable design (RSM-CCRD) was applied for modeling the non-linear behavior of dyeing with RB5 considering the following process variables: temperature, NaCl, Na2CO3, NaOH, processing time, and RB5 concentration. The model was obtained by the least-squares method and validated through the analysis of variance (ANOVA). The determination coefficient achieved (R2 ​= ​0.945) indicates its good accuracy for making predictions. Then, we compared the results of a multiobjective genetic algorithm (MOGA) and a multiobjective particle swarm optimization (MOPSO) applied to obtain the optimized values for the process variables for obtaining maximum K/S values within predetermined ranges at the lowest production costs using the model produced by RSM-CCRD as objective function. According to the results obtained from the conducted simulations, both algorithms proved to be very useful computational tools to assist the dyeing process in the textile industry promoting economic and environmental benefits and being easy to adapt to other types of dyes or K/S ranges, although MOGA showed more consistent results.