# Textile Flexible Job-Shop Scheduling Based on a Modified Ant Colony Optimization Algorithm
## 5 Conclusions  
This paper introduces the concept of product ant colony optimization (PACO) for the textile-flexible job-shop scheduling problem (T-FSP), focusing on the internal processes of textile workshops and the constraints between textile machines and products. By constructing a simulation model of textile workshops, the effectiveness of the PACO algorithm in addressing the T-FSP is validated. To further enhance the performance of the PACO algorithm in handling the T-FSP, two improvements are proposed: the transformation of the invariant parameter \(\rho\) in the PACO algorithm into a variable parameter \(\rho\), and the enhancement of the local pheromone update rule from single ant colony pheromones to the combination of multiple ant colony pheromones. Additionally, three sets of experiments are conducted to compare the results of the PACO algorithm with those of the improved \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Algorithm** & \(Avg\) & \(RPE\_A\) (\%) & \(Best\) & \(RPE\_B\) (\%) \\ \hline \multirow{4}{*}{Group 1} & PACO & 348.225 & 6.24 & 323.5 & 2.86 \\  & MACO 1 & 348.775 & 6.41 & 336 & 6.84 \\  & MACO 2 & 331.225 & 1.05 & 315.5 & 0.32 \\  & IPACO & 327.775 & 0 & 314.5 & 0 \\ \hline \multirow{4}{*}{Group 2} & PACO & 104.85 & 3.45 & 101 & 4.12 \\  & MACO 1 & 103.35 & 1.97 & 99 & 2.06 \\  & MACO 2 & 102.1 & 0.74 & 99 & 2.06 \\  & IPACO & 101.35 & 0 & 97 & 0 \\ \hline \multirow{4}{*}{Group 3} & PACO & 203 & 5.65 & 196 & 4.81 \\  & MACO 1 & 200.85 & 4.53 & 189 & 1.07 \\  & MACO 2 & 194.15 & 1.04 & 187 & 0 \\  & IPACO & 192.15 & 0 & 187 & 0 \\ \hline \multirow{4}{*}{Group 4} & PACO & 551.825 & 2.55 & 540 & 3.35 \\  & MACO 1 & 552.6 & 2.69 & 540.5 & 3.44 \\  & MACO 2 & 540.3 & 0.4 & 529 & 1.24 \\  & IPACO & 538.125 & 0 & 522.5 & 0 \\ \hline \multirow{4}{*}{Group 5} & PACO & 997.5 & 4.9 & 979 & 6.76 \\  & MACO 1 & 991.55 & 4.27 & 962 & 4.91 \\ \cline{1-1}  & MACO 2 & 957.35 & 0.67 & 943 & 2.84 \\ \cline{1-1}  & IPACO & 950.95 & 0 & 917 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The \(RPE\) values of each algorithm in the experimental groups. algorithms: MPACO 1 algorithm, MPACO 2 algorithm, and IPACO algorithm. Through the comparison of results and the visualization of Gantt charts and iterative optimization processes, the superiority of the IPACO algorithm is demonstrated. It not only improves the convergence speed and global search capability of the algorithm but also achieves better optimization results for the objective function. To verify that the PACO algorithm is not limited to textile workshops, this paper designs five sets of experiments to validate its applicability across varying numbers of operations and product types. The final experimental results demonstrate that the PACO algorithm can effectively solve workshop scheduling problems under constraints similar to those in textile workshops, even with varying numbers of operations and product types. Furthermore, through experiments conducted with modified algorithms in the five sets, the results and RPE indicators indicate that the proposed enhancements to the initial PACO algorithm are highly effective. In this paper, the machine load generated during the machine run is not considered. In reality, the machine load has a greater impact on workshop production. In the future, to better improve the economic benefits of textile workshops, minimizing machine load can be used as the objective function and combined with the objective of this paper to research multi-objective optimization of workshop scheduling. Methodology, F.C. and W.X. ; software, F.C. and X.W. ; validation, F.C., J.M. and W.X. ; formal analysis, F.C., X.W. and W.X. ; investigation, F.C., J.C and W.X. ; resources, X.W., J.M. and J.C.; data curation, F.C., J.C., J.M. and X.W. ; writing--original draft preparation, F.C. ; writing--review and editing, W.X., X.W. and J.C.; project administration, W.X., J.M. and J.C. All authors have read and agreed to the published version of the manuscript.