## 6 Flow Shop Scheduling--A Case Study
### Comparative Study: Pure GA vs. Improved-ART-1-Guided GA
#### 6.3.3 Performance Analysis When Solving Large Problems  
Here, we examined the algorithm's performance in a small-size problem. However, the previous analysis is insufficient since the problem size is small and cannot picture the real-world scenario and complexity. Therefore, we will compare pure GA and our proposed algorithm Improved-ART-1 neural-network-guided GA considering binary conversion method-1 for large-size problems. In this regard, six large problems were considered for this comparative study. These problems were generated and solved using the first 20 trials considering Pure GA with and without ANN intervention. Table 7 presents the general features of large problems with a considered number of jobs, number of stages, and minimum number of parallel machines, and the maximum number of batch sizes for each problem. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(s\) & \(n\) & \(i\) & \(m\) & Illustration of Steps \\ \hline
1 & 1 & 1 & 1 & **Step 1:** This is the 1 st stage for \(n_{1}\) and the 1 st job to be processed on this machine, according to the conditions, **Case 1** will be considered; **Step 2:** Set (\(n\), \(i\)) = (1, 1), then \(C_{1,1}\) = \(F_{1,1}\) + \(S_{1,1,1,0}\) + \(Q_{1}\times T_{1,1,1}\) = \(0+120+(20\times 6)\) = 240 min & Machine  
We present six large problems in which we adopted our proposed binary conversion method-1 using Improved-ART-1 neural-network-guided GA and pure GA to solve FFSP. The problem lies in determining an effective sequence for the jobs at the first stage, so that all the jobs can be completed within a minimal amount of time (makespan). Each ordered sequence can be assigned a measure of goodness, which is makespan. Twenty trials were performed during the experiment by changing the seed to generate multiple solutions. Most of the trials show that the Improved-ART-1 guided GA provides better solutions with a lower makespan compared to pure GA (see Figure 11). It is clearly noticeable from the analysis of the six problems mentioned in Table 7 that ANN-guided GA not only converges quickly but also comes up with a better result (lower makespan) compared to pure GA.  
One of the limitations of pure GA is that GA explores only specific clusters. This limits the searching process, which indicates GA's exploitation, because regions that were previously explored by GA prevent the searching option blind from exploring other clusters. According to the proposed algorithm, ANN-guided GA architecture combines GA, ART, and SWCM, where SWCM helps GA to avoid being stuck in a specific search region. Thus, the intervention promotes exploration of the solution space so that other clusters find the optimal solution. Therefore, the results show that ANN-guided GA has an improved exploration ability compared to pure GA and can find an optimal solution by searching almost all clusters. The investigation of the assumed six different problem sizes provides further insight into the analysis, from which we can see that pure GA has been stuck in one region of the search space. GA without ANN is exploited in a particular cluster. Moreover, it can be said that GA is trapped in some regions: it is not clear that the result provided by GA is actually the optimal one, and it is still possible to obtain a better result from other clusters that have not been explored to date (as shown in Figure 12a,c,e). However, ANN intervention helps GA to explore almost all the clusters in the search space (see in Figure 12b,d,f). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Problem** & **No. of** & **No. of** & **No. of Parallel** & **No. of** \\
**No.** & **Jobs** & **Stages** & **Machine** & **Batch Size** \\  & **(_n_)** & **(_i_)** & **(_m_)** & **(Q\({}_{n}\))** \\ \hline
1 & 20 & 10 & 4 to 2 & 30 to 60 \\
2 & 6 & 10 & 5 to 2 & 20 to 50 \\
3 & 60 & 20 & 4 to 3 & 20 to 50 \\
4 & 90 & 6 & 4 to 3 & 20 to 50 \\
5 & 90 & 1 & 6 to 4 & 20 to 50 \\
6 & 90 & 8 & 8 to 4 & 20 to 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Features of considered large size problems.