# Hybrid Genetic and Spotted Hyena Optimizer for Flow Shop Scheduling Problem
## 5 Experimental Outcomes  
The performance of the hybrid GA-SHO algorithm was assessed using over 50 instances from the OR library. The evaluation results are presented in Table 2, which include the instance name (\"Instance\"), the number of jobs (n) and machines (m) for each instance (\"n \(\times\) m\"), the best result achieved by other algorithms (\"\(BKS\)\"), the best and worst results obtained through the SHO method (\"Best\" and \"Worst\"), the average results (\"\(Average\)\") and the average execution time in seconds for 20 runs (\"Time\"). The \"\(PDav(\%)\)\" column displays the percentage deviation of the average solution length from the optimal solution length, computed using Equation (12). \[PDav(\%)=\frac{((Average-BKS)\times\ 100\%)}{BKS} \tag{12}\]  
The \"\(PDav(\%)\)\" column emphasizes values of 0.00 in bold when all solutions found in the 20 runs are equal to the length of the best-known solution. If the average of the solutions discovered in all tests is less than the length of the best-known solution, these values are highlighted in bold and blue. This suggests that the GA-SHO algorithm managed to find solutions that either match or surpass the best-known solutions for these instances. To properly evaluate the effectiveness of the GA-SHO algorithm, it is crucial to compare it with other methods for solving problems. The comparison is made with the following algorithms: CLS-BFE [20], DEO [19], GA [19], IHSA [19], PSO [19], AGGA [20] and SSO [20]. The initial parameters are described in Table 2:  
Figure 2 shows the comparison of the best-obtained results, clearly demonstrating that the GA-SHOA algorithm outperforms other methods (CLS-BFO, IHSA, PSO, DEO, SSO, GA, AGGA) across all instances (REC01 to REC23). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline The population of rat size: N & 100 \\ B & A random value between [0, 1] \\ E & A random value between [0, 1] \\ Nb iteration & 400 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of Discrete GA-SHO. Figure 2: The comparison of the best-obtained results. Tables 3 and 4 clearly demonstrates that the GA-SHOA algorithm outperforms other methods (CLS-BFO, IHSA, PSO, DEO, SSO, GA, AGGA) across all instances (REC01 to REC23). Here's a more detailed analysis of the data:  
* Objective Function Value (Best): For all instances, GA-SHOA consistently attains the most optimal or near-optimal solution. This highlights GA-SHOA's superior ability to find the most optimal or best solutions compared to the other algorithms. * Standard Deviation (STD): GA-SHOA exhibits notably lower standard deviation values compared to other methods. This suggests that GA-SHOA's results are more reliable and exhibit less variation. A low standard deviation implies that the values are close to the mean or expected value, whereas a high standard deviation implies a wider spread of values. In an optimization context, a lower standard deviation is favorable as it indicates consistent solution quality near the optimal. * Computation Time: GA-SHOA also outshines other methods in terms of computational efficiency, showcasing faster computation times. For instance, in the case of REC01, GA-SHOA takes a mere 0.042 units of time, while other methods, such as CLS-BFO (0.247 units), IHSA (7.750 units) and PSO (6.042 units), require significantly more time. Conclusively, based on the data provided, GA-SHOA excels over the other algorithms in terms of solution quality (best), solution consistency (std) and computational speed (time). This superior performance is consistent across all instances, positioning GA-SHOA as a more reliable and efficient choice for this specific problem. To further scrutinize GA-SHOA's performance against other algorithms, we can conduct an Analysis of Variance (ANOVA) to ascertain if there is a significant difference in the mean objective function values.