## 5 Experimental Results
### Algorithm Effectiveness Analysis  
When analyzing the effectiveness of the algorithm, according to the standard examples, only the makespan is calculated and compared with the optimization algorithms in other articles. We select eight benchmark problems from the article by [PERSON] [24] and the article [PERSON] [25] to be tested. The SFLA-uGSA is an algorithm proposed in this paper, which runs 10 times to record the optimal value and the average deviation. Five evolutionary algorithms, CCGA [26], GRASP [27], SLGA [28], PSO [29], and MSCGA [30], are selected for comparison. Table 2 shows the results of this experiment, where \(\alpha\) represents the number of jobs, \(\beta\) represents the number of machines, _Size_ represents the number of operations, \(LB\) represents the known optimal solution, and \(SD\) represents the average deviation. The experimental results show that the algorithm runs well in the problem MK03, Kacem01, Kacem02, Kacem03, and Kacem04, which is the best at present, and runs generally in the problems MK06, MK07, and Kacem05, which are better than some algorithms but not the best. This is because the algorithm follows the parallel sequential movement mode when decoding the solution. One machine needs to work continuously when processing the same operation. Some jobs that can be processed in advance are delayed to ensure the continuous operation of the machine. It can be predicted that the greater the number of work procedures, the greater the deviation of the completion time from the standard time, which is the inevitable result of getting lower shutdown. Overall, the algorithm can stably get a satisfactory solution by minimizing the makespan in small-scale problems. In the parallel sequential movement mode, in order to further explore the superiority of the strategies introduced in this paper, such as population initialization rules and local evolutionary rules, the proposed SFLA-uGSA is compared with the standard SFLA. A total of 20 benchmark problems (rdata, where most operations can be assigned to a few different \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Problem** & \(\mathbf{\alpha}\times\mathbf{\beta}\) & _Size_ & \(LB\) & **CCGA** & **GRASP** & **SLGA** & **PSO** & **MSCGA** & **SFLA-uGSA** & **SD** \\ \hline MK03 & \(15\times 8\) & 150 & 204 & **204** & **204** & **204** & **204** & **204** & **204** & 0 \\ MK06 & \(15\times 10\) & 150 & 57 & 64 & 58 & 69 & 77 & 57 & 63 & 1.8 \\ MK07 & \(20\times 5\) & 100 & 139 & 140 & **139** & 144 & 145 & **139** & 144 & 2.1 \\ Kacem 01 & \(4\times 5\) & 20 & 11 & **11** & **11** & **11** & **11** & **11** & 0 \\ Kacem 02 & \(8\times 8\) & 64 & 14 & 17 & 15 & 15 & **14** & 15 & **14** & 0 \\ Kacem 03 & \(10\times 7\) & 70 & 11 & 13 & 13 & **11** & **11** & 12 & **11** & 0.32 \\ Kacem 04 & \(10\times 10\) & 100 & 7 & 8 & 7 & **7** & **7** & **7** & **7** & 0 \\ Kacem 05 & \(15\times 10\) & 150 & 11 & 12 & 13 & 12 & **11** & **11** & 12 & 0.54 \\ Optimal & - & - & - & 25\% & 37.5\% & 37.5\% & 75\% & 62.5\% & 62.5\% & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental results of comparison with other algorithms. Figure 8: Average effect results under different parameters. machines.) from the article [PERSON] [31] are selected to be tested, and every example runs 10 times. Table 3 shows the results of this experiment, where _Best_ represents the optimal value and the _Average_ represents the average value. The data in Table 3 shows that the SFLA-uGSA has better results and stability than the SFLA. Compared with the known optimal solution _LB_, both the SFLA-uGSA and the SFLA achieve the best in a few small-scale examples, but it is difficult to achieve the _LB_ in other examples, which is the inevitable result of following the parallel sequence movement mode. In the comparison between the SFLA-uGSA and the SFLA, the overall performance of the former is superior to that of the latter in terms of optimal value, average value, and stability.