## 4 Experimental Results and Analysis  
The algorithm of this paper was coded in Matlab language. The program running environment was Intel Corei5, 2.19 GHz CPU, and 8 GB RAM. We selected 120 classic examples proposed by [PERSON] as test data, and the data size of the Taillard benchmark was from 20 jobs-5 machines to 500 jobs-20 machines. The experimental parameters of the algorithm were set as follows [57; 58]: the population size was 100, the crossover probability was 0.9, and the mutation probability was 0.1. In order to compare the performance of the HGSA with different Hill coefficients (n = 1; 1.2; 1.5; 2.5), the average relative percentage deviation (ARPD) values of different Hill coefficients with other parameters fixed are shown in Table 3. In these experiments, we chose the 200 \(\times\) 20 and 500 \(\times\) 20 instance in Talliard as the benchmarks. The results show that algorithm obtained the minimum ARPD when the Hill coefficient was equal to 1.5. So, the value of the Hill coefficient was chosen to be 1.5. In order to analyze the performance of the proposed algorithm, it was compared with the hybrid genetic algorithm (HGA) in [18], the improved iterated greedy algorithm (IIGA) in [19], the iterated greedy algorithm with a referenced insertion scheme (IG-RIS) in [20], the memetic algorithm (MA) in [21], and the discrete self-organizing migrating algorithm (DSOMA) in [22]. Table 4 shows the makespan results of the proposed algorithm and the other four algorithms tested in different sizes of Taillard benchmark. Each data scale has 10 sets of data, and the boldface figure in Table 4 represents the optimal solution obtained by the algorithms. It can be seen from the table that the algorithm proposed in this paper improved the results of 109 out of 120 examples, which indicates that the best results obtained by HGSA are better than the other four metaheuristics, reflecting the better search quality of HGSA. Compared with the MA, IG-RIS, and HIGA algorithms, the results of HGSA were greatly improved. Only in 11 cases with a small problem size were the results of HGSA slightly inferior to DSOMA. As the scale of the study increased, HGSA reflected a more obvious advantage. At the same time, the comparison with the HIGA and HGA algorithms showed that the MME initial population generation method and SA local search method based on hormone regulation mechanism could improve the optimization effect of the algorithm more effectively, especially for large-scale examples. Figure 6 is the Gantt chart of the ta001. The chart shows that the makespan obtained by proposed algorithm was 1324. The optimal schedule we got was [3; 17; 15; 16; 8; 6; 9; 18; 4; 2; 14; 5; 7; 11; 12; 10; 1; 19; 13; 20]. In order to further compare the advantages and disadvantages of the proposed algorithm and the other algorithms, three parameters of average error (AE), improvement percentage (IP), and ARPD were introduced to compare the effects of each algorithm. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Problem Size** & **Function Factor (n)** & **ARPD\%** \\ \hline  & 1.0 & 9.21 \\  & 1.2 & 7.82 \\
200 \(\times\) 20 & 1.5 & 5.16 \\  & 2.0 & 8.34 \\  & 2.5 & 11.06 \\ \hline  & 1.0 & 6.28 \\  & 1.2 & 5.49 \\
500 \(\times\) 20 & 1.5 & 3.29 \\  & 2.0 & 7.13 \\  & 2.5 & 9.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The average relative percentage deviation (ARPD) value of different Hill coefficients on the performance of HGSA. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline