## 4 Simulation Experiment and Analysis
### Parameter Setting  
The MHBSA proposed in this paper mainly involves three parameters: population size \(N\), crossover probability \(CR\), and mutation probability \(MR\). To obtain the best combination of factor levels, the Taguchi method is used for experimental design to explore the influence of algorithm parameters on the solution effect [30], and DFJSP 01 is used as a test example.  
The specific process is to set four factor levels for each parameter. According to the number of experimental groups, the number of experimental factors, and the number of factor levels, the orthogonal table of \(L_{16}\big{(}4^{3}\big{)}\) is adopted, as shown in Table 1. For each factor-level combination in the orthogonal table, the MHSSA runs independently 20 times and records the obtained non-dominated solutions. Since the index \(\Omega\) represents the percentage of the number of non-inferior solution sets falling into the optimal Pareto frontier, which can reflect the dominance of the algorithm, the index \(\Omega\) is used as the response variable (RV). The larger the RV value, the better the performance of the parameter combination. The experimental results are shown in Table 2. The average value of response characteristics (ARV) and the importance ranking of each parameter are shown in Table 3.  
As can be seen from Table 3, the population size \(N\) is the most significant among the three parameters. The \(N\) value is too large, the convergence speed of the algorithm is slow, and the running time is too long. A small \(N\) value may cause premature convergence of the algorithm. The variation probability \(MR\) is the second most significant, and the factor  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Factor**} & \multicolumn{4}{c}{**Factor Level**} \\ \cline{2-5}  & **1** & **2** & **3** & **4** \\ \hline \(N\) & 50 & 100 & 150 & 200 \\ \(CR\) & 0.2 & 0.5 & 0.7 & 0.9 \\ \(MR\) & 0.1 & 0.2 & 0.3 & 0.4 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Factor level setting of MHSSA parameters.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Experimental**} & \multicolumn{4}{c}{**Factor**} \\ \cline{2-5}  & **N** & **CR** & **MR** \\ \hline
2 & 1 & 2 & 2 & 0.0098 \\
3 & 1 & 3 & 3 & 0.0392 \\
4 & 1 & 4 & 4 & 0.0196 \\
5 & 2 & 1 & 2 & 0.0196 \\
6 & 2 & 2 & 1 & 0.0392 \\
7 & 2 & 3 & 4 & 0.0392 \\
8 & 2 & 4 & 3 & 0.0784 \\
9 & 3 & 1 & 3 & 0.0686 \\
10 & 3 & 2 & 4 & 0.0686 \\
11 & 3 & 3 & 1 & 0.0882 \\
12 & 3 & 4 & 2 & 0.0490 \\
13 & 4 & 1 & 4 & 0.0882 \\
14 & 4 & 2 & 3 & 0.1471 \\
15 & 4 & 3 & 2 & 0.1275 \\
16 & 4 & 4 & 1 & 0.1078 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Orthogonal table and response eigenvalues.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Factor Level**} & \(N\) & **CR** & **MR** \\ \hline
1 & 0.0196 & 0.04655 & 0.06125 \\
2 & 0.0441 & 0.066175 & 0.051475 \\
3 & 0.0686 & 0.073525 & 0.083325 \\
4 & 0.11765 & 0.0637 & 0.0539 \\ Delta & 0.09805 & 0.026975 & 0.03185 \\ Rank & 1 & 3 & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Response table.  
significance level of the crossover probability \(CR\) is the lowest. According to the above parameters, the main parameters of the MHSSA are set to \(N=200\), \(CR=0.7\), and \(MR=0.3\), which are the best combination of factor levels for simulation. Other parameters of the algorithm are set as follows: the maximum number of iterations \(t_{max}=100\), and the external file _Archive_size_ = \(100\).