## 5 Testing Study
### Parameter Settings  
Initialization parameters include the number of subproblems in the population N, the number of neighboring subproblems for each subproblem (T), the number of neighboring solutions generated (M), the maximum number of consecutive update failures for solutions using the current neighborhood structure (C), and the number of consecutive failures to abandon a solution in successive generations (L). In MD/ABC, there are five parameters containing N, T, M, C, and L. This ensures that the five different neighborhood structures are fully utilized under the selection strategy and scouting mechanism. To gain empirical insights into the impact of these five parameters and to set them efficiently, the Taguchi method is used to apply examples [39]. Table 3 lists four plausible levels for the five parameters, with their combinations determined by the L16 orthogonal array listed in Table 4. Each combination undergoes independent execution of the MD/ABC algorithm 30 times, where the average IGD metric (AVG) is collected as the response variable and is shown in Table 4. Based on the factor level trends shown in Table 4 and presented in Figure 9, for each parameter, the significance rankings are listed in Table 5. As can be seen from Table 4 and Figure 9, larger N values can promote exploratory capabilities but contradict the goal of deep search of subproblems under the finite termination criterion. The parameter T has a significant effect, and the algorithm performs best when T = 20, whereas too small a value may promote collaboration of very similar solutions, which may lead to insufficient global exploration, whereas too large a value may lead to a waste of computational resources. From Figure 9, it can be seen that the performance of the algorithm gets progressively worse as the value of M increases; this is because when M = 2, individuals make optimal use of neighboring solutions. As the value of M increases, more computational resources will be consumed, thus decreasing the performance of the algorithm. The results obtained through designed experiments show that the algorithm performs best when N = 150, M = 2, T = 20, C = 10, and L = 50.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Experiment Number**} & \multicolumn{5}{c}{**Parameter**} & \multirow{2}{*}{**AVG**} \\ \cline{2-2} \cline{5-7}  & **N** & **M** & **T** & **C** & **L** \\ \hline
1 & 100 & 2 & 5 & 8 & 20 & 0.0904 \\
2 & 100 & 3 & 10 & 10 & 30 & 0.0922 \\
3 & 100 & 5 & 15 & 15 & 50 & 0.0873 \\
4 & 100 & 8 & 20 & 18 & 80 & 0.0762 \\
5 & 150 & 2 & 10 & 15 & 80 & 0.0785 \\
6 & 150 & 3 & 5 & 18 & 50 & 0.0931 \\
7 & 150 & 5 & 20 & 8 & 30 & 0.0792 \\
8 & 150 & 8 & 15 & 10 & 20 & 0.0901 \\
9 & 200 & 2 & 15 & 18 & 30 & 0.0882 \\
10 & 200 & 3 & 20 & 15 & 20 & 0.0742 \\
11 & 200 & 5 & 5 & 10 & 80 & 0.0942 \\
12 & 200 & 8 & 10 & 8 & 50 & 0.0933 \\
13 & 250 & 2 & 20 & 10 & 50 & 0.0543 \\
14 & 250 & 3 & 15 & 8 & 80 & 0.0921 \\
15 & 250 & 5 & 10 & 18 & 20 & 0.1255 \\
16 & 250 & 8 & 5 & 15 & 30 & 0.1121 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The orthogonal array L16.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{5}{c}{**Parameter Level**} \\ \cline{2-5}  & **1** & **2** & **3** & **4** \\ \hline N & 100 & 150 & 200 & 250 \\ M & 2 & 3 & 5 & 8 \\ T & 5 & 10 & 15 & 20 \\ C & 8 & 10 & 15 & 18 \\ L & 20 & 30 & 50 & 80 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Level of the parameters.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Level**} & **N** & **M** & **T** & **C** & **L** \\ \hline
1 & 0.0865 & 0.0779 & 0.0975 & 0.0886 & 0.0951 \\
2 & 0.0852 & 0.0879 & 0.0974 & 0.0827 & 0.0929 \\
3 & 0.0875 & 0.0966 & 0.0894 & 0.0880 & 0.0820 \\
4 & 0.0960 & 0.0929 & 0.07