## 5 Experiments and Results
### The Advantage of DLMVO Components  
As described in Section 4, in the DLMVO, three improvements were used to enhance the performance of the MVO. To analyze the effectiveness of different components, three DLMVO variants were developed, i.e., the MVO that only uses adaptive _WEP_ repair technology is called DLMVO-1, the MVO with the self-adaptive _TDR_ strategy is called DLMVO-2, and the MVO with the dynamic leaders for traveling for short is called DLMVO-3. The convergence curves and statistical results are reported in Figure 12 and Table 7, respectively. In Table 7, for each model, the overall best result among these five algorithms is highlighted in boldface. Figure 11: Convergence curves of different algorithms for three models. Figure 12: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{**Algorithm**} & \multicolumn{4}{c}{_RMSE_} & \multirow{2}{*}{**Sig**} \\ \cline{3-4} \cline{6-7}  & & **Min** & **Max** & **Mean** & **Std** & \\ \hline \multirow{4}{*}{SDM} & MVO & 1.1399 \(\times\)\(10^{-3}\) & 1.4446 \(\times\)\(10^{-3}\) & 1.1752 \(\times\)\(10^{-3}\) & 4.2032 \(\times\)\(10^{-4}\) & + \\  & DLMVO-1 & 9.8708 \(\times\)\(10^{-3}\) & 1.0323 \(\times\)\(10^{-3}\) & 9.9630 \(\times\)\(10^{-4}\) & 3.1392 \(\times\)\(10^{-5}\) & + \\  & DLMVO-2 & 9.8793 \(\times\)\(10^{-4}\) & 1.0849 \(\times\)\(10^{-3}\) & 1.01322 \(\times\)\(10^{-3}\) & 9.1139 \(\times\)\(10^{-5}\) & + \\  & DLMVO-3 & 9.8659 \(\times\)\(10^{-4}\) & 1.0443 \(\times\)\(10^{-4}\) & 9.9350 \(\times\)\(10^{-4}\) & 3.4414 \(\times\)\(10^{-5}\) & + \\  & DLMVO & **9.8602 \(\times\)\(10^{-4}\)** & **9.8602 \(\times\)\(10^{-4}\)** & **9.8602 \(\times\)\(10^{-4}\)** & **2.5287 \(\times\)\(10^{-7}\)** & \\ \hline \multirow{4}{*}{DDM} & MVO & 1.0236 \(\times\)\(10^{-3}\) & 1.5810 \(\times\)\(10^{-3}\) & 1.2112 \(\times\)\(10^{-3}\) & 7.5526 \(\times\)\(10^{-4}\) & + \\  & DLMVO-1 & 9.8550 \(\times\)\(10^{-4}\) & 1.2183 \(\times\)\(10^{-3}\) & 1.0300 \(\times\)\(10^{-3}\) & 2.3635 \(\times\)\(10^{-4}\) & + \\  & DLMVO-2 & 9.8469 \(\times\)\(10^{-4}\) & 1.0301 \(\times\)\(10^{-3}\) & 1.0023 \(\times\)\(10^{-3}\) & 4.6550 \(\times\)\(10^{-5}\) & + \\  & DLMVO-3 & 9.8262 \(\times\)\(10^{-4}\) & 1.0037 \(\times\)\(10^{-3}\) & 9.9117 \(\times\)\(10^{-4}\) & 1.9165 \(\times\)\(10^{-5}\) & + \\  & DLMVO & **9.8248 \(\times\)\(10^{-4}\)** & **9.8602 \(\times\)\(10^{-4}\)** & **9.82603 \(\times\)\(10^{-4}\)** & **1.2698 \(\times\)\(10^{-6}\)** & \\ \hline \multirow{4}{*}{SMM} & MVO & 2.4589 \(\times\)\(10^{-3}\) & 2.5723 \(\times\)\(10^{-3}\) & 2.4809 \(\times\)\(10^{-3}\) & 3.3093 \(\times\)\(10^{-4}\) & + \\  & DLMVO-1 & 2.4262 \(\times\)\(10^{-3}\) & 2.5441 \(\times\)\(10^{-3}\) & 2.4739 \(\times\)\(10^{-3}\) & 1.4744 \(\times\)\(10^{-4}\) & + \\ \cline{1-1}  & DLMVO-2 & 2.4268 \(\times\)\(10^{-3}\) & 2.5856 \(\times\)\(10^{-3}\) & 2.4771 \(\times\)\(10^{-3}\) & 1.6727 \(\times\)\(10^{-4}\) & + \\ \cline{1-1}  & DLMVO-3 & 2.4251 \(\times\)\(10^{-3}\) & 2.4259 \(\times\)\(10^{-3}\) & 2.4251 \(\times\)\(10^{-3}\) & 4.5366 \(\times\)\(10^{-7}\) & + \\ \cline{1-1}  & DLMVO & **2.4251 \(\times\)\(10^{-3}\)** & **2.4251 \(\times\)\(10^{-3}\)** & **2.4251 \(\times\)\(10^{-3}\)** & **2.3838 \(\times\)\(10^{-17}\)** & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Influence of different components on the performance of DLMVO. Figure 12: Convergence curves of different components in DLMVO on three models. From the reported results, it can be observed that:  
* The Wilcoxon's signed-rank test results in Table 7 demonstrate that DLMVO-1, DLMVO-2, and DLMVO-3 provided better results than MVO, which indicates that each improvement is beneficial for MVO to find the optimal solution. * Concerning the Max, Mean, and Std of RMSE values, DLMVO-3 was significantly better than DLMVO-1 and DLMVO-2, especially for Mean and Std, which shows that the dynamic leader travel strategy has an advantage on improving the robustness of the MVO.