## 4 Experiments
### The Component Analysis  
To validate the effectiveness of the proposed strategies, we conducted ablation experiments on our strategies. On the one hand, we replaced the random initialization step of NSGAIII with our proposed GIS population initialization strategy to examine the enhancing effect of GIS on the algorithm. On the other hand, the NSGAIII-GIS, the MoGA-GIS, and the AMoGA-GIS algorithms constituted tests for the adaptive mutation strategy. The NSGAIII-GIS can be considered an NSGAIII that incorporates GIS but still uses a single mutation strategy, while the MoGA-GIS employs the eight mutation operators without adaptation. The overall experimental results are presented in Table 2, with bold values indicating the best performance in each evaluation metric. \begin{table}
\begin{tabular}{c|c|c|c|c|c|c|c|c} \hline \multirow{2}{*}{**Func**} & \multicolumn{4}{c|}{**IGD**} & \multicolumn{4}{c}{**HV**} \\ \cline{2-10}  & \multicolumn{1}{c|}{**NSGAIII**} & \multicolumn{1}{c|}{**NSGAIII-GIS**} & \multicolumn{1}{c|}{**MoGA-GIS**} & \multicolumn{1}{c|}{**AGAG-GIS**} & \multicolumn{1}{c|}{**NSGAIII**} & \multicolumn{1}{c|}{**NSGAIII-GIS**} & \multicolumn{1}{c|}{**MoGA-GIS**} & \multicolumn{1}{c|}{**AMoGA-GIS**} \\ \hline C1\_1 & \({}^{*}6.05\times 10^{5}\) & \(7.48\times 10^{5}\) & \(\mathbf{4.91\times 10^{5}}\) & \(5.03\times 10^{5}\) & \({}^{*}1.08\times 10^{22}  
As depicted in Table 2, the AMoGA-GIS consistently achieves optimal results, surpassing the performance of NSGAIII in the majority of cases. The rare exceptions, where NSGAIII outperforms, are noted but do not detract from the overall superiority of our approach. It can be observed that after incorporating the GIS strategy into NSGAIII, the relative difference in IGD compared to AMOGA-GIS improved by 3% (i.e., 29.62% and 26.01%), while the improvement in HV was nearly doubled (i.e., 316.26% and 167.32%). Moreover, the enhancement in MoGA-GIS after adding the adaptive strategy increases by 0.86% and 5.21% in the average IGD and HV, respectively. The incorporation of our eight carefully designed mutation operators is a key factor in this success, significantly enhancing the spatial search efficiency of the algorithm and facilitating a rapid convergence toward optimal solutions. Furthermore, Figure 8 presents a visual representation of the results that corroborates the effectiveness of our algorithmic components, which not only substantiates the numerical data but also illustrates the tangible benefits of our enhancements in a more accessible format. The visual results in Figure 8, coupled with the quantitative data from Table 2, collectively demonstrate the efficacy of our mutation operators in improving the exploration and exploitation capabilities of the algorithm. This leads to a more effective search process that is not only efficient in reaching optimal solutions but also robust against local optima traps. NSGAIII, with the inclusion of the GIS strategy, generally achieved better IGD results, especially in the C2 problem, where the NSGAIII-GIS demonstrated a significant lead. On HV, the NSGAIII-GIS also exhibited good performance, demonstrating the promoting effect of the GIS strategy. Furthermore, for the adaptive search operators, their effectiveness varied across different test problems. In the C1 and R problem sets, adaptive search operators generally took a leading position. However, in the C2 and RC test sets, algorithms without adaptive operators achieved better results. This variability may stem from different sensitivities of problem sets to the search process. Adaptive operators provide more opportunities for optimal strategies from the previous generation to be carried over to the current one, potentially overshadowing superior strategies in the current generation and leading to slower convergence. In such cases, a fair selection may be more suitable for a more efficient convergence. Overall, our proposed algorithm demonstrates excellent performance in addressing the HGCVRPTW problem.