## 6 Computational Experiments
### The Effect of Adaptive Local Search  
In order to evaluate the performance of our proposed algorithm, especially the proposed adaptive local search operator, our algorithm is compared to the standard NSGA-II [45]. The difference between our algorithm and the standard NSGA-II is that ours invokes an adaptive local search operator, which is not present in the latter. In addition, we perform a comparison of our adaptive method and that of using the local search operators for every iteration. The parameters used in our algorithms are presented in Table 9. We note that a single run may not produce enough good solutions due to the inherent randomness of the algorithm. Therefore, each algorithm was run 100 times to produce as many good solutions as possible. The output results were combined, and all Pareto-optimal solutions were filtered out. The results and comparisons are presented in Table 10. Figure 5 shows all Pareto-optimal solutions found by each algorithm. The set coverage and spacing metrics from Collette and Siarry [46] are used to assess the convergence and diversity of these algorithms. The results are presented in Tables 11 and 12. In Table 10, we can see that the introduction of an adaptive local search operator leads to better results in terms of total movement distance. However, in terms of total closeness rating score, there was no significant improvement between the standard NSGA-II and our proposed algorithm. Performing a local search in for iteration can decrease total movement distance a lot, but fails to increase the total closeness rating score producing even worse results than the standard NSGA-II. As for CPU time, our adaptive local search operator just needs several additional seconds to obtain better results, while performing a local search in every iteration requires a much longer period of time (22.56 vs. 441.54). In Tables 11 and 12, our algorithm outperforms the standard NSGA-II in both convergence and spacing metrics. Even though performing a local search in every iteration can produce the best results in both convergence and spacing metrics, it takes too long and is thus not practical.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Comparing Methods**}} & \multicolumn{1}{c}{**SISGA-II with a Local**} & \multirow{2}{*}{**NSGA-II with a Local**} & \multirow{2}{*}{**NSGA-II with**} \\  & & **Search Performed in** & \\  & & **Every Iteration** & \\ \hline Total movement & Best & 12,933,696.13 & 12,637,313.96 & 12,705,847.76 \\ distance & AVG & 16,619,552.49 & 15,302,851.60 & 16,121,966.65 \\ Total closeness rating & Best & 64 & 62 & 64 \\ score & AVG & 55.33333 & 53.28 & 55.74 \\ CPU time & & 19.46 & 441.54 & 21.39 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Comparison of results.  
Figure 5: Pareto-optimal solutions.  
In conclusion, the results clearly show that the introduction of the adaptive local search operator leads to better solutions in terms of both the best and the average values of two objective functions. Additionally, in comparison to performing a local search in every iteration, the adaptive local search operator can obtain results of little difference in a very short period of time.