# An Iterative Optimization Algorithm for Planning Spacecraft Pathways Through Asteroids
## 6 Experiments
### Results in the Uninformed Setting  
The results of the uninformed experimental setting were analyzed from two different points of view: average performance and peak performance. The average performance of algorithm \(\mathcal{A}\) on instance \(\mathcal{I}\) is evaluated using the _average relative percentage deviation_ (ARPD) measure, defined as follows:  
\[ARPD_{\mathcal{A}\mathcal{I}}=100\cdot\frac{1}{k}\sum_{i=1}^{k}\frac{val_{ \mathcal{A},\mathcal{I},i}-best_{\mathcal{I}}}{best_{\mathcal{I}}}, \tag{7}\]  
where \(k=30\) is the number of executions carried out, \(val_{\mathcal{A},\mathcal{I},i}\) is the final objective value achieved by algorithm \(\mathcal{A}\) on its \(i\)-th execution on instance \(\mathcal{I}\), and \(best_{\mathcal{I}}\) is the best objective value found on instance \(\mathcal{I}\) considering all the executions of every algorithm. The ARPDs are summarized in Table 1. Performance comparisons between FAT-RLS and the competitor algorithms (CEGO, UMM, and RS) are indicated by the following symbols: \(\blacktriangle\) marks cases where FAT-RLS significantly outperformed the competitor, \(\triangledown\)indicates cases where FAT-RLS was significantly outperformed, and the absence of a mark means the difference was not statistically significant. Statistical significance was evaluated using the Mann-Whitney U test [46], with a standard significance level of 0.05. Table 1 shows that while FAT-RLS does not perform competitively on the two smaller instances with size \(n=10\), it is the best algorithm in average on all the instances where \(n\geq 15\). Most notably, the advantage of FAT-RLS is also statistically significant on the larger instances with \(n\geq 20\). Regarding peak performances, Table 2 provides the objective values obtained in the best execution of each algorithm for every instance. The values in bold highlight, for each instance, the best value achieved by any algorithm. Table 2 reveals that FAT-RLS achieved the best results in 9 out of 10 instances, with the only exception being instance 10_73_, where it achieved the second-best peak performance after CEGO. This observation, along with the trends seen in Table 1, where the ARPDs of FAT-RLS seem to improve on larger instances, suggests that FAT-RLS is capable of delivering competitive results across a wide range of benchmarks. However, it demonstrates a lack of robustness on smaller instances. In order to further validate these observations, in Figure 3 we provide a boxplot graph showing the distributions of the single relative percentage deviations--actually, the sum's arguments in Equation (7)--obtained by any single run of an algorithm on an instance of a given size. The graph clearly confirms the provided conclusions. \begin{table}
\begin{tabular}{c c c c c} \hline
**Instance** & **FAT-RLS** & **CEGO** & **UMM** & **RS** \\ \hline
10\_42 & 13.90 & 9.39 \(\triangledown\) & 12.11 & 20.92 \(\blacktriangle\) \\
10\_73 & 16.13 & 6.55 \(\triangledown\) & 11.30 \(\triangledown\) & 15.53 \\
15\_42 & 12.84 & 13.80 & 17.66 \(\blacktriangle\) & 25.89 \(\blacktriangle\) \\
15\_73 & 10.64 & 13.08 & 15.57 \(\blacktriangle\) & 23.53 \(\blacktriangle\) \\
20\_42 & 10.31 & 15.35 \(\blacktriangle\) & 20.42 \(\blacktriangle\) & 25.59 \(\blacktriangle\) \\
20\_73 & 14.95 & 24.08 \(\blacktriangle\) & 29.63 \(\blacktriangle\) & 32.66 \(\blacktriangle\) \\
25\_42 & 14.42 & 25.25 \(\blacktriangle\) & 28.60 \(\blacktriangle\) & 34.01 \(\blacktriangle\) \\
25\_73 & 9.46 & 20.26 \(\blacktriangle\) & 25.47 \(\blacktriangle\) & 28.19 \(\blacktriangle\) \\
30\_42 & 7.56 & 19.75 \(\blacktriangle\) & 26.82 \(\blacktriangle\) & 27.77 \(\blacktriangle\) \\
30\_73 & 9.15 & 20.28 \(\blacktriangle\) & 23.89 \(\blacktriangle\) & 27.36 \(\blacktriangle\) \\ \hline \end{tabular}
\end{table} 
Table 1: Average relative percentage deviations for uninformed experiments. Algorithms marked with \(\blacktriangle\) were significantly outperformed by FAT-RLS, whereas those indicated by \(\triangledown\) showed a significant performance advantage over FAT-RLS.