## 5 Application to the Satellite Module Layout Problem
### Results and Analysis
#### 5.2.1 Global Performance  
The algorithm detailed in Section 4 is run over 50 independently initialized instances. The obtained results are compared with those published in [19; 20] according to the following indicators and reported in Table 1:  
* The mean value of the final obtained layout objective functions, i.e., their global inertia;
* The standard deviation (STD) of the final obtained layout inertia;
* The best layout obtained in terms of inertia (among the 50 repetitions);
* The worst layout obtained in terms of inertia (among the 50 repetitions);
* The success rate, i.e., the percentage of runs leading to a feasible layout (all the constraints are satisfied). Table 2 reports the allocated budget in terms of the number of objective function evaluations for the assignment and layout tasks and for the three compared algorithms. The proposed algorithm allows to improve the average final inertia by 5% and 1.6%, respectively, in comparison to the Oboe-CCEA algorithm with the fixed component assignment scheme based on human experience and to the Dynamic FS algorithm with optimized assignment schemes. It also improves the best obtained layout by 5.08% and 1.78%, respectively, in comparison with the two same algorithms. Moreover, it must be highlighted that the worst layout obtained using the GA assisted-CSO-VF algorithm remains better than the best layouts obtained by both the Oboe-CCEA and Dynamic FS algorithms. The success rate reaches 100% for the proposed algorithm against 80% for the Dynamic FS algorithm and 60% for the Oboe-CCEA algorithm. In other words, the proposed algorithm provides a feasible solution for each of the 50 runs. It means that, for each run, at least one feasible layout has been found by the lower stage, corresponding to an optimized assignment list given by the upper stage. On the contrary, a success rate not equal to 100% shows that the corresponding algorithm fails to provide a feasible solution at every run. However, the Oboe-CCEA has the smaller standard deviation, which is increased by 12.1% by the Dynamic FS algorithm and 3.1% by the proposed algorithm. It should be noted that the objective function considered in this paper is a multimodal function and that the problem geometry involves rotational symmetry. Consequently, local minima can be reached. However, the standard deviation of the final objective function values over the different experiments is quite low, showing that the algorithm finds globally good and relatively equivalent solutions. In addition, as shown in [124; 136], the proposed algorithm \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metrics** & **Oboe-CCEA [20]** & **Dynamic FS [19]** & **GA+CSO-VF** \\ \hline Mean of final inertia & 718.93 & 694.06 & **682.96** \\ \hline STD of final inertia & **2.64** & 2.96 & 2.73 \\ \hline Best layout & 712.99 & 689.00 & **676.75** \\ \hline Worst layout & 726.59 & 700.37 & **688.45** \\ \hline Success rate & 60\% & 80\% & **100\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Numerical results for the multi-container SMLP obtained thanks to the three compared algorithms. In bold, the best obtained results according to each algorithm. For each metric, bold characters are used to highlight the best obtained value. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Oboe-CCEA [20]** & **Dynamic FS [19]** & **GA+CSO-VF** \\ \hline Assignment & x & \(1\times 10^{6}\) & \(1.75\times 10^{5}\) \\ \hline Layout & \(1\times 10^{6}\) & \(1\times 10^{6}\) & \(2.7\times 10^{5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Allocated budget in terms of function evaluations for the assignment and layout tasks and the three compared algorithms. “x” is written when the metric is irrelevant. uses the swap operator as well as multistart to find new configurations in cases of blocked layout and non-symmetric geometries; thus, it manages to escape from local minima.