# Automated Design of CubeSats using Evolutionary Algorithm for Trade Space Selection
## 5 Results  
For the test case the orbit of the satellite is simulated for an altitude of 400 km, inclination of 90\({}^{\circ}\), eccentricity of 0 (circular orbit), RAAN of 90\({}^{\circ}\), argument of perigee of 0\({}^{\circ}\), and mean anomaly of 0\({}^{\circ}\). The values of the constants used in the simulation are shown in Table 2. The optimization problem is simulated for 10 orbits in MATLAB, and the results are presented in Figures 10 and 11. Figure 10a shows the evolution of the fitness function \(\mathcal{F}(\mathcal{G})\) over 250 generations with 100 populations in each generation. Figure 10b shows the evolution of the total downloadable ground area  
Figure 11: Evolution of the constraints \(g_{2}\) to \(g_{10}\) for the CubeSat design MMKP. Figure 10: Performance of evolutionary algorithm on the CubeSat design multidimensional multiple-choice knapsack problem (MMKP): evolution of the (**a**) fitness function; (**b**) total downloadable ground area coverage; (**c**) total mass of the CubeSat; (**d**) total cost of the CubeSat, over generations along with the 95% confidence interval over 20 runs. coverage, \(AC_{D}\), Figure 10c shows that of the total mass, \(m_{T}\), and Figure 10d shows that of the total cost, \(c_{T}\), of the CubeSat over 250 generations. The shaded region of each of the plots show the 95% confidence interval over 20 runs. The results of the plots show that the fitness function decreased with generations converging to a constant fitness, while the total downloadable ground area coverage increased, and the total mass and total cost decreased with generations as implemented in the optimization problem. Figure 11 shows the evolution of the constraints \(g_{2}\) to \(g_{10}\). The constraint \(g_{1}\) is already presented in Figure 10c, which shows that the total mass is below the 4 kg allotted mass of a 3U CubeSat. Figure 11a,b shows the evolution of the dimension of the assembled CubeSat components along z, x, and y directions, showing it is within the 340 mm and 105 mm limit (shown by the dashed lines). Figure 11c shows the evolution of the average solar power generated per orbit, \(P_{avg}\), and the total power requirement of the CubeSat, \(P_{T}\), satisfying the requirement \(P_{avg}\geq P_{T}\). Figure 11d shows the evolution of the state of charge, SOC, of the battery system with the dashed line showing the minimum requirement of 0.2. Figure 11e shows the evolution of the pointing accuracy of the ADCS system, which satisfies the constraint _Pointing Accuracy_\(\leq 1^{\circ}\). Figure 11f,g shows the evolution of the clock frequency and storage capacity of the on-board computer, which are greater than the specified values of 730 MHz and 1.25 Gb, respectively (shown by the dashed lines). Figure 11h shows the evolution of the antenna frequency (\(f_{ant}\)) along with the upper (\(f_{trans}^{(U)}\)) and lower (\(f_{trans}^{(L)}\)) limit of the frequency of the transceiver, showing the antenna frequency is within the limit of the bandwidth of the transceiver. It is clearly evident that all the constraints have been satisfied when the optimization process was terminated, and as such, the final solutions found are in the feasible region of the design space. Figure 12 shows the rendering of the evolution of the best design over generations 1, 12, 15, 20, 30, 80, 100, and 150. It can be seen that the number of solar panels and their positions changed over generations, and at the same time, the internal components vertically stacked inside the structure also changed. Figures 13 and 14 show the variation of the design variables (represented by the gene in Figure 3) of the best individual over generations. The color of the design variables represents the component selected from the inventory in Figure 13 and the number of batteries and solar panels in Figure 14. It can be seen that the combination of the subsystems and the number of batteries and solar panels changed until generation 150, and then an optimal combination was found.