design space pruning heuristics and global optimization method for ...
design space pruning heuristics and global optimization method for ...
design space pruning heuristics and global optimization method for ...
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N<br />
∑<br />
i<br />
W i<br />
= 0.5⋅<br />
⎛<br />
max⎜<br />
⎝<br />
θ wedge,Legi<br />
N<br />
∑<br />
i<br />
θ wedge,Legi<br />
N<br />
∑<br />
i<br />
+ 0.5⋅<br />
⎞ ⎛<br />
⎟ max⎜<br />
⎠ ⎝<br />
∆V opt,Legi<br />
N<br />
∑<br />
i<br />
∆V opt,Legi<br />
⎞<br />
⎟<br />
⎠<br />
(17)<br />
Each <strong>pruning</strong> metric is summed over all of the legs in the sequence, where each leg<br />
represents each asteroid pair in the sequence, <strong>and</strong> then normalized to fall between zero<br />
<strong>and</strong> one. The two summed metrics are then combined with an equal weighting. By<br />
ranking all of the asteroid sequences using this single value, a user-defined percentage of<br />
sequences can be eliminated.<br />
Final Mass (kg)<br />
1000<br />
900<br />
800<br />
700<br />
600<br />
500<br />
400<br />
300<br />
200<br />
100<br />
0<br />
0 0.2 0.4 0.6 0.8 1 1.2<br />
Summed Pruning Metrics<br />
Figure 28: Final mass as a function of the summed <strong>pruning</strong> metric (Equation 17) <strong>for</strong> each asteroid<br />
sequence remaining in the small sample problem.<br />
Figure 28 plots W i from Equation 17 against the corresponding optimal low-thrust<br />
final mass <strong>for</strong> each asteroid sequence in the small sample problem. In order to keep all<br />
feasible solutions (all solutions with a final mass greater than 500 kg) in the <strong>design</strong> <strong>space</strong>,<br />
up to 55% of the asteroid sequences can be eliminated. In order to keep all of the top ten<br />
asteroid sequences in the <strong>design</strong> <strong>space</strong>, up to 85% of the sequences can be eliminated.<br />
Finally, to keep just the optimum solution in the <strong>design</strong> <strong>space</strong>, up to 99% of the<br />
sequences can be eliminated. The main drawback to this <strong>method</strong>, however, is that each<br />
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