design space pruning heuristics and global optimization method for ...

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