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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1000<br />
900<br />
Final Mass (kg)<br />
800<br />
700<br />
600<br />
500<br />
400<br />
300<br />
200<br />
100<br />
Ballistic x 1.25<br />
Low-Thrust<br />
0<br />
0 100 200 300 400 500 600<br />
Asteroid Sequence #<br />
Figure 33: Comparison of mass-optimal low-thrust <strong>and</strong> two-impulse solutions <strong>for</strong> all Earth –<br />
Asteroid 1 – Asteroid 2 – Asteroid 3 sequences.<br />
The figures above indicate that as calculated, the two-impulse solutions do not<br />
provide a reliable upper bound. However, if the two-impulse solutions are shifted<br />
slightly, then they could provide an upper bound <strong>for</strong> the low-thrust solutions. For the<br />
sample problem, this would require a multiplication factor of 1.09, 1.14, <strong>and</strong> 1.21 <strong>for</strong> Leg<br />
1, Leg 1 + Leg 2, <strong>and</strong> Leg 1 + Leg 2 + Leg 3, respectively. Of course, on a larger<br />
problem, this multiplication factor is not known a priori. Choosing a value of this<br />
parameter that is too small will result in a number of good sequences being pruned out<br />
during the branch-<strong>and</strong>-bound procedure. Choosing a value that is too large, however,<br />
will result in an unnecessarily large number of low-thrust trajectory <strong>optimization</strong>s to be<br />
carried out because very few asteroid sequences will be pruned. The solution is to iterate<br />
on the best value of this multiplication factor during the branch-<strong>and</strong>-bound procedure, as<br />
will be illustrated on the sample problem.<br />
Another important aspect of the branch-<strong>and</strong>-bound <strong>method</strong> is the order in which<br />
the branches are evaluated. Choosing this order in an intelligent fashion can significantly<br />
reduce the number of asteroid sequences that require low-thrust trajectory <strong>optimization</strong>.<br />
If an asteroid sequence with a high final mass is evaluated early in the process, then more<br />
branches will be pruned out than if all low mass sequences are evaluated initially. One<br />
way to choose the order in which to evaluate the various branches is based on the <strong>pruning</strong><br />
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