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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Table 8 lists the 10 best asteroid sequences, ordered in terms of final mass. Table<br />
9 lists the Keplerian orbital elements of each of the asteroids that appear in Table 8, in the<br />
J2000 heliocentric ecliptic frame.<br />
4.2 Application of Methodology to Intermediate Problem<br />
4.2.1 Pruning Phase<br />
First, the <strong>pruning</strong> phase of the <strong>method</strong>ology is applied to the intermediate<br />
problem. The first step of the <strong>pruning</strong> phase requires keeping only asteroid sequences<br />
where the semi-major axis of each asteroid increases from one asteroid to the next. This<br />
first step reduces the number of asteroid sequences in the <strong>design</strong> <strong>space</strong> from 10,368 to<br />
1,728 (a factor of 6 reduction). Only two sequences were eliminated that yield feasible<br />
solutions (final mass greater than 500 kg), <strong>and</strong> their optimum final masses are 608 kg <strong>and</strong><br />
524 kg. These solutions rank 191 st <strong>and</strong> 467 th , respectively. There<strong>for</strong>e, this first <strong>pruning</strong><br />
step is effective in reducing the size of the <strong>design</strong> <strong>space</strong> without eliminating the best<br />
asteroid sequences.<br />
The second <strong>and</strong> third steps in the <strong>pruning</strong> phase use two metrics to eliminate a<br />
user-chosen percentage of asteroid pairs from each leg of the trajectory. Since this<br />
problem is not significantly larger than the small sample problem, the same percentage<br />
reductions are applied to each leg: k 1 = 0.3, k 2 = 0.25, <strong>and</strong> k 3 = 0.15. The first of these<br />
two metrics – the angle between two asteroids’ angular momentum vectors – reduces the<br />
number of asteroid sequences from 1,728 to 824 (factor of 2). The second metric – the<br />
optimal, phase-free, impulsive ∆V – further reduces the number of asteroid sequences<br />
from 824 to 416 (factor of 2).<br />
Overall, the <strong>pruning</strong> procedure reduces the number of asteroid sequences by a<br />
factor of 25, from 10,368 to 416. While 199 feasible sequences are eliminated, only one<br />
sequence in the top ten is eliminated (M f = 831, ranked 7 th overall). The next best<br />
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