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

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