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

Of the remaining sequences, the 1 st , 3 rd , 4 th , and 7 th best known solutions from Table 20
all remain in the design space.
Next, the global optimization phase is applied to the reduced design space,
beginning with ranking the remaining asteroid sequences by the normalized sum of the
pruning metrics. Due to the GTOC2 objective function, which includes the overall time
of flight, a slight modification was made in the calculation of the optimal two-impulse
solutions, which are used to determine the upper bounds during the branch-and-bound
process. When the optimal two-impulse solutions were initially being calculated, it was
discovered that many of the optimal solutions were falling in the very low time of flight
range. As the low-thrust optimal solutions were calculated, it became apparent that most
of the asteroid sequences that yield very good impulsive solutions at low times of flight
do not translate to good low-thrust solutions. While low times of flight are possible for
impulsive trajectories, low-thrust trajectories generally require longer times of flight to be
feasible. Therefore, a restriction was placed on the minimum time of flight when
calculating the impulsive solutions. This change was initially made in order to better
model the low-thrust trajectories. However, it also served to reduce the number of lowthrust
optimizations that would be required, since the optimal impulsive objective
function for many of the asteroid sequences was greatly reduced when applying the time
of flight restriction. For this problem, this minimum allowable time of flight for the
impulsive solutions was chosen at 7 years, which was estimated as the minimum realistic
time of flight for the low-thrust trajectories. Figure 52 plots the optimal impulsive
solutions for the asteroid sequences remaining after the pruning phase, with and without a
time of flight restriction.
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