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

of 10,000 asteroid sequences in the design space, which is small enough to be handled by
the global optimization phase, but large enough to be confident that many of the best
asteroid sequences have not been pruned out. Because all of the asteroids are near-Earth
asteroids, and therefore have similar semi-major axes, the first pruning metric will not be
employed on this problem – the requirement that the asteroid sequence must increase
sequentially in semi-major axis. Furthermore, because only total time of flight is
constrained, and not part of the objective function, this pruning metric becomes even less
relevant. Therefore, only the last two pruning metrics will be used: θ wedge and optimal
phase-free, two-impulse ∆V. In order to achieve the desired size of the design space, the
following percentage reductions are applied to the problem, for both pruning metrics:
70% for Leg 1, 60% for Leg 2, 50% for Leg 3, and 25% for Leg 4. This reduces the
number of asteroid sequences to 10,311. As a check, the best known sequence, presented
above, is still in the design space.
Next, the global optimization step, combining the branch-and-bound method with
the genetic algorithm, is applied to the reduced problem. Because there is already a best
known asteroid sequence, it is used as the initial lower bound on low-thrust final mass
Note that this sequence also happens to be the highest ranked sequence based on the
normalized sum of the pruning metrics and so would be the first low-thrust trajectory
evaluated by the branch-and-bound algorithm. For each asteroid sequence where the
low-thrust optimum must be computed, the genetic algorithm is run three times, using the
settings listed in Table 15 and Table 16.
Table 15: Settings for genetic algorithm within branch-and-bound, as applied to the modified
GTOC3 problem.
GA Setting
Population Size 90
Stall Generations 10
Tournament Size 4
Crossover Probability 0.8
Mutation Probability 0.1
Value
109