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

In an attempt to reduce the number of required function calls, the number of stall
generations required for convergence was lowered in Case 2. While the number of outer
loop function calls was reduced to 144 and the number of MALTO function calls was
reduced to just over 43,000, the solution success rate also decreased to 40%. Therefore,
more runs of the genetic algorithm would be required to find the optimal solution with
the same confidence as for Case 1. Next, the number of runs of the inner loop GA per
function call was increased to five, keeping the remaining settings the same as from Case
2. This resulted in raising the success rate of the GA back to 60%, while reducing the
number of required MALTO calls from Case 1. Finally, the population size was
increased to 100 for both the inner and outer loops to try to raise the success rate above
60%. While the success rate was increased to 80%, the number of calls to MALTO also
increased to over 140,000. The results presented in Table 7 indicate that the multi-level
genetic algorithm is successful at locating the optimal solution more than half the time
(depending on the settings chosen). The number of MALTO runs required, however,
makes this method prohibitive, particularly as the problem size increases. Each end-toend
MALTO run takes on the order of 10 seconds, which would require anywhere from 5
days (for Case 2) to 16 days (for Case 4) for a single run of the genetic algorithm on a
single processor.
Next, the branch-and-bound method presented in Section 2.3.2 is evaluated as the
outer-loop optimizer. As aforementioned, it relies on the ability of the two-impulse
approximation to act as an upper bound for the optimal low-thrust solution. For each
trajectory leg (Earth – Asteroid 1, Earth – Asteroid 1 – Asteroid 2, and Earth – Asteroid 1
– Asteroid 2 – Asteroid 3), the mass-optimal two-impulse solution is compared to the
mass-optimal low-thrust solution for each possible asteroid sequence. The two-impulse
optimal solutions represent the minimum ∆V solutions over all possible number of
revolutions, using the same departure date range and times of flight as the sample
problem. The optimal solutions are found using a grid search. The corresponding mass
77