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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two-impulse optimum solutions. There<strong>for</strong>e, a larger sample size is available to more<br />
accurately determine the next required value <strong>for</strong> the impulsive multiplier. This procedure<br />
can also be carried out at the end of the branch-<strong>and</strong>-bound algorithm (after multiple<br />
iterations) to ensure that the correct value of the impulsive multiplier has been converged<br />
on. This process also serves to potentially locate additional good solutions that were not<br />
calculated during the branch-<strong>and</strong>-bound algorithm. This is especially important if the<br />
optimal solution is located early in the branch-<strong>and</strong>-bound algorithm, since the high value<br />
of the lower bound will eliminate a large number of potentially good solutions. While<br />
locating the optimum solution early in the algorithm will minimize the number of lowthrust<br />
<strong>optimization</strong>s that must be carried out, it also results in a larger number of good<br />
solutions being pruned out. The number of good solutions desired (in addition to the<br />
optimum) will determine the number of additional low-thrust <strong>optimization</strong>s to be carried<br />
out after the branch-<strong>and</strong>-bound algorithm as terminated.<br />
Furthermore, if the branch-<strong>and</strong>-bound algorithm is started with an estimate made<br />
<strong>for</strong> the initial value of the lower bound (step 1c), <strong>and</strong> a satisfactory set of low-thrust<br />
solutions is not found, the lower bound can be incrementally decreased <strong>and</strong> the branch<strong>and</strong>-bound<br />
algorithm re-run with the new initial lower bound. Both in this scenario <strong>and</strong><br />
in the iterative approach to setting the impulsive multiplier, it is not necessary to re-run<br />
the two-impulse or low-thrust <strong>optimization</strong>s that have already been calculated. In order<br />
to minimize computation time, both the two-impulse <strong>and</strong> low-thrust optima should be<br />
saved <strong>for</strong> each asteroid sequence <strong>for</strong> which they are evaluated. A simple table look-up<br />
can then be used <strong>for</strong> these sequences as opposed to rerunning the <strong>optimization</strong>s <strong>for</strong> each<br />
iteration through the branch-<strong>and</strong>-bound algorithm. In this manner, only the new asteroid<br />
sequences requiring <strong>optimization</strong> need to be evaluated.<br />
A similar iterative approach can also be taken with regards to the <strong>pruning</strong> phase.<br />
If time permits upon completion of the <strong>method</strong>ology, the <strong>pruning</strong> percentages could then<br />
also be relaxed, increasing the number of asteroid sequences passed to the <strong>global</strong><br />
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