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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Table 29: Best known solutions remaining in <strong>design</strong> <strong>space</strong> <strong>for</strong> varying orders of magnitude reduction<br />
during the <strong>pruning</strong> phase, <strong>for</strong> the modified GTOC3 problem.<br />
Asteroid Sequence<br />
MBfB<br />
(kg)<br />
4+ orders of<br />
magnitude<br />
65<br />
sequences<br />
remaining<br />
4 orders of<br />
magnitude<br />
299<br />
sequences<br />
remaining<br />
3 orders of<br />
magnitude<br />
2,306<br />
sequences<br />
remaining<br />
2 orders of<br />
magnitude<br />
10,311<br />
sequences<br />
remaining<br />
85%-80%-<br />
75%-60%<br />
80%-75%-<br />
70%-60%<br />
75%-70%-<br />
60%-40%<br />
E - 76 - 88 - 49 - E 1621 √ √ √<br />
E - 88 - 76 - 49 - E 1597 √ √ √ √<br />
E - 49 - 37 - 85 - E 1590 √ √ √ √<br />
E - 96 - 88 - 49 - E 1589 √ √ √<br />
E - 88 - 19 - 49 - E 1587 √ √ √ √<br />
E - 88 - 49 - 19 - E 1567 √ √ √ √<br />
E - 96 - 76 - 49 - E 1565 √ √ √<br />
E - 88 - 11 - 49 - E 1558 √ √ √ √<br />
E - 88 - 129 - 49 - E 1557 √ √ √<br />
E - 88 - 76 - 96 - E 1554 √ √ √ √<br />
70%-60%-<br />
50%-25%<br />
5.3.2 Global Optimization Phase Sensitivity to Selection of Initial Lower Bound<br />
For the <strong>global</strong> <strong>optimization</strong> portion of the <strong>method</strong>ology, the algorithm can be<br />
tuned based on the initial value of the lower bound chosen <strong>for</strong> the branch-<strong>and</strong>-bound<br />
algorithm. Shown previously, Figure 53 illustrates the evolution of the branch-<strong>and</strong>bound<br />
algorithm <strong>for</strong> the modified GTOC2 problem. In this figure, all of the asteroid<br />
sequences with impulsive optima (plotted in red) greater than the current lower bound<br />
(plotted in blue) must be optimized in low-thrust. These results were based on running<br />
the branch-<strong>and</strong>-bound algorithm without an initial value <strong>for</strong> the lower bound – there<strong>for</strong>e,<br />
the lower bound is set by applying the genetic algorithm to the first asteroid sequence to<br />
determine its low-thrust optimum. If an estimate is made <strong>for</strong> the initial value of the lower<br />
bound based on the underlying physics of the problem, this would eliminate some of the<br />
up-front low-thrust <strong>optimization</strong>s, few of which generally yield good solutions.<br />
For the modified GTOC2 problem, without an initial estimate of the lower bound<br />
of the objective function, the low-thrust <strong>optimization</strong> of 809 asteroid sequences was<br />
138