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

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