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

sequences were optimized in low-thrust and the entire branch-and-bound algorithm
required just over one month to complete. For the large problems examined in full – the
modified GTOC2 and modified GTOC2 problems – the methodology was able to locate
at least 70% of the best known solutions.
For the GTOC3 problem, the methodology was applied to a modified version that
did not include gravity assists and did not take asteroid stay time into account in the
objective function. However, the asteroid sequence that yielded the winning solution in
the GTOC3 competition was identified, along with the asteroid sequences that yielded
eight of the top ten competition solutions. Only 17 asteroid sequences had to be
optimized in low-thrust. Applying this algorithm to the GTOC3 competition would have
clearly left ample time to add gravity assists to the best sequences found, and to add the
stay time consideration back into the objective function. This illustrates the ability of the
methodology to be used as an initial screening technique for problems that require more
complicated trajectories, such as gravity assists, and/or additional objective function
terms.
For the modified GTOC2 problem, the methodology was able to locate four of the
seven known solutions with objective function values greater than 80 kg/yr, including the
best known solution. Additionally, three additional asteroid sequences greater than 80
kg/yr, which were not reported by the GTOC2 competitors were also found.
Due to resource limitations, the methodology was not run to completion for the
full GTOC2 problem. However, in just two weeks of run time, three new solutions
greater than 80 kg/yr were identified, the best of which would have placed 3 rd in the
original GTOC2 competition. If more time and/or computing resources were available,
an incremental approach could be taken, as presented in Section 5.3. In order to locate
the best known solution and eight of the top thirteen known solutions (all with J > 80
kg/yr), approximately 4,620 asteroid sequences would have to be optimized in low-thrust
(assuming an initial lower bound of 100 kg/yr and that no solutions greater than 100
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