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 ...
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
≤<br />
Because these are all near-Earth asteroids, their semi-major axes all fall between 0.9 AU<br />
<strong>and</strong> 1.1 AU. All have low inclination orbits – less than 10 degrees – while their<br />
eccentricities range from near circular to a maximum value of 0.87. Note that this is a<br />
significantly different <strong>design</strong> <strong>space</strong> than in the GTOC2 problem.<br />
In addition, the objective function <strong>for</strong> GTOC3 is also slightly different, as it<br />
involves maximizing a combination of final mass <strong>and</strong> stay time at the asteroids:<br />
J =<br />
m<br />
m<br />
f<br />
i<br />
min<br />
j=<br />
1,3<br />
+ K<br />
τ<br />
( τ )<br />
max<br />
j<br />
(19)<br />
In Equation 19, m i <strong>and</strong> m f are the <strong>space</strong>craft initial <strong>and</strong> final mass, τ j is the stay time at the<br />
j th asteroid, τ max is the maximum allowable flight time, <strong>and</strong> K = 0.2. Unlike GTOC2,<br />
gravity assists using Earth were permitted. Additional problem constraints are listed in<br />
Table 13.<br />
Table 13: Constraints on GTOC3 problem.<br />
Constraint Value Notes<br />
Earth Launch VB∞B 0.5 km/s Unconstrained direction<br />
Earth Launch Date 2016 – 2025 Inclusive<br />
Asteroid Stay Time ≥ 60 days<br />
Total Flight Time ≤ 10 years<br />
Spacecraft Initial Mass 2000 kg<br />
Thruster Isp<br />
3000 s<br />
Maximum Thrust 0.15 N<br />
Can be turned on/off at will<br />
No constraint on direction<br />
For the purpose of validating the proposed <strong>method</strong>ology, the problem is altered<br />
slightly. The objective function is changed to maximizing the final mass at Earth return.<br />
This does not change the problem significantly, since the maximum value of the stay time<br />
portion of the GTOC3 objective function contributes only marginally to the overall<br />
objective function. The first portion of the original objective function will be on the<br />
107