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

CHAPTER III
OVERVIEW OF METHODOLOGY
The final methodology combines a three-level heuristic pruning step, which
quickly reduces the size of the design space, with a multi-level global optimization step,
which locates a suite of good solutions. Each of the steps of the methodology is
presented here, followed by a discussion of the assumptions and scope.
3.1 Overview of Methodology
The pruning phase of the methodology applies three pruning metrics, in order of
required computation time:
(1) a i ≤ a i+1 – keep only asteroid sequences where the semi-major axis of the
asteroids increases from one asteroid to the next
(2) θ wedge – angle between the angular momentum vectors of asteroid pairs
a. θ wedge is computed for all Leg 1 (Earth – 1 st asteroid) asteroid pairs; the
worst k 1 percent is eliminated from the design space.
b. θ wedge is computed for all remaining Leg 2 (1 st asteroid – 2 nd asteroid)
asteroid pairs; the worst k 2 percent is eliminated from the design space.
c. θ wedge is computed for all remaining Leg 3 (2 nd asteroid – 3 rd asteroid)
asteroid pairs; the worst k 3 percent is eliminated from the design space.
d. θ wedge is computed for all remaining Leg 4 (3 rd asteroid – 4 th asteroid)
asteroid pairs; the worst k 3 percent is eliminated from the design space.
(3) ∆V opt – optimal two-impulse, phase-free delta-V between asteroid pairs
a. ∆V opt is computed for all remaining Leg 1 (Earth – 1 st asteroid) asteroid
pairs; the worst k 1 percent is eliminated from the design space.
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