The Jet Propulsion Laboratory recently hosted the 10th Global Trajectory Optimization Competition or GTOC X with a challenge to see how many star systems could be colonized with the the most uniform spacial distribution. The contest constraints were based on time to populate, a limit of 100,000 predefined stars, a fixed number of colonizing ships and as little propulsive velocity change as possible.
What's most interesting is that the nuances of the challenge require thinking about the motion of the ships as well as the motion of the stars around the center of the galaxy. Each ship has a limit of impulsive maneuvers to successfully rendezvous with a star system which forces some optimization on trajectories of the colonizing ships to keep the propulsive change to a minimum(use this link to the deeper descriptive rules in pdf).
Seems Team 7 from China of the College of Aerospace Science and Engineering, National University of Defense Technology and Key Laboratory of Astronautic Dynamics organizations bested all of the competition by colonizing 3798 systems (well above 2nd place). You can see the results here.
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