“Solving the SpOC GECCO Trappist Tour challenge” — ESA set the task: a space probe has to visit all seven exoplanets of the TRAPPIST-1 system, with minimal time and minimal propellant. My bachelor thesis solves it without prior astrophysics knowledge — using decomposition, permutation analysis and genetic algorithms. Scroll down and experience how.
A probe starts 10 AU outside the TRAPPIST-1 system and has to visit all seven exoplanets (b to h) exactly once — with minimal time and minimal ΔV (propellant). The catch: the planets keep moving on their orbits — this is no ordinary travelling salesman problem, it has moving targets. And the probe must never come closer than 834,840 km to the star. There are 5040 possible sequences, and each one flies differently.
Every mission lives inside a 34-dimensional decision vector: three values for entering the system, six legs with four flight parameters each — and on the right, seven green integers for the planetary sequence. Nobody optimizes 34 entangled values at once. The core of my thesis is decomposition: splitting the problem into two manageable sub-problems.
Computing all 5040 sequences would be far too expensive, and blind guessing wastes compute. My approach: test random sequences and analyze which planet pairs show up next to each other in good solutions — if “4-5” appears in several strong routes, “4-5” is probably a good building block. The best pairs are then assembled into new sequences, with clean transitions between the blocks.
For each promising sequence, a genetic algorithm optimizes the 27 flight parameters — in my thesis, R-NSGA2 surprisingly beat NSGA-II, NSGA-III, U-NSGA-III and AGE-MOEA. Since time and ΔV conflict, the result is not a single solution but a Pareto front. It is scored with the hypervolume: the area between the front and the reference point [2500 ΔV, 4000 days] — the more area, the better the (negative) score. Watch the population push the front towards the bottom left.
The approach ran again and again over several weeks: build new sequences, optimize them with high-complexity R-NSGA2 runs (population up to 400, offspring up to 1500), merge the fronts of all runs and re-check for dominance. The final Pareto front ranges from frugal ~550 m/s in ~3850 days to fast ~1950 days for ~2500 m/s — showing how differently good trajectories can look.