heilbronn-17
17 points in the unit square; make the smallest triangle they span as large as possible.
Metric min-triangle-area, maximize · Best known 0.016481 (Stead 2026) ·
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hillclimb problem get heilbronn-17 # copies the problem into hillclimb/problems/
hillclimb verify heilbronn-17 # scores the floor; spread 0, the verifier is exact
hillclimb run heilbronn-17 --budget 15mThe problem
Place exactly 17 points inside the unit square [0, 1] x [0, 1] so that the
smallest triangle formed by any 3 of the points has as large an area as
possible (a max-min objective over all C(17,3) = 680 triangles).
Constraints (verified programmatically):
- all points inside the unit square (
0 <= x, y <= 1) - exactly 17 rows
- no 3 points may be exactly collinear (that makes the minimum area 0)
This is a classic hard continuous optimization problem. The best known value for n = 17 is about 0.0165 (Stead 2026).
Regular grids are terrible (many nearly collinear triples). Good approaches:
random/structured starts + local optimization of the max-min objective (e.g.
maximize the smallest area with SLSQP or a soft-min surrogate), simulated
annealing on point positions, and restarts. numpy and scipy are available.
Submission format
Write submission.csv in the working directory with the header id,x,y and 17
rows (id = 0..16), like sample_submission.csv (a weak valid baseline:
points on a parabola).
Scoring
The orchestrator runs problem/verify.py after your script finishes. The
verifier validates the layout and prints val_score: <min triangle area> (0.0
if invalid). Higher is better.
There is no train/test data; this is a pure optimization problem. Keep total runtime well within the execution time limit.