heilbronn-14

Metric min-triangle-area, maximize · Best known 0.0243 (Beyleveld 2006) · Play · Code · All example problems

hillclimb problem get heilbronn-14      # copies the problem into hillclimb/problems/
hillclimb verify heilbronn-14           # scores the floor; spread 0, the verifier is exact
hillclimb run heilbronn-14 --budget 15m

The problem

Place exactly 14 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(14,3) = 364 triangles).

Constraints (verified programmatically):

• all points inside the unit square (0 <= x, y <= 1)
• exactly 14 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 = 14 is about 0.0243 (Beyleveld 2006). 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 14 rows (id = 0..13), 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.