Circle Packing
Pack 26 non-overlapping circles in a unit square to maximize the sum of their radii (AlphaEvolve B.12). Target: 2.635.
Problem
- Pack exactly 26 circles inside a unit square
- No circles may overlap
- Each circle must lie entirely within the square
- Maximize the sum of all radii
Run
# From repo root
uv run skydiscover-run \
benchmarks/math/circle_packing/initial_program.py \
benchmarks/math/circle_packing/evaluator.py \
-c benchmarks/math/circle_packing/config.yaml \
-s [your_algorithm] \
-i 100
A codebase/reference/ directory is provided with geometric insights (hex grids, optimization patterns, packing strategies) that can be used with agentic mode (--agentic).
Scoring
- combined_score:
sum_of_radii / 2.635(ratio to AlphaEvolve target) - Evaluator validates no overlaps and boundary constraints
Files
| File | Description |
|---|---|
initial_program.py |
Seed: simple ring-based circle arrangement |
evaluator.py |
Validates constraints, computes sum-of-radii ratio to target |
config.yaml |
LLM and evaluator settings |
codebase/reference/ |
Geometric reference material for agentic mode |