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Merged
codelion merged 1 commit into from
Oct 10, 2026
Merged

Record better circle packing result (2.635977) from issue #156 #500

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18 changes: 13 additions & 5 deletions examples/circle_packing/README.md
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Expand Up @@ -178,20 +178,28 @@ The key innovation in the final solution:
- Representing both circle positions and radii as optimization variables
- Carefully crafted constraints to enforce non-overlap and boundary conditions

This approach achieved a sum of radii of 2.634, matching the AlphaEvolve paper's result of 2.635 to within 0.04%!
This approach achieved a sum of radii of 2.634, matching the AlphaEvolve paper's result of 2.635 to within 0.04%. Subsequent evolution has since produced a program that exceeds the paper's result (see Results below).

![Final Packing Solution](circle_packing_460.png)

## Results

Our final solution achieves:
Our best solution to date, reported in issue #156 and found at iteration 206 (generation 13) of a run configured as phase_1 x100 -> phase_2 x100 -> phase_2 x250, achieves:

```
Sum of radii: 2.634292402141039
Target ratio: 0.9997314619131079 (99.97% of AlphaEvolve's result)
Sum of radii: 2.635977394746595
Target ratio: 1.0003709277975694 (100.04% of AlphaEvolve's 2.635, i.e. ~0.037% above it)
```

This demonstrates that OpenEvolve can successfully reproduce the results from the AlphaEvolve paper on this mathematical optimization problem.
This demonstrates that OpenEvolve can not only reproduce but exceed the results from the AlphaEvolve paper on this mathematical optimization problem.

**Reproducibility note**: the recorded best program (`best_program.py`) is deterministic — it uses no random initialization, so its result can be independently re-verified with the repository evaluator (an earlier recorded best used an unseeded `np.random` fallback and was not reproducible):

```bash
python -c "import importlib.util; spec = importlib.util.spec_from_file_location('evaluator', 'examples/circle_packing/evaluator.py'); ev = importlib.util.module_from_spec(spec); spec.loader.exec_module(ev); print(ev.evaluate('examples/circle_packing/best_program.py'))"
```

This reports `validity=1.0` and `sum_radii=2.6359773947...` (the last digits may vary by ~1e-11 across scipy/BLAS versions). The result is also covered by the `tests/test_circle_packing_best_program.py` regression test.

## Key Observations

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