Reproducing circle packing without providing `TARGET_VALUE = 2.635` from AlphaEvolve paper

[myazdani]

The evaluator is using the TARGET_VALUE = 2.635 from the AlphaEvolve paper which might be considered cheating.

Was anyone able to reproduce the result without including this?

[maisyhoang]

In my opinion, maybe that could be considered cheating if the model can access the Internet and found the solution somewhere. The Gemini model use in the circle packing config might be able to access the Internet. But if it is figuring it out by its own trial after trial, I would call it "encouragement". I would not call my boss a cheater if he comes to my desk and says: "The competitor has produced circle packing = 2.635. That means it is possible and we need to find a solution to match that". Also, what would be the result if we lied to the model, saying in system prompt that AlphaEvolve got 2.8? Or 2.6, would this demotivate the model from going beyond that? Well, this is getting philosophical here.

[codelion]

You can put any other value for the target like 3.0 and it will still work. The target is used to compute the metrics and create evolutionary pressure. It by itself doesn't give a solution. The solution program to the circle problem was not published by AlphaEvolve so it cannot be found on the internet. They only released the construction that is the output from the solution program.

To the best of my knowledge the only place to find the actual program that solves it is here - https://github.com/codelion/openevolve/blob/main/examples/circle_packing/best_program.py which was discovered by OpenEvolve.

[yyh-sjtu]

You can put any other value for the target like 3.0 and it will still work. The target is used to compute the metrics and create evolutionary pressure. It by itself doesn't give a solution. The solution program to the circle problem was not published by AlphaEvolve so it cannot be found on the internet. They only released the construction that is the output from the solution program.

To the best of my knowledge the only place to find the actual program that solves it is here - https://github.com/codelion/openevolve/blob/main/examples/circle_packing/best_program.py which was discovered by OpenEvolve.

How many generations or iterations you used to reach the result 2.634 ?

[codelion]

How many generations or iterations you used to reach the result 2.634 ?

800

[yyh-sjtu]

How many generations or iterations you used to reach the result 2.634 ?

800

Thank you.

[maisyhoang]

@yyh-sjtu fyi, someone managed to find a new SOTA of circle packing in about 450 iterations here. I guess luck is also a factor (or maybe the recently fixed map-elites feature)

[yyh-sjtu]

@yyh-sjtu fyi, someone managed to find a new SOTA of circle packing in about 450 iterations here. I guess luck is also a factor (or maybe the recently fixed map-elites feature)

He said that he briefly ran the code a month ago. The fixing of map-elites feature was added to the main branch last week. Maybe I think the category of LLM is also very important. I ran circle packing with gemini-2.5-flash and gemini-2.5-pro. I found that the evolution speed of gemini-2.5-flash and pro was much faster than that of the combination of gemini-2.0-flash and claude-3.7-sonnet used by the author, while the performance stopped advancing when the sum_radii approached 2.630.

Thanks for your great job, about a month ago I briefly run your code (100 step stage 1 + 100 step stage 2 + 250 step stage 2) and obtain a 2.635977 bound for 26 circle packing problem.

[pudepiedj]

I am new to this, and I've been running the whole thing on local consumer hardware with two Qwen2.5 LLMs operating in tandem through llama-swap. I am sure there are better ways to do it, but there you go ...
Whereas most of the solutions posted seem to be one-shot runs, my sequence actually generated a program that generates multiple solutions. IOW you run it and each time it produces a different quasi-optimal answer. This was achieved by the algorithm having the idea of loading the scipy.optimizer.basinhoppingcode.

import numpy as np
from scipy.optimize import minimize, NonlinearConstraint
from scipy.optimize import basinhopping
import random

Running it in a loop regenerates different solutions each time. Not sure how interesting this is compared with the other ways the scipy.optimizer has been used, but a program that generates multiple solutions is not the same, I think, as one that always deterministically produces just one. Best is very close to the openEvolve best.