Researcher Wes Sander published a paper on arXiv about the Discovery Loop system, in which an LLM agent evolves optimization algorithms under the control of an independent mathematical verifier. In a single cycle, the system broke ten active records in the Packomania database in the circle packing problem, and the total LLM cost was $27.72.

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What happened

The paper with number 2609.05093 (category cs.AI) appeared on arXiv on September 4, 2026. The system works on a simple principle: evolution starts with a simple seed solver, then the model proposes improvements based on a results table and the history of past ideas, each candidate is checked by an independent verifier, and only successful changes are saved, while adaptive plateau-detection stops the cycle when the gains no longer justify the costs. On the Packomania csqv benchmark, where N circles of variable radius must be packed into a unit square, maximizing the sum of radii, the system improved the best known solutions for ten values of N: 101, 102, 103, 105, 106, 107, 108, 109, 111, and 114, by 2.4–5.4% compared to previous records, spending no more than 15 iterations on the entire cycle. The Packomania database itself independently accepted the ten new candidates: in the changelog for September 2–4, 2026, they are recorded as obtained by an LLM-evolved optimizer. The system code is published under the MIT license in the repository github.com/ucsandman/discovery-loop.

Context

Circle packing is a classic combinatorial optimization problem, and Packomania maintains an open table of the best known solutions: in fact, the “referee” here is not a reviewer, but a competitive community record database where any new solution can be independently verified. It is important that the found variants are not new mathematics: the LLM recombines known optimization primitives — penalty L-BFGS-B, basin hopping on the active solution, SLSQP polishing on the contact graph — with precise parameterization. The novelty of the result is in the automatic search and verification: the “LLM proposal → independent check → success preservation” cycle at a cost of about $2.77 per broken record is a reproducible pattern, not a one-off trick.

Why this matters for the industry

For the industry, this is a documented and externally verified example that an LLM agent is capable of autonomously generating verifiable improvements in classic optimization, not just writing code on a developer's request. The mechanism with an independent verifier and plateau-detection significantly lowers the barrier to entry for automated research in optimization problems: neither a large computing budget nor months of manual work are needed. The repository already contains plugins for MIPLIB, CVRP, and power grids — the author marks them as unvalidated, but the plugin structure itself sets a roadmap: if other groups reproduce the scheme in these domains with external validation, “LLM hyperheuristic” with an independent checker may become a standard tool for finding new solutions. Currently, this is not a service: there is no API, pricing, or SLA, and latency is not stated.

Why this matters for users

For the reader, the result is useful right now: the 8-page paper is available on arXiv under the CC BY 4.0 license, and the repository can be cloned and deployed for your own optimization problem — all you need is your own objective function and a fast independent verifier. Fresh records can be seen live on the Packomania csqv page, and the best/ folder in the repository contains .pck files with accepted solutions, so the geometry of each packing can be checked independently. Essentially, this is a ready-made open-source template for the “LLM + verifier” cycle, on which you can practice agent-based search in the space of algorithms for a few cents of LLM cost.

What is still unknown / limitations

The sources do not specify the identifier and version of the LLM used. There is no ablation experiment — the same cycle without an LLM — no baseline with a human expert or ordinary evolutionary search, and no descriptions of repeated runs, so the robustness of the result to chance cannot be assessed. External validation has only been passed for circle packing: the MIPLIB, CVRP, and power grid plugins are directly marked by the author as unvalidated, and the system's production characteristics — latency, run stability, cost in other domains — are not stated.

Sources

Author

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