A research team has reworked how large language models tackle hard optimization problems — and the results outperform existing best-known solutions on several classical benchmarks.
Most LLM-guided evolutionary approaches, including Google's AlphaEvolve, ask the model to generate a single program that handles everything from start to finish. ImprovEvolve breaks that into three smaller, specialized subroutines: one that initializes candidate solutions, one that refines them locally, and one that perturbs them to escape dead ends. The system then applies those subroutines in a loop using a strategy borrowed from chemistry called basin-hopping — a way of searching a solution landscape by systematically shaking it to find lower valleys. The claimed results are concrete: new best-known hexagon packing configurations for several counts, a tightened bound on a signal-processing inequality, and improved spherical codes across 90 test cases.
The key insight is cognitive load reduction. A monolithic prompt asking a model to solve a hard optimization problem from scratch is a big ask; a prompt asking it to write a local-improvement subroutine is a much smaller one. That modularity also makes it easier for human experts to step in and tune individual components, which the paper credits for several of its stronger results.
The obvious question is how much of the performance gain comes from the LLM and how much from the basin-hopping structure that any competent algorithm could use — the paper does not fully disentangle those contributions, which will be worth watching as independent groups try to replicate the numbers.