# ImprovEvolve: Basin-Hopping Meets LLM-Guided Evolutionary Search

arXiv: https://arxiv.org/abs/2602.10233 · HTML: https://mlsanity.com/paper/2602.10233/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 23 references that are in the map.
- First posted on arXiv 10 Feb 2026.

## Builds on (most cited first, 8 of 8)

- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolution](https://mlsanity.com/paper/2509.19349/) (2025)
- [Learning to Discover at Test Time](https://mlsanity.com/paper/2601.16175/) (2026)
- [Mathematical exploration and discovery at scale](https://mlsanity.com/paper/2511.02864/) (2025)
- [GigaEvo: An Open Source Optimization Framework Powered By LLMs And Evolution Algorithms](https://mlsanity.com/paper/2511.17592/) (2025)
- [Global Optimization for Combinatorial Geometry Problems Revisited in the Era of LLMs](https://mlsanity.com/paper/2601.05943/) (2026)

## Built on by (most cited first, 1 of 1)

- [HeurEvo: Agentic Evolution of Hybrid Solver-Augmented Heuristics for Time-Critical Mathematical Optimization](https://mlsanity.com/paper/2609.36303/) (2026)

## Abstract (arXiv)

LLM-guided evolutionary computation, most notably AlphaEvolve, has been remarkably successful in discovering novel mathematical constructions by solving challenging optimization problems. The standard approach is to evolve a monolithic program that directly outputs a candidate solution. We present ImprovEvolve, an algorithmic alternative that drastically reduces cognitive load on the LLM. Instead of prompting the model for an end-to-end optimizer, we evolve a program with three specialized operators of initialization, local improvement, and perturbation. We then approach the optimum by iteratively applying local improvements and intensity-scheduled perturbations, effectively driving a basin-hopping search with LLM-evolved subroutines. For hexagon in hexagon packing, ImprovEvolve discovers new state-of-the-art packings of 11, 12, 15, and 16 hexagons, and additionally for 14, 17, and 23 hexagons after minimal expert tuning of the generated code. For the second autocorrelation inequality, the evolved and human-scaled program pushes the lower bound from 0.96102 to 0.96258. For spherical codes, the ImprovEvolve program lowers the best-known maximum cosine for the majority of 90 randomly chosen diverse state-of-the-art spherical codes, achieving relative improvements of up to 2.4%.