# Learning to Solve and Optimize by Evolving Code

arXiv: https://arxiv.org/abs/2605.31049 · HTML: https://mlsanity.com/paper/2605.31049/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 52 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 13 of 13)

- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolution](https://mlsanity.com/paper/2509.19349/) (2025)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [Mathematical exploration and discovery at scale](https://mlsanity.com/paper/2511.02864/) (2025)
- [Scientific Algorithm Discovery by Augmenting AlphaEvolve with Deep Research](https://mlsanity.com/paper/2510.06056/) (2025)
- [Autonomous Code Evolution Meets NP-Completeness](https://mlsanity.com/paper/2509.07367/) (2025)
- [Conflict Generalisation in ASP: Learning Correct and Effective Non-Ground Constraints](https://mlsanity.com/paper/2008.03100/) (2020)
- [Decomposition Strategies and Multi-shot ASP Solving for Job-shop Scheduling](https://mlsanity.com/paper/2205.07537/) (2022)
- [Investigating the Grounding Bottleneck for a Large-Scale Configuration Problem: Existing Tools and Constraint-Aware Guessing](https://mlsanity.com/paper/2601.03850/) (2026)
- [A Heuristic Algorithm Based on Beam Search and Iterated Local Search for the Maritime Inventory Routing Problem](https://mlsanity.com/paper/2505.13522/) (2025)

## Abstract (arXiv)

Combinatorial and optimization problems are fundamental to many industrial AI applications. Solving large-scale real-world instances of such problems typically requires careful problem formalization, specialized solvers, and expert-designed heuristics. Thus, experts need to specify not only what solutions are, but also how they are derived. By introducing the tool CHECKMATE, we show that algorithm generation via code evolution represents a paradigm shift by eliminating the need to formulate the how. CHECKMATE solely relies on the what. Specifically, a formal specification ensures solutions' correctness and enables systematic performance evaluation of the generated programs, while a natural language description guides the evolutionary process. The effectiveness of our method is demonstrated on selected problems from two industrial domains: configuration and scheduling. In all cases, the evolved algorithms consistently outperform state-of-the-art solvers. This underscores the potential of formal methods in guiding code evolution for automatically solving complex real-world problems.