# HeurEvo: Agentic Evolution of Hybrid Solver-Augmented Heuristics for Time-Critical Mathematical Optimization

arXiv: https://arxiv.org/abs/2609.36303 · HTML: https://mlsanity.com/paper/2609.36303/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 57 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

- LLM agents and tool use

## Builds on (most cited first, 30 of 31)

- [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)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [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)
- [Evolution through Large Models](https://mlsanity.com/paper/2206.08896/) (2022)
- [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2501.08603/) (2025)
- [LLaMEA: A Large Language Model Evolutionary Algorithm for Automatically Generating Metaheuristics](https://mlsanity.com/paper/2405.20132/) (2024)
- [Mathematical exploration and discovery at scale](https://mlsanity.com/paper/2511.02864/) (2025)
- [HSEvo: Elevating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMs](https://mlsanity.com/paper/2412.14995/) (2024)
- [ThetaEvolve: Test-time Learning on Open Problems](https://mlsanity.com/paper/2511.23473/) (2025)
- [AdaEvolve: Adaptive LLM Driven Zeroth-Order Optimization](https://mlsanity.com/paper/2602.20133/) (2026)
- [EvoX: Meta-Evolution for Automated Discovery](https://mlsanity.com/paper/2602.23413/) (2026)
- [Algorithm Evolution Using Large Language Model](https://mlsanity.com/paper/2311.15249/) (2023)
- [Multi-objective Evolution of Heuristic Using Large Language Model](https://mlsanity.com/paper/2409.16867/) (2024)
- [CodeEvolve: an open source evolutionary coding agent for algorithmic discovery and optimization](https://mlsanity.com/paper/2510.14150/) (2025)
- [DeltaEvolve: Accelerating Scientific Discovery through Momentum-Driven Evolution](https://mlsanity.com/paper/2602.02919/) (2026)
- [LoongFlow: Directed Evolutionary Search via a Cognitive Plan-Execute-Summarize Paradigm](https://mlsanity.com/paper/2512.24077/) (2025)
- [HeurAgenix: Leveraging LLMs for Solving Complex Combinatorial Optimization Challenges](https://mlsanity.com/paper/2506.15196/) (2025)
- [Constructing Industrial-Scale Optimization Modeling Benchmark](https://mlsanity.com/paper/2602.10450/) (2026)
- [GigaEvo: An Open Source Optimization Framework Powered By LLMs And Evolution Algorithms](https://mlsanity.com/paper/2511.17592/) (2025)
- [MOTIF: Multi-strategy Optimization via Turn-based Interactive Framework](https://mlsanity.com/paper/2508.03929/) (2025)
- [Global Optimization for Combinatorial Geometry Problems Revisited in the Era of LLMs](https://mlsanity.com/paper/2601.05943/) (2026)
- [LLM-Driven Co-Evolutionary Automated Heuristic Design for Bi-Component Coupled Combinatorial Optimization](https://mlsanity.com/paper/2606.00718/) (2026)
- [RefineEvo: Planning-Guided Heuristic Evolution with Bidirectional Experience](https://mlsanity.com/paper/2607.11358/) (2026)
- [ImprovEvolve: Basin-Hopping Meets LLM-Guided Evolutionary Search](https://mlsanity.com/paper/2602.10233/) (2026)
- [Out-of-the-Box Global Optimization for Packing Problems: New Models and Improved Solutions](https://mlsanity.com/paper/2605.04850/) (2026)
- [GRIMIP: A General Framework for Instance-Specific Configuration of MIP Solvers Using LLMs](https://mlsanity.com/paper/2606.23299/) (2026)
- [MILP-Evo: Closed-Loop Fully Automatic Design of MILP Solvers](https://mlsanity.com/paper/2607.18252/) (2026)
- [MuEvo: LLM-Driven Evolution of Multi-Heuristic Ensemble](https://mlsanity.com/paper/2608.03636/) (2026)

## Abstract (arXiv)

Recent advances in agentic heuristic design use AI agents and execution feedback to automate algorithm discovery for challenging optimization problems. In many practical settings, high-quality solutions must be obtained under strict runtime constraints, motivating hybrid approaches that combine problem-specific heuristics with powerful mathematical programming solvers. However, existing approaches typically improve heuristic components within predefined procedures or tune solver configurations in isolation. This limits holistic adaptation of where to allocate computation, how to leverage solvers, and how to refine the overall algorithmic structure. To address these limitations, we propose HeurEvo, an automated plan--code--component co-evolution framework that jointly evolves the high-level algorithmic structures, their implementations, and a shared pool of reusable components. A planner determines which algorithmic components to use, how to combine them, and how to allocate runtime across stages, a coder realizes the resulting plan as executable code, while a component evolver updates the shared component pool. Within an island-based evolutionary framework, plans and implementations co-evolve with feedback from an interpreter agent that analyzes execution results and identifies opportunities for improvement. Across diverse combinatorial optimization benchmarks and challenging MIPLIB instances, HeurEvo finds high-quality solutions within tight runtime budgets, often matching or surpassing state-of-the-art optimization solvers given hours or days of computation. On several nonlinear geometry problems such as hexagon packing, it also improves upon the best previously reported results. These results highlight the value of jointly searching over algorithmic structure and implementation for agentic heuristic design.