# HSEvo: Elevating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMs

arXiv: https://arxiv.org/abs/2412.14995 · HTML: https://mlsanity.com/paper/2412.14995/

## Key facts

- Cited by 73 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 31 references that are in the map.
- First posted on arXiv 19 Dec 2024.

## Builds on (most cited first, 6 of 6)

- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Large Language Models as Evolutionary Optimizers](https://mlsanity.com/paper/2310.19046/) (2023)
- [Language Model Crossover: Variation through Few-Shot Prompting](https://mlsanity.com/paper/2302.12170/) (2023)
- [BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimization](https://mlsanity.com/paper/2301.03313/) (2023)

## Built on by (most cited first, 30 of 73)

- [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2501.08603/) (2025)
- [CUDA-L1: Improving CUDA Optimization via Contrastive Reinforcement Learning](https://mlsanity.com/paper/2507.14111/) (2025)
- [EoH-S: Evolution of Heuristic Set using LLMs for Automated Heuristic Design](https://mlsanity.com/paper/2508.03082/) (2025)
- [Recursive Self-Improvement in AI: From Bounded Self-Refinement to Autonomous Research Loops](https://mlsanity.com/paper/2607.07663/) (2026)
- [Large Language Models as End-to-end Combinatorial Optimization Solvers](https://mlsanity.com/paper/2509.16865/) (2025)
- [HeuriGym: An Agentic Benchmark for LLM-Crafted Heuristics in Combinatorial Optimization](https://mlsanity.com/paper/2506.07972/) (2025)
- [HiFo-Prompt: Prompting with Hindsight and Foresight for LLM-based Automatic Heuristic Design](https://mlsanity.com/paper/2508.13333/) (2025)
- [Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learning](https://mlsanity.com/paper/2506.02392/) (2025)
- [A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solving](https://mlsanity.com/paper/2509.08269/) (2025)
- [Generalizable Heuristic Generation Through LLMs with Meta-Optimization](https://mlsanity.com/paper/2505.20881/) (2025)
- [URS: A Unified Neural Routing Solver for Cross-Problem Zero-Shot Generalization](https://mlsanity.com/paper/2509.23413/) (2025)
- [Combinatorial Optimization for All: Using LLMs to Aid Non-Experts in Improving Optimization Algorithms](https://mlsanity.com/paper/2503.10968/) (2025)
- [MOTIF: Multi-strategy Optimization via Turn-based Interactive Framework](https://mlsanity.com/paper/2508.03929/) (2025)
- [VRPAgent: LLM-Driven Discovery of Heuristic Operators for Vehicle Routing Problems](https://mlsanity.com/paper/2510.07073/) (2025)
- [Leveraging Large Language Models to Develop Heuristics for Emerging Optimization Problems](https://mlsanity.com/paper/2503.03350/) (2025)
- [LLM-Meta-SR: In-Context Learning for Evolving Selection Operators in Symbolic Regression](https://mlsanity.com/paper/2505.18602/) (2025)
- [Large Language Models in Operations Research: Methods, Applications, and Challenges](https://mlsanity.com/paper/2509.18180/) (2025)
- [PathWise: Planning through World Model for Automated Heuristic Design via Self-Evolving LLMs](https://mlsanity.com/paper/2601.20539/) (2026)
- [TrajEvo: Designing Trajectory Prediction Heuristics via LLM-driven Evolution](https://mlsanity.com/paper/2505.04480/) (2025)
- [TrajEvo: Trajectory Prediction Heuristics Design via LLM-driven Evolution](https://mlsanity.com/paper/2508.05616/) (2025)
- [An Agentic Framework with LLMs for Solving Complex Vehicle Routing Problems](https://mlsanity.com/paper/2510.16701/) (2025)
- [LLM-Guided Search for Deletion-Correcting Codes](https://mlsanity.com/paper/2504.00613/) (2025)
- [RedAHD: Reduction-Based End-to-End Automatic Heuristic Design with Large Language Models](https://mlsanity.com/paper/2505.20242/) (2025)
- [Pareto-Grid-Guided Large Language Models for Fast and High-Quality Heuristics Design in Multi-Objective Combinatorial Optimization](https://mlsanity.com/paper/2507.20923/) (2025)
- [Discovering heuristics in a complex SAT solver with large language models](https://mlsanity.com/paper/2507.22876/) (2025)
- [LLM4Branch: Large Language Model for Discovering Efficient Branching Policies of Integer Programs](https://mlsanity.com/paper/2605.10401/) (2026)
- [TIDE: Tuning-Integrated Dynamic Evolution for LLM-Based Automated Heuristic Design](https://mlsanity.com/paper/2601.21239/) (2026)
- [AHD Agent: Agentic Reinforcement Learning for Automatic Heuristic Design](https://mlsanity.com/paper/2605.08756/) (2026)
- [Game-Theoretic Co-Evolution for LLM-Based Heuristic Discovery](https://mlsanity.com/paper/2601.22896/) (2026)
- [Beyond the Node: Clade-level Selection for Efficient MCTS in Automatic Heuristic Design](https://mlsanity.com/paper/2602.00549/) (2026)

## Abstract (arXiv)

Automatic Heuristic Design (AHD) is an active research area due to its utility in solving complex search and NP-hard combinatorial optimization problems in the real world. The recent advancements in Large Language Models (LLMs) introduce new possibilities by coupling LLMs with evolutionary computation to automatically generate heuristics, known as LLM-based Evolutionary Program Search (LLM-EPS). While previous LLM-EPS studies obtained great performance on various tasks, there is still a gap in understanding the properties of heuristic search spaces and achieving a balance between exploration and exploitation, which is a critical factor in large heuristic search spaces. In this study, we address this gap by proposing two diversity measurement metrics and perform an analysis on previous LLM-EPS approaches, including FunSearch, EoH, and ReEvo. Results on black-box AHD problems reveal that while EoH demonstrates higher diversity than FunSearch and ReEvo, its objective score is unstable. Conversely, ReEvo's reflection mechanism yields good objective scores but fails to optimize diversity effectively. With this finding in mind, we introduce HSEvo, an adaptive LLM-EPS framework that maintains a balance between diversity and convergence with a harmony search algorithm. Through experimentation, we find that HSEvo achieved high diversity indices and good objective scores while remaining cost-effective. These results underscore the importance of balancing exploration and exploitation and understanding heuristic search spaces in designing frameworks in LLM-EPS.