# QDEvo: A Multi-Objective Quality-Diversity Framework for Automated Heuristic Design

arXiv: https://arxiv.org/abs/2607.11916 · HTML: https://mlsanity.com/paper/2607.11916/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 14 references that are in the map.
- First posted on arXiv 6 Jul 2026.

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

- [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)
- [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2501.08603/) (2025)
- [HSEvo: Elevating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMs](https://mlsanity.com/paper/2412.14995/) (2024)
- [Multi-objective Evolution of Heuristic Using Large Language Model](https://mlsanity.com/paper/2409.16867/) (2024)
- [HeuriGym: An Agentic Benchmark for LLM-Crafted Heuristics in Combinatorial Optimization](https://mlsanity.com/paper/2506.07972/) (2025)
- [MOTIF: Multi-strategy Optimization via Turn-based Interactive Framework](https://mlsanity.com/paper/2508.03929/) (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)

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

- [Loreley: Repository-Scale Program Evolution with Quality-Diversity Search](https://mlsanity.com/paper/2608.19703/) (2026)

## Abstract (arXiv)

The integration of Large Language Models (LLMs) with evolutionary computation has emerged as a powerful paradigm for automated heuristic design in combinatorial optimization. However, existing approaches suffer from mode collapse, converging to homogeneous populations that lack semantic diversity and fail to explore the full algorithmic space. We propose Quality-Diversity Evolution (QDEvo), a multi-objective framework that integrates Quality-Diversity optimization with LLM-driven heuristic search, maintaining an unbounded archive of semantically diverse algorithms using pre-trained code embeddings and incorporating hierarchical self-reflection to guide the evolutionary process. Extensive experiments across standard benchmarks and real-world industrial applications demonstrate that QDEvo significantly outperforms state-of-the-art methods in both Hypervolume and Inverted Generational Distance metrics. Our framework enables the discovery of heuristics that are simultaneously high-performing, computationally efficient, and semantically diverse, providing practitioners with a rich portfolio of solutions for complex optimization problems.