# HMACE: Heterogeneous Multi-Agent Collaborative Evolution for Combinatorial Optimization

arXiv: https://arxiv.org/abs/2605.07214 · HTML: https://mlsanity.com/paper/2605.07214/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 33 of its 51 references that are in the map.
- First posted on arXiv 8 May 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 30 of 33)

- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [MetaGPT: Meta Programming for A Multi-Agent Collaborative Framework](https://mlsanity.com/paper/2308.00352/) (2023)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [AgentBench: Evaluating LLMs as Agents](https://mlsanity.com/paper/2308.03688/) (2023)
- [ChatDev: Communicative Agents for Software Development](https://mlsanity.com/paper/2307.07924/) (2023)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [AgentVerse: Facilitating Multi-Agent Collaboration and Exploring Emergent Behaviors](https://mlsanity.com/paper/2308.10848/) (2023)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [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)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (2023)
- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2501.08603/) (2025)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [HSEvo: Elevating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMs](https://mlsanity.com/paper/2412.14995/) (2024)
- [Using Centroidal Voronoi Tessellations to Scale Up the Multi-dimensional Archive of Phenotypic Elites Algorithm](https://mlsanity.com/paper/1610.05729/) (2016)
- [Multi-objective Evolution of Heuristic Using Large Language Model](https://mlsanity.com/paper/2409.16867/) (2024)
- [CORAL: Towards Autonomous Multi-Agent Evolution for Open-Ended Discovery](https://mlsanity.com/paper/2604.01658/) (2026)
- [When Single-Agent with Skills Replace Multi-Agent Systems and When They Fail](https://mlsanity.com/paper/2601.04748/) (2026)
- [Large Language Models as End-to-end Combinatorial Optimization Solvers](https://mlsanity.com/paper/2509.16865/) (2025)
- [AgencyBench: Benchmarking the Frontiers of Autonomous Agents in 1M-Token Real-World Contexts](https://mlsanity.com/paper/2601.11044/) (2026)
- [Large Language Models for Combinatorial Optimization: A Systematic Review](https://mlsanity.com/paper/2507.03637/) (2025)
- [LM4OPT: Unveiling the Potential of Large Language Models in Formulating Mathematical Optimization Problems](https://mlsanity.com/paper/2403.01342/) (2024)
- [MAPF-GPT: Imitation Learning for Multi-Agent Pathfinding at Scale](https://mlsanity.com/paper/2409.00134/) (2024)
- [Efficient Heuristics Generation for Solving Combinatorial Optimization Problems Using Large Language Models](https://mlsanity.com/paper/2505.12627/) (2025)
- [How Multimodal Integration Boost the Performance of LLM for Optimization: Case Study on Capacitated Vehicle Routing Problems](https://mlsanity.com/paper/2403.01757/) (2024)
- [LLMs can Schedule](https://mlsanity.com/paper/2408.06993/) (2024)

## Abstract (arXiv)

Large Language Models have recently emerged as a promising paradigm for automated heuristic design for NP-hard combinatorial optimization problems. Despite this progress, existing LLM-based methods typically rely on monolithic workflows constrained by rigid templates, thereby restricting memory-guided exploration and triggering premature convergence to local optima. To design an autonomous and collaborative architecture, we introduce HMACE, a Heterogeneous Multi-Agent Collaborative Evolution framework that reconceptualizes heuristic search as an organizational design problem. HMACE decomposes each evolutionary generation into an autonomous, role-specialized loop with four coordinated agents: a Proposer for strategy exploration, a Generator for executable heuristic synthesis, an Evaluator for empirical assessment, and a Reflector for archive-backed memory update. By coupling behavior-aware retrieval, lightweight candidate filtering, and fitness-grounded archive updates, HMACE guides the search toward diverse and promising heuristic behaviors while avoiding redundant evaluations. Extensive evaluations on representative COPs, including TSP, Online BPP, MKP, and PFSP, show that HMACE achieves a favorable quality-efficiency trade-off compared to state-of-the-art single-agent and multi-agent baselines. In the matched LLM-driven reference comparison, HMACE achieves the lowest average gaps on TSP and Online BPP (0.464% and 0.223%, respectively), while requiring only 0.13M and 0.42M tokens for the two tasks, substantially fewer than the compared baselines.