# Pareto-Grid-Guided Large Language Models for Fast and High-Quality Heuristics Design in Multi-Objective Combinatorial Optimization

arXiv: https://arxiv.org/abs/2507.20923 · HTML: https://mlsanity.com/paper/2507.20923/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 29 references that are in the map.
- First posted on arXiv 28 Jul 2025.

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

- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [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)
- [Evolutionary Computation in the Era of Large Language Model: Survey and Roadmap](https://mlsanity.com/paper/2401.10034/) (2024)
- [HSEvo: Elevating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMs](https://mlsanity.com/paper/2412.14995/) (2024)
- [Pareto Set Learning for Neural Multi-objective Combinatorial Optimization](https://mlsanity.com/paper/2203.15386/) (2022)
- [Neural Multi-Objective Combinatorial Optimization with Diversity Enhancement](https://mlsanity.com/paper/2310.15195/) (2023)

## Built on by (most cited first, 4 of 4)

- [RefineEvo: Planning-Guided Heuristic Evolution with Bidirectional Experience](https://mlsanity.com/paper/2607.11358/) (2026)
- [QDEvo: A Multi-Objective Quality-Diversity Framework for Automated Heuristic Design](https://mlsanity.com/paper/2607.11916/) (2026)
- [MMP-A*: Multimodal Perception Enhanced Incremental Heuristic Search on Path Planning](https://mlsanity.com/paper/2601.01910/) (2026)
- [Language-Grounded Multi-Agent Planning for Personalized and Fair Participatory Urban Sensing](https://mlsanity.com/paper/2603.24014/) (2026)

## Abstract (arXiv)

Multi-objective combinatorial optimization problems (MOCOP) frequently arise in practical applications that require the simultaneous optimization of conflicting objectives. Although traditional evolutionary algorithms can be effective, they typically depend on domain knowledge and repeated parameter tuning, limiting flexibility when applied to unseen MOCOP instances. Recently, integration of Large Language Models (LLMs) into evolutionary computation has opened new avenues for automatic heuristic generation, using their advanced language understanding and code synthesis capabilities. Nevertheless, most existing approaches predominantly focus on single-objective tasks, often neglecting key considerations such as runtime efficiency and heuristic diversity in multi-objective settings. To bridge this gap, we introduce Multi-heuristics for MOCOP via Pareto-Grid-guided Evolution of LLMs (MPaGE), a novel enhancement of the Simple Evolutionary Multiobjective Optimization (SEMO) framework that leverages LLMs and Pareto Front Grid (PFG) technique. By partitioning the objective space into grids and retaining top-performing candidates to guide heuristic generation, MPaGE utilizes LLMs to prioritize heuristics with semantically distinct logical structures during variation, thus promoting diversity and mitigating redundancy within the population. Through extensive evaluations, MPaGE demonstrates superior performance over existing LLM-based frameworks, and achieves competitive results to traditional Multi-objective evolutionary algorithms (MOEAs), with significantly faster runtime. Our code is available at: https://github.com/langkhachhoha/MPaGE.