# Large Language Models for Combinatorial Optimization: A Systematic Review

arXiv: https://arxiv.org/abs/2507.03637 · HTML: https://mlsanity.com/paper/2507.03637/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 68 references that are in the map.
- First posted on arXiv 4 Jul 2025.

## Builds on (most cited first, 20 of 20)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Open-TI: Open Traffic Intelligence with Augmented Language Model](https://mlsanity.com/paper/2401.00211/) (2023)
- [Diagnosing Infeasible Optimization Problems Using Large Language Models](https://mlsanity.com/paper/2308.12923/) (2023)
- [When Large Language Model Meets Optimization](https://mlsanity.com/paper/2405.10098/) (2024)
- [GPT Models in Construction Industry: Opportunities, Limitations, and a Use Case Validation](https://mlsanity.com/paper/2305.18997/) (2023)
- [Visual Reasoning and Multi-Agent Approach in Multimodal Large Language Models (MLLMs): Solving TSP and mTSP Combinatorial Challenges](https://mlsanity.com/paper/2407.00092/) (2024)
- ["I Want It That Way": Enabling Interactive Decision Support Using Large Language Models and Constraint Programming](https://mlsanity.com/paper/2312.06908/) (2023)
- [LM4OPT: Unveiling the Potential of Large Language Models in Formulating Mathematical Optimization Problems](https://mlsanity.com/paper/2403.01342/) (2024)
- [Accelerating Material Design with the Generative Toolkit for Scientific Discovery](https://mlsanity.com/paper/2207.03928/) (2022)
- [Robot-Enabled Construction Assembly with Automated Sequence Planning based on ChatGPT: RoboGPT](https://mlsanity.com/paper/2304.11018/) (2023)
- [Towards Next-Generation Urban Decision Support Systems through AI-Powered Construction of Scientific Ontology using Large Language Models -- A Case in Optimizing Intermodal Freight Transportation](https://mlsanity.com/paper/2405.19255/) (2024)
- [ChatGPT-based Investment Portfolio Selection](https://mlsanity.com/paper/2308.06260/) (2023)
- [Approximation-Aware Dependency Parsing by Belief Propagation](https://mlsanity.com/paper/1508.02375/) (2015)
- [Biased Random-Key Genetic Algorithms: A Review](https://mlsanity.com/paper/2312.00961/) (2023)
- [Metaheuristics "In the Large"](https://mlsanity.com/paper/2011.09821/) (2020)
- [Educational Timetabling: Problems, Benchmarks, and State-of-the-Art Results](https://mlsanity.com/paper/2201.07525/) (2022)
- [Data-Driven Portfolio Management for Motion Pictures Industry: A New Data-Driven Optimization Methodology Using a Large Language Model as the Expert](https://mlsanity.com/paper/2404.07434/) (2024)

## Built on by (most cited first, 20 of 20)

- [Reasoning in a Combinatorial and Constrained World: Benchmarking LLMs on Natural-Language Combinatorial Optimization](https://mlsanity.com/paper/2602.02188/) (2026)
- [G-LNS: Generative Large Neighborhood Search for LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2602.08253/) (2026)
- [Large Language Models in Operations Research: Methods, Applications, and Challenges](https://mlsanity.com/paper/2509.18180/) (2025)
- [DRAGON: LLM-Driven Decomposition and Reconstruction Agents for Large-Scale Combinatorial Optimization](https://mlsanity.com/paper/2601.06502/) (2026)
- [Behavior and Representation in Open-Weight Large Language Models for Combinatorial Optimization: From Feature Extraction to Algorithm Selection](https://mlsanity.com/paper/2512.13374/) (2025)
- [PyVRP^+: LLM-Driven Metacognitive Heuristic Evolution for Hybrid Genetic Search in Vehicle Routing Problems](https://mlsanity.com/paper/2604.07872/) (2026)
- [LLM-Based Instance-Driven Heuristic Bias In the Context of a Biased Random Key Genetic Algorithm](https://mlsanity.com/paper/2509.09707/) (2025)
- [Failing to Explore: Language Models on Interactive Tasks](https://mlsanity.com/paper/2601.22345/) (2026)
- [Graph Property Inference in Small Language Models: Effects of Representation and Reasoning Strategy](https://mlsanity.com/paper/2603.06635/) (2026)
- [Learning to Staff: Offline Reinforcement Learning and Fine-Tuned LLMs for Warehouse Staffing Optimization](https://mlsanity.com/paper/2603.24883/) (2026)
- [Infeasibility Aware Large Language Models for Combinatorial Optimization](https://mlsanity.com/paper/2604.01455/) (2026)
- [HMACE: Heterogeneous Multi-Agent Collaborative Evolution for Combinatorial Optimization](https://mlsanity.com/paper/2605.07214/) (2026)
- [Large Language Models as Amortized Pareto-Front Generators for Constrained Bi-Objective Convex Optimization](https://mlsanity.com/paper/2605.12106/) (2026)
- [Sim2Schedule: A Simulator-Guided LLM Framework for Autonomous Open-Pit Mine Scheduling](https://mlsanity.com/paper/2606.10286/) (2026)
- [Large Language Models as Optimizers: A Survey of Direct vs. Tool-Augmented Approaches and Their Performance Frontiers](https://mlsanity.com/paper/2606.15577/) (2026)
- [Adaptive Cluster-First Route-Second Decomposition for Industrial-Scale Vehicle Routing](https://mlsanity.com/paper/2606.31820/) (2026)
- [Neural Certificate Pricing for Combinatorial Optimization Problems](https://mlsanity.com/paper/2607.01185/) (2026)
- [Robust Feasible Route Construction through Collaborative Partition Optimization](https://mlsanity.com/paper/2607.03694/) (2026)
- [From Hand-Crafted to LLM-Based Variation Operators in Metaheuristics: A Tutorial](https://mlsanity.com/paper/2609.31649/) (2026)
- [Think in Strategies, Act with Tools: Traceable Agentic Optimization for Combinatorial Problems](https://mlsanity.com/paper/2610.14736/) (2026)

## Abstract (arXiv)

This systematic review explores the application of Large Language Models (LLMs) in Combinatorial Optimization (CO). We report our findings using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. We conduct a literature search via Scopus and Google Scholar, examining over 2,000 publications. We assess publications against four inclusion and four exclusion criteria related to their language, research focus, publication year, and type. Eventually, we select 103 studies. We classify these studies into semantic categories and topics to provide a comprehensive overview of the field, including the tasks performed by LLMs, the architectures of LLMs, the existing datasets specifically designed for evaluating LLMs in CO, and the field of application. Finally, we identify future directions for leveraging LLMs in this field.