mlsanityData to 14 Oct 2026

Large Language Models for Combinatorial Optimization: A Systematic Review

arXiv 2507.03637 ↗First posted 4 Jul 2025cs.AIcited by 20

Not on the map. Why?

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.

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

20 of 68 references.

References · 20

  1. 2022Training language models to follow instructions with human feedbackcited by 15,971
  2. 2022Scaling Instruction-Finetuned Language Modelscited by 3,024
  3. 2023A Survey on Large Language Model based Autonomous Agentscited by 2,242
  4. 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 623
  5. 2023Open-TI: Open Traffic Intelligence with Augmented Language Modelcited by 38
  6. 2023Diagnosing Infeasible Optimization Problems Using Large Language Modelscited by 27
  7. 2024When Large Language Model Meets Optimizationcited by 22
  8. 2023GPT Models in Construction Industry: Opportunities, Limitations, and a Use Case Validationcited by 21
  9. 2024Visual Reasoning and Multi-Agent Approach in Multimodal Large Language Models (MLLMs): Solving TSP and mTSP Combinatorial Challengescited by 21
  10. 2023"I Want It That Way": Enabling Interactive Decision Support Using Large Language Models and Constraint Programmingcited by 19
  11. 2024LM4OPT: Unveiling the Potential of Large Language Models in Formulating Mathematical Optimization Problemscited by 18
  12. 2022Accelerating Material Design with the Generative Toolkit for Scientific Discoverycited by 16
8 more
  1. 2023Robot-Enabled Construction Assembly with Automated Sequence Planning based on ChatGPT: RoboGPTcited by 11
  2. 2024Towards Next-Generation Urban Decision Support Systems through AI-Powered Construction of Scientific Ontology using Large Language Models -- A Case in Optimizing Intermodal Freight Transportationcited by 10
  3. 2023ChatGPT-based Investment Portfolio Selectioncited by 8
  4. 2015Approximation-Aware Dependency Parsing by Belief Propagationcited by 6
  5. 2023Biased Random-Key Genetic Algorithms: A Reviewcited by 6
  6. 2020Metaheuristics "In the Large"cited by 4
  7. 2022Educational Timetabling: Problems, Benchmarks, and State-of-the-Art Resultscited by 4
  8. 2024Data-Driven Portfolio Management for Motion Pictures Industry: A New Data-Driven Optimization Methodology Using a Large Language Model as the Expertcited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 17.

20 papers.

Sort:

By area:

  1. 2026Reasoning in a Combinatorial and Constrained World: Benchmarking LLMs on Natural-Language Combinatorial Optimizationcited by 9
  2. 2026G-LNS: Generative Large Neighborhood Search for LLM-Based Automatic Heuristic Designcited by 7
  3. 2025Large Language Models in Operations Research: Methods, Applications, and Challengescited by 6
  4. 2026DRAGON: LLM-Driven Decomposition and Reconstruction Agents for Large-Scale Combinatorial Optimizationcited by 3
  5. 2025Behavior and Representation in Open-Weight Large Language Models for Combinatorial Optimization: From Feature Extraction to Algorithm Selectioncited by 1
  6. 2026PyVRP^+: LLM-Driven Metacognitive Heuristic Evolution for Hybrid Genetic Search in Vehicle Routing Problemscited by 1
  7. 2025LLM-Based Instance-Driven Heuristic Bias In the Context of a Biased Random Key Genetic Algorithmcited by 0
  8. 2026Failing to Explore: Language Models on Interactive Taskscited by 0
  9. 2026Graph Property Inference in Small Language Models: Effects of Representation and Reasoning Strategycited by 0
  10. 2026Learning to Staff: Offline Reinforcement Learning and Fine-Tuned LLMs for Warehouse Staffing Optimizationcited by 0
  11. 2026Infeasibility Aware Large Language Models for Combinatorial Optimizationcited by 0
  12. 2026HMACE: Heterogeneous Multi-Agent Collaborative Evolution for Combinatorial Optimizationcited by 0
8 more
  1. 2026Large Language Models as Amortized Pareto-Front Generators for Constrained Bi-Objective Convex Optimizationcited by 0
  2. 2026Sim2Schedule: A Simulator-Guided LLM Framework for Autonomous Open-Pit Mine Schedulingcited by 0
  3. 2026Large Language Models as Optimizers: A Survey of Direct vs. Tool-Augmented Approaches and Their Performance Frontierscited by 0
  4. 2026Adaptive Cluster-First Route-Second Decomposition for Industrial-Scale Vehicle Routingcited by 0
  5. 2026Neural Certificate Pricing for Combinatorial Optimization Problemscited by 0
  6. 2026Robust Feasible Route Construction through Collaborative Partition Optimizationcited by 0
  7. 2026From Hand-Crafted to LLM-Based Variation Operators in Metaheuristics: A Tutorialcited by 0
  8. 2026Think in Strategies, Act with Tools: Traceable Agentic Optimization for Combinatorial Problemscited by 0