{"id":44484514,"url":"https://github.com/ai4co/awesome-fm4co","last_synced_at":"2026-02-13T01:47:38.592Z","repository":{"id":226732108,"uuid":"768441087","full_name":"ai4co/awesome-fm4co","owner":"ai4co","description":"Recent research papers about Foundation Models for Combinatorial Optimization","archived":false,"fork":false,"pushed_at":"2026-02-03T13:12:49.000Z","size":150,"stargazers_count":461,"open_issues_count":0,"forks_count":36,"subscribers_count":17,"default_branch":"main","last_synced_at":"2026-02-04T03:45:00.135Z","etag":null,"topics":["awesome","awesome-list","combinatorial-optimization","foundation-models","lists","machine-learning","neural-combinatorial-optimization"],"latest_commit_sha":null,"homepage":"","language":null,"has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/ai4co.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null,"notice":null,"maintainers":null,"copyright":null,"agents":null,"dco":null,"cla":null}},"created_at":"2024-03-07T04:53:46.000Z","updated_at":"2026-02-03T13:14:19.000Z","dependencies_parsed_at":"2025-11-12T09:01:58.548Z","dependency_job_id":null,"html_url":"https://github.com/ai4co/awesome-fm4co","commit_stats":null,"previous_names":["royalskye/fm-cop"],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/ai4co/awesome-fm4co","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ai4co%2Fawesome-fm4co","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ai4co%2Fawesome-fm4co/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ai4co%2Fawesome-fm4co/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ai4co%2Fawesome-fm4co/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/ai4co","download_url":"https://codeload.github.com/ai4co/awesome-fm4co/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ai4co%2Fawesome-fm4co/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":29392157,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-02-13T00:53:09.511Z","status":"ssl_error","status_checked_at":"2026-02-13T00:53:09.126Z","response_time":55,"last_error":"SSL_connect returned=1 errno=0 peeraddr=140.82.121.5:443 state=error: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["awesome","awesome-list","combinatorial-optimization","foundation-models","lists","machine-learning","neural-combinatorial-optimization"],"created_at":"2026-02-13T01:47:38.029Z","updated_at":"2026-02-13T01:47:38.583Z","avatar_url":"https://github.com/ai4co.png","language":null,"funding_links":[],"categories":[],"sub_categories":[],"readme":"\u003ch1 align=\"center\"\u003eFoundation Models for Combinatorial Optimization\u003c/h1\u003e\n\nFM4CO contains interesting research papers (1) using **Existing Large Language Models for Combinatorial Optimization**, and (2) building **Domain Foundation Models for Combinatorial Optimization**.\n\n----\n\n### LLMs for Combinatorial Optimization\n\nMost research utilizes existing FMs from language and vision domains to generate/improve solutions\\* or algorithms\\* (hyper-heuristic), yielding impressive results when integrated with problem-specific heuristics or general meta-heuristics. Other studies employ LLMs to investigate the interpretability\\* of COP solvers, automate problem formulation*, or simplify the use of domain-specific tools through text prompts. Given the capabilities of LLMs, this area of research is likely to garner increasing interest.\n\n|  Date   |                            Paper                             |                             Link                             |        Problem        |     Venue      |     Remark*      |\n| :-----: | :----------------------------------------------------------: | :----------------------------------------------------------: | :-------------------: | :------------: | :--------------: |\n| 2023.07 | [Large Language Models for Supply Chain Optimization](https://arxiv.org/pdf/2307.03875) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/microsoft/OptiGuide) | `Supply_Chain` | *arXiv* | Algorithm w. Interpretability |\n| 2023.09 | [Can Language Models Solve Graph Problems in Natural Language?](https://arxiv.org/pdf/2305.10037) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/Arthur-Heng/NLGraph) |        `Graph`        | *NeurIPS 2023* |     Solution     |\n| 2023.09 | [Large Language Models as Optimizers](https://arxiv.org/pdf/2309.03409) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/google-deepmind/opro) |         `TSP`         |  *ICLR 2024*   |     Solution     |\n| 2023.10 | [Chain-of-Experts: When LLMs Meet Complex Operations Research Problems](https://openreview.net/pdf?id=HobyL1B9CZ) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/xzymustbexzy/Chain-of-Experts) |        `MILP`         |  *ICLR 2024*   |    Formulation    |\n| 2023.10 | [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://arxiv.org/pdf/2402.10172) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/teshnizi/OptiMUS) |        `MILP`         |  *ICML 2024*   |    Formulation    |\n| 2023.10 | [AI-Copilot for Business Optimisation: A Framework and A Case Study in Production Scheduling](https://arxiv.org/pdf/2309.13218) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/pivithuruthejanamarasinghe/AI-Copilot-Data) |        `JSSP`         |    *arXiv*    |    Formulation    |\n| 2023.11 | [Large Language Models as Evolutionary Optimizers](https://arxiv.org/pdf/2310.19046) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/cschen1205/LMEA) |         `TSP`         | *CEC 2024* |     Solution     |\n| 2023.11 | [Algorithm Evolution Using Large Language Model](https://arxiv.org/pdf/2311.15249) |                                             \u0026emsp;\u0026emsp;\u0026emsp;                 |         `TSP`         |    *arXiv*    |    Algorithm     |\n| 2023.12 | [Mathematical discoveries from program search with large language models](https://www.nature.com/articles/s41586-023-06924-6) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/google-deepmind/funsearch) |         `BPP`         |    *Nature*    |    Algorithm     |\n| 2023.12 | [NPHardEval: Dynamic Benchmark on Reasoning Ability of Large Language Models via Complexity Classes](https://arxiv.org/pdf/2312.14890) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/casmlab/NPHardEval) | `TSP,KP, GCP,MSP` | *ACL 2024* | Benchmark |\n| 2024.02 | [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://arxiv.org/pdf/2402.01145) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/ai4co/reevo) \u003cbr\u003e [![Project-Page](https://img.shields.io/badge/Page-74aa9c?style=for-the-badge)](https://github.com/ai4co/reevo) | `TSP,VRP,OP, MKP,BPP,EDA` |    *NeurIPS 2024*    |    Algorithm     |\n| 2024.02 | [AutoSAT: Automatically Optimize SAT Solvers via Large Language Models](https://arxiv.org/pdf/2402.10705) |                                                              |         `SAT`         |    *arXiv*    |    Algorithm     |\n| 2024.02 | [From Large Language Models and Optimization to Decision Optimization CoPilot: A Research Manifesto](https://arxiv.org/pdf/2402.16269) |                                                              |        `MILP`         |    *arXiv*    |    Formulation    |\n| 2024.03 | [How Multimodal Integration Boost the Performance of LLM for Optimization: Case Study on Capacitated Vehicle Routing Problems](https://arxiv.org/pdf/2403.01757) |  |         `VRP`         |    *arXiv*    |     Solution     |\n| 2024.03 | [RouteExplainer: An Explanation Framework for Vehicle Routing Problem](https://arxiv.org/pdf/2403.03585.pdf) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/ntt-dkiku/route-explainer) \u003cbr\u003e [![Project-Page](https://img.shields.io/badge/Page-74aa9c?style=for-the-badge)](https://ntt-dkiku.github.io/xai-vrp) |         `VRP`         |  *PAKDD 2024*  | Interpretability |\n| 2024.03 | [Can Large Language Models Solve Robot Routing?](https://arxiv.org/pdf/2403.10795) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/Zhehui-Huang/LLM_Routing) \u003cbr\u003e [![Project-Page](https://img.shields.io/badge/Page-74aa9c?style=for-the-badge)](https://sites.google.com/view/words-to-routes) |         `TSP,VRP`         |    *arXiv*    |    Algorithm     |\n| 2024.05 | [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://arxiv.org/pdf/2401.02051) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/FeiLiu36/EoH) | `TSP,BPP,FSSP` |  *ICML 2024*   |    Algorithm     |\n| 2024.05 | [ORLM: Training Large Language Models for Optimization Modeling](https://arxiv.org/pdf/2405.17743) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/Cardinal-Operations/ORLM) | `General OPT` | *Operations Research* | Formulation |\n| 2024.05 | [Self-Guiding Exploration for Combinatorial Problems](https://arxiv.org/pdf/2405.17950) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/Zangir/LLM-for-CP) | `TSP,VRP,BPP, AP,KP,JSSP` | *NeurIPS 2024* | Solution |\n| 2024.06 | [Eyeballing Combinatorial Problems: A Case Study of Using Multimodal Large Language Models to Solve Traveling Salesman Problems](https://arxiv.org/pdf/2406.06865) |  | `TSP` | *ISBCom 2024* | Solution |\n| 2024.07 | [Visual Reasoning and Multi-Agent Approach in Multimodal Large Language Models (MLLMs): Solving TSP and mTSP Combinatorial Challenges](https://arxiv.org/pdf/2407.00092) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/ahmed-abdulhuy/Solving-TSP-and-mTSP-Combinatorial-Challenges-using-Visual-Reasoning-and-Multi-Agent-Approach-MLLMs-) | `TSP,mTSP` | *arXiv* | Solution |\n| 2024.07 | [Solving General Natural-Language-Description Optimization Problems with Large Language Models](https://arxiv.org/pdf/2407.07924) | [![Code](https://img.shields.io/badge/Demo-74aa9c?style=for-the-badge)](https://opt.alibabacloud.com/chat) | `MILP` | *NAACL 2024* | Formulation |\n| 2024.08 | [Diagnosing Infeasible Optimization Problems Using Large Language Models](https://arxiv.org/pdf/2308.12923) |  | `MILP` | *INFOR* | Formulation |\n| 2024.08 | [LLMs can Schedule](https://arxiv.org/pdf/2408.06993) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/starjob42/datasetjsp) | `JSSP` | *arXiv* | Solution |\n| 2024.09 | [Multi-objective Evolution of Heuristic Using Large Language Model](https://arxiv.org/pdf/2409.16867) |  | `TSP,BPP` | *AAAI 2025* | Algorithm |\n| 2024.10 | [Towards Foundation Models for Mixed Integer Linear Programming](https://arxiv.org/pdf/2410.08288) |  |          `MILP`           |    *ICLR 2025*    | Formulation |\n| 2024.10 | [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://arxiv.org/pdf/2410.13213) | | `General OPT` | *ICLR 2025* | Formulation |\n| 2024.10 | [OptiBench: Benchmarking Large Language Models in Optimization Modeling with Equivalence-Detection Evaluation](https://openreview.net/forum?id=KD9F5Ap878) | | `MILP` | *Under Review* | Benchmark |\n| 2024.10 | [OptiBench Meets ReSocratic: Measure and Improve LLMs for Optimization Modeling](https://openreview.net/forum?id=fsDZwS49uY) | | `MILP` | *ICLR 2025* | Benchmark |\n| 2024.10 | [DRoC: Elevating Large Language Models for Complex Vehicle Routing via Decomposed Retrieval of Constraints](https://openreview.net/forum?id=s9zoyICZ4k) | | `48VRPs` | *ICLR 2025* | Formulation |\n| 2024.10 | [STARJOB: Dataset for LLM-Driven Job Shop Scheduling](https://openreview.net/forum?id=t0fU6t3Skw) | | `JSSP` | *Under Review* | Solution |\n| 2024.10 | [LLM4Solver: Large Language Model for Efficient Algorithm Design of Combinatorial Optimization Solver](https://openreview.net/forum?id=XTxdDEFR6D) | | `MILP` | *Under Review* | Algorithm |\n| 2024.10 | [Unifying All Species: LLM-based Hyper-Heuristics for Multi-objective Optimization](https://openreview.net/forum?id=sUywd7UhFT) | | `TSP` | *Under Review* | Algorithm |\n| 2024.10 | [Evo-Step: Evolutionary Generation and Stepwise Validation for Optimizing LLMs in OR](https://openreview.net/forum?id=aapUBU9U0D) | | `MILP` | *Under Review* | Formulation |\n| 2024.10 | [Automatic programming via large language models with population self-evolution for dynamic job shop scheduling problem](https://arxiv.org/pdf/2410.22657) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/huangjin-collab/LHH_DFJSP_SeEvo)| `DyJSSP` | *IEEE Trans. Fuzzy Syst.* | Algorithm |\n| 2024.11 | [Large Language Models for Combinatorial Optimization of Design Structure Matrix](https://arxiv.org/pdf/2411.12571) | | `DSM` | *arXiv* | Solution |\n| 2024.12 | [HSEvo: Elevating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMs](https://arxiv.org/pdf/2412.14995) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/datphamvn/HSEvo) | `TSP,BPP,OP` | *AAAI 2025* | Algorithm |\n| 2024.12 | [Evaluating LLM Reasoning in the Operations Research Domain with ORQA](https://arxiv.org/pdf/2412.17874) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/nl4opt/ORQA) | `General OR` | *AAAI 2025* | Benchmark |\n| 2024.12 | [QUBE: Enhancing Automatic Heuristic Design via Quality-Uncertainty Balanced Evolution](https://arxiv.org/pdf/2412.20694) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/zzjchen/QUBE_code) | `OBP,TSP,CSP` | *arxiv* | Algorithm |\n| 2025.01 | [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://arxiv.org/pdf/2501.08603) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/zz1358m/MCTS-AHD-master) | `TSP,CVRP,KP, BPP,MKP,ASP` | *ICML 2025* | Algorithm |\n| 2025.01 | [Bridging Visualization and Optimization: Multimodal Large Language Models on Graph-Structured Combinatorial Optimization](https://arxiv.org/pdf/2501.11968) || `Influence Maximization, Network Dismantling` | *arXiv* | Algorithm |\n| 2025.01 | [Can Large Language Models Be Trusted as Black-Box Evolutionary Optimizers for Combinatorial Problems?](https://arxiv.org/pdf/2501.15081) || `Influence Maximization` | *arXiv* | Algorithm |\n| 2025.02 | [Improving Existing Optimization Algorithms with LLMs](https://arxiv.org/pdf/2502.08298) || `MIS` | *arXiv* | Algorithm |\n| 2025.02 | [Planning of Heuristics: Strategic Planning on Large Language Models with Monte Carlo Tree Search for Automating Heuristic Optimization](https://arxiv.org/pdf/2502.11422) || `TSP,FSSP` | *arXiv* | Algorithm |\n| 2025.02 | [GraphThought: Graph Combinatorial Optimization with Thought Generation](https://arxiv.org/pdf/2502.11607) || `MIS,MVC,TSP` | *arXiv* | Algorithm |\n| 2025.02 | [EquivaMap: Leveraging LLMs for Automatic Equivalence Checking of Optimization Formulations](https://arxiv.org/pdf/2502.14760) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/HumainLab/EquivaMap)| `MILP` | *arXiv* | Algorithm |\n| 2025.02 | [ARS: Automatic Routing Solver with Large Language Models](https://arxiv.org/pdf/2502.15359) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/Ahalikai/ARS-Routbench)| `VRP` | *arXiv* | Benchmark \u0026 Algorithm |\n| 2025.02 | [Text2Zinc: A Cross-Domain Dataset for Modeling Optimization and Satisfaction Problems in MiniZinc](https://arxiv.org/pdf/2503.10642) | [![Data](https://img.shields.io/badge/Data-20B2AA?style=for-the-badge)](https://huggingface.co/datasets/skadio/text2zinc)| `LP,MIP,CP` | *arXiv* | Formulation (Dataset) |\n| 2025.02 | [GraphArena: Evaluating and Exploring Large Language Models on Graph Computation](https://openreview.net/pdf?id=Y1r9yCMzeA) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/squareRoot3/GraphArena/tree/master) | `MVC,MIS,MCP, TSP,MCS,GED` | *ICLR 2025* | Benchmark \u0026 Dataset \u0026 Model|\n| 2025.03 | [Leveraging Large Language Models to Develop Heuristics for Emerging Optimization Problems](https://arxiv.org/pdf/2503.03350) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/nico-koltermann/contextual-evolution-of-heuristics)| `UPMP` | *arXiv* | Algorithm |\n| 2025.03 | [OR-LLM-Agent: Automating Modeling and Solving of Operations Research Optimization Problem with Reasoning Large Language Model](https://arxiv.org/pdf/2503.10009) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/bwz96sco/or_llm_agent)| `OP` | *arXiv* | Formulation |\n| 2025.03 | [Combinatorial Optimization for All: Using LLMs to Aid Non-Experts in Improving Optimization Algorithms](https://arxiv.org/pdf/2503.10968) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/camilochs/comb-opt-for-all)\u003cbr\u003e [![Project-Page](https://img.shields.io/badge/Page-74aa9c?style=for-the-badge)](https://camilochs.github.io/comb-opt-for-all/)| `TSP` | *arXiv* | Algorithm |\n| 2025.03 | [Automatic MILP Model Construction for Multi-Robot Task Allocation and Scheduling Based on Large Language Models](https://arxiv.org/pdf/2503.13813) || `MILP` | *IROS 2025* | Formulation |\n| 2025.03 | [Code Evolution Graphs: Understanding Large Language Model Driven Design of Algorithms](https://arxiv.org/pdf/2503.16668) || `BBO,TSP,BPP` | *GECCO 2025* | Interpretability |\n| 2025.04 | [CO-Bench: Benchmarking Language Model Agents in Algorithm Search for Combinatorial Optimization](https://arxiv.org/pdf/2504.04310) || `General COP` | *AAAI 2026* | Benchmark |\n| 2025.04 | [Algorithm Discovery With LLMs: Evolutionary Search Meets Reinforcement Learning](https://arxiv.org/pdf/2504.05108) || `BPP,TSP,FP` | *COLM 2025* | Algorithm |\n| 2025.04 | [OptimAI: Optimization from Natural Language Using LLM-Powered AI Agents](https://arxiv.org/pdf/2504.16918) || `MILP` | *arXiv* | Formulation |\n| 2025.04 | [Fitness Landscape of Large Language Model-Assisted Automated Algorithm Search](https://arxiv.org/pdf/2504.19636) || `OBP,TSP, CVRP,VRPTW` | *arXiv* | Benchmark \u0026 Interpretability |\n| 2025.04 | [Large Language Models powered Neural Solvers for Generalized Vehicle Routing Problems](https://openreview.net/pdf?id=EVqlVjvlt8) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/Fsoft-AIC/NCO-LLM)| `VRP` | *ICLR 2025 Workshop AgenticAI* | Algorithm |\n| 2025.05 | [Efficient Heuristics Generation for Solving Combinatorial Optimization Problems Using Large Language Models](https://arxiv.org/pdf/2505.12627v1) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/wuuu110/Hercules)| `TSP,CVRP,BPP, MKP,OP` | *KDD 2025* | Algorithm |\n| 2025.05 | [CALM: Co-evolution of Algorithms and Language Model for Automatic Heuristic Design](https://arxiv.org/pdf/2505.12285v1) || `TSP,KP,OBP,OP` | *ICLR 2026* | Algorithm |\n| 2025.05 | [Know the Ropes: A Heuristic Strategy for LLM-based Multi-Agent System Design](https://arxiv.org/pdf/2505.16979) || `KP` | *arXiv* | Solution |\n| 2025.05 | [A Comprehensive Evaluation of Contemporary ML-Based Solvers for Combinatorial Optimization](https://arxiv.org/pdf/2505.16952) | [![Data](https://img.shields.io/badge/Data-20B2AA?style=for-the-badge)](https://huggingface.co/datasets/CO-Bench/FrontierCO)| `MIS,MDS, TSP,CVRP,CFLP, CPMP,FJSP,STP` | *ICML 2025 Workshop AI4Math* | Benchmark |\n| 2025.05 | [LLM-Meta-SR: In-Context Learning for Evolving Selection Operators in Symbolic Regression](https://arxiv.org/abs/2505.18602) || `SR` | *arXiv* | Algorithm |\n| 2025.05 | [RedAHD: Reduction-Based End-to-End Automatic Heuristic Design with Large Language Models](https://arxiv.org/pdf/2505.20242) || `TSP,CVRP, KP,BPP,MKP` | *arXiv* | Algorithm |\n| 2025.05 | [Generalizable Heuristic Generation Through Large Language Models with Meta-Optimization](https://arxiv.org/pdf/2505.20881) || `TSP,CVRP,BPP` | *arXiv* | Algorithm |\n| 2025.05 | [Large Language Model-driven Large Neighborhood Search for Large-Scale MILP Problems](https://openreview.net/pdf?id=teUg2pMrF0) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/thuiar/LLM-LNS)| `MILP` | *ICML 2025* | Algorithm |\n| 2025.05 | [Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling](https://arxiv.org/pdf/2505.11792) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/Cardinal-Operations/SIRL)| `General OPT` | *NeurIPS 2025* | Formulation |\n| 2025.06 | [LLM-Driven Instance-Specific Heuristic Generation and Selection](https://arxiv.org/pdf/2506.00490) || `OBPP,CVRP` | *arXiv* | Algorithm |\n| 2025.06 | [ORMind: A Cognitive-Inspired End-to-End Reasoning Framework for Operations Research](https://arxiv.org/pdf/2506.01326) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/XiaoAI1989/ORMind)| `OR` | *ACL 2025* | Formulation |\n| 2025.06 | [EALG: Evolutionary Adversarial Generation of Language Model–Guided Generators for Combinatorial Optimization](https://arxiv.org/pdf/2506.02594) || `TSP,OP` | *arXiv* | Algorithm |\n| 2025.06 | [CP-Bench: Evaluating Large Language Models for Constraint Modelling](https://arxiv.org/pdf/2506.06052) || `CP` | *arXiv* | Benchmark |\n| 2025.06 | [REMoH: A Reflective Evolution of Multi-objective Heuristics approach via Large Language Models](https://arxiv.org/pdf/2506.07759) || `FJSSP` | *arXiv* | Algorithm |\n| 2025.06 | [HeuriGym: An Agentic Benchmark for LLM-Crafted Heuristics in Combinatorial Optimization](https://arxiv.org/pdf/2506.07972) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/cornell-zhang/heurigym)| `TSP,SAT` | *ICLR 2026* | Benchmark |\n| 2025.06 | [ALE-Bench: A Benchmark for Long-Horizon Objective-Driven Algorithm Engineering](https://arxiv.org/pdf/2506.09050) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/SakanaAI/ALE-Bench)\u003cbr\u003e [![Data](https://img.shields.io/badge/Data-20B2AA?style=for-the-badge)](https://huggingface.co/datasets/SakanaAI/ALE-Bench)| `General OPT` | *NeurIPS 2025 Datasets and Benchmarks Track* | Benchmark |\n| 2025.06 | [OPT-BENCH: Evaluating LLM Agent on Large-Scale Search Spaces Optimization Problems](https://arxiv.org/pdf/2506.10764) | [![Data](https://img.shields.io/badge/Data-20B2AA?style=for-the-badge)](https://huggingface.co/datasets/OPT-Bench/OPT-Bench)\u003cbr\u003e [![Project-Page](https://img.shields.io/badge/Page-74aa9c?style=for-the-badge)](https://github.com/OliverLeeXZ/OPT-BENCH)| `GCP,KP,MCP, MIS,SCP,TSP` | *arXiv* | Benchmark |\n| 2025.06 | [STRCMP: Integrating Graph Structural Priors with Language Models for Combinatorial Optimization](https://arxiv.org/pdf/2506.11057) || `SAT` | *NeurIPS 2025* | Solution |\n| 2025.06 | [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://arxiv.org/pdf/2506.13131) |[![Code](https://img.shields.io/badge/Demo-74aa9c?style=for-the-badge)](https://colab.research.google.com/github/google-deepmind/alphaevolve_results/blob/master/mathematical_results.ipynb)| `OPT` | *arXiv* | Algorithm |\n| 2025.06 | [OpenEvolve: an open-source evolutionary coding agent](https://huggingface.co/blog/codelion/openevolve) |[![Code](https://img.shields.io/badge/Demo-74aa9c?style=for-the-badge)](https://github.com/algorithmicsuperintelligence/openevolve)| `OPT` | *GitHub* | Algorithm |\n| 2025.06 | [HeurAgenix: Leveraging LLMs for Solving Complex Combinatorial Optimization Challenges](https://arxiv.org/pdf/2506.15196) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/microsoft/HeurAgenix)| `TSP,CVRP,JSSP, MaxCut,MKP` | *arXiv* | Algorithm |\n| 2025.07 | [Large Language Models for Combinatorial Optimization: A Systematic Review](https://arxiv.org/pdf/2507.03637) || `CO` | *arXiv* | Review |\n| 2025.07 | [Fine-tuning Large Language Model for Automated Algorithm Design](https://arxiv.org/pdf/2507.10614) || `ASP,TSP,CVRP` | *arXiv* | Algorithm |\n| 2025.07 | [DHEvo: Data-Algorithm Based Heuristic Evolution for Generalizable MILP Solving](https://arxiv.org/pdf/2507.15615) || `MILP` | *arXiv* | Algorithm |\n| 2025.07 | [MeLA: A Metacognitive LLM-Driven Architecture for Automatic Heuristic Design](https://arxiv.org/pdf/2507.20541) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/Qzs1335/MeLA)| `TSP,BPP,ACS` | *arXiv* | Algorithm |\n| 2025.07 | [Pareto-Grid-Guided Large Language Models for Fast and High-Quality Heuristics Design in Multi-Objective Combinatorial Optimization](https://arxiv.org/pdf/2507.20923) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/langkhachhoha/MPaGE)| `TSP,CVRP,KP` | *AAAI 2026* | Algorithm |\n| 2025.07 | [Automatically discovering heuristics in a complex SAT solver with large language models](https://arxiv.org/pdf/2507.22876) || `SAT` | *arXiv* | Algorithm |\n| 2025.07 | [Nested-Refinement Metamorphosis: Reflective Evolution for Efficient Optimization of Networking Problems](https://aclanthology.org/2025.findings-acl.895.pdf) || `TSP,MKP,CVRP` | *ACL 2025* | Algorithm |\n| 2025.08 | [ReflecSched: Solving Dynamic Flexible Job-Shop Scheduling via LLM-Powered Hierarchical Reflection](https://arxiv.org/pdf/2508.01724) || `DFJSP` | *arxiv* | Solution |\n| 2025.08 | [OptiHive: Ensemble Selection for LLM-Based Optimization via Statistical Modeling](https://arxiv.org/pdf/2508.02503) || `MDVRP,WSCP` | *arxiv* | Formulation |\n| 2025.08 | [EoH-S: Evolution of Heuristic Set using LLMs for Automated Heuristic Design](https://arxiv.org/pdf/2508.03082) || `OBP,TSP,CVRP` | *AAAI 2026* | Algorithm |\n| 2025.08 | [X-evolve: Solution space evolution powered by large language models](https://arxiv.org/pdf/2508.07932) || `CSP,BPP, Shannon capacity` | *arxiv* | Algorithm |\n| 2025.08 | [EvoCut: Strengthening Integer Programs via Evolution-Guided Language Models](https://arxiv.org/pdf/2508.11850) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/milad1378yz/EvoCut)| `MILP` | *arxiv* | Formulation |\n| 2025.08 | [HIFO-PROMPT: Prompting with Hindsight and Foresight For LLM-Based Automatic Heuristic Design](https://arxiv.org/pdf/2508.13333) || `TSP,OBP,FSSP` | *ICLR 2026* | Algorithm |\n| 2025.09 | [LLM-QUBO: An End-to-End Framework for Automated QUBO Transformation from Natural Language Problem Descriptions](https://arxiv.org/pdf/2509.00099) || `MILP` | *arxiv* | Formulation |\n| 2025.09 | [AutoPBO: LLM-powered Optimization for Local Search PBO Solvers](https://arxiv.org/pdf/2509.04007) || `PBO` | *arxiv* | Solution |\n| 2025.09 | [Autonomous Code Evolution MeetsNP-Completeness](https://arxiv.org/pdf/2509.07367) || `SAT` | *arxiv* | Solution |\n| 2025.09 | [LLM-based Instance-driven Heuristic Bias in the Context of a Biased Random Key Genetic Algorithm](https://arxiv.org/pdf/2509.09707) || `LRS` | *arxiv* | Algorithm |\n| 2025.09 | [Learn to Relax with Large Language Models: Solving Nonlinear Combinatorial Optimization Problems via Bidirectional Coevolution](https://arxiv.org/pdf/2509.12643) || `MDD,SFL,TSPTW` | *arxiv* | Algorithm |\n| 2025.09 | [DaSAThco: Data-Aware SAT Heuristics Combinations Optimization via Large Language Models](https://arxiv.org/pdf/2509.12602) || `SAT` | *arxiv* | Algorithm |\n| 2025.09 | [Large Language Models as End-to-end Combinatorial Optimization Solvers](https://arxiv.org/pdf/2509.16865) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/Summer142857/LLMCoSolver)| `TSP,OP,CVRP, MIS,MVC,PFSP,JSSP` | *NeurIPS 2025* | Solution |\n| 2025.09 | [Large Language Models and Operations Research: A Structured Survey](https://arxiv.org/pdf/2509.18180) || `OR` | *arxiv* | Review |\n| 2025.09 | [ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolution](https://arxiv.org/pdf/2509.19349) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/SakanaAI/ShinkaEvolve)| `OPT` | *ICLR 2026* | Algorithm |\n| 2025.09 | [StepORLM: A Self-Evolving Framework With Generative Process Supervision For Operations Research Language Models](https://arxiv.org/pdf/2509.22558) || `OR` | *arxiv* | Formulation |\n| 2025.09 | [OptiMind: Teaching LLMs to Think Like Optimization Experts](https://arxiv.org/pdf/2509.22979) || `MILP` | *arxiv* | Formulation |\n| 2025.09 | [AutoEP: LLMs-Driven Automation of Hyperparameter Evolution for Metaheuristic Algorithms](https://arxiv.org/pdf/2509.23189) || `TSP,CVRP,FSSP` | *ICLR 2026* | Algorithm |\n| 2025.09 | [ViTSP: A Vision Language Models Guided Framework for Large-Scale Traveling Salesman Problems](https://arxiv.org/pdf/2509.23465) || `TSP` | *arxiv* | Algorithm |\n| 2025.09 | [Experience-guided reflective co-evolution of prompts and heuristics for automatic algorithm design](https://arxiv.org/pdf/2509.24509) || `TSP,BPP` | *arxiv* | Algorithm |\n| 2025.10 | [EvoSpeak: Large Language Models for Interpretable Genetic Programming-Evolved Heuristics](https://arxiv.org/pdf/2510.02686) || `DFJSS` | *arxiv* | Algorithm |\n| 2025.10 | [VRPAgent: LLM-Driven Discovery of Heuristic Operators for Vehicle Routing Problems](https://arxiv.org/pdf/2510.07073) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/ai4co/vrpagent)| `VRP` | *arxiv* | Algorithm |\n| 2025.10 | [Refining Hybrid Genetic Search for CVRP via Reinforcement Learning-Finetuned LLM](https://arxiv.org/pdf/2510.11121) || `CVRP` | *arxiv* | Algorithm |\n| 2025.10 | [CodeEvolve: an open source evolutionary coding agent for algorithm discovery and optimization](https://arxiv.org/pdf/2510.14150) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/inter-co/science-codeevolve)| `OPT` | *arXiv* | Algorithm |\n| 2025.10 | [An Agentic Framework with LLMs for Solving Complex Vehicle Routing Problems](https://arxiv.org/pdf/2510.16701) || `VRP` | *arxiv* | Formulation |\n| 2025.10 | [OptiTree: Hierarchical Thoughts Generation with Tree Search for LLM Optimization Modeling](https://arxiv.org/pdf/2510.22192) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/MIRALab-USTC/OptiTree)| `OR` | *NeurIPS 2025* | Formulation |\n| 2025.10 | [Glia: A Human-Inspired AI for Automated Systems Design and Optimization](https://arxiv.org/abs/2510.27176) || `Systems routing + scheduling` | *arxiv* | Algorithm |\n| 2025.10 | [Discovering Heuristics with Large Language Models (LLMs) for Mixed-Integer Programs: Single-Machine Scheduling](https://arxiv.org/pdf/2510.24013) || `SMTT` | *arxiv* | Algorithm |\n| 2025.11 | [Bridging Synthetic and Real Routing Problems via LLM-Guided Instance Generation and Progressive Adaptation](https://arxiv.org/pdf/2511.10233) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/HenryZhu1029/EvoReal)| `TSP,CVRP` | *AAAI 2026* | Algorithm |\n| 2025.11 | [irace-evo: Automatic Algorithm Configuration Extended With LLM-Based Code Evolution](https://arxiv.org/pdf/2511.14794) || `VSBPP` | *arxiv* | Algorithm |\n| 2025.11 | [LLM4EO: Large Language Model for Evolutionary Optimization in Flexible Job Shop Scheduling](https://arxiv.org/pdf/2511.16485) || `FJSP` | *arxiv* | Algorithm |\n| 2025.11 | [ACCORD: Autoregressive Constraint-satisfying Generation for COmbinatorial Optimization with Routing and Dynamic attention](https://openreview.net/pdf?id=f0TBAdcJ8m) || `FSSP,JSSP,BPP, KP,TSP,VRP` | *Under Review* | Solution \u0026 Benchmark |\n| 2025.11 | [AutoFloorplan: Evolving Heuristics for Chip Floorplanning with Large Language Models and Textual Gradient-Guided Repair](https://openreview.net/pdf?id=DS2iool3nv) || `Floorplanning` | *Under Review* | Algorithm |\n| 2025.11 | [TPD-AHD: Textual Preference Differentiation for LLM-Based Automatic Heuristic Design](https://openreview.net/pdf?id=VEMknlIPtM) || `TSP,CVRP,JSSP, MKP, VRP,MASP,CFLP` | *Under Review* |Algorithm  |\n| 2025.11 | [ALIGNING LLMS WITH GRAPH NEURAL SOLVERS FOR COMBINATORIAL OPTIMIZATION](https://openreview.net/pdf?id=KSfLDk3jxI) || `TSP,CVRP,KP, MVCP,MISP` | *Under Review* | Algorithm |\n| 2025.11 | [Large Language Model Guided Dynamic Branching Rule Scheduling in Branch-and-Bound](https://openreview.net/pdf?id=8LCdjf7uIk) || `MILP` | *Under Review* | Algorithm |\n| 2025.11 | [Online Algorithm Configuration for MILP Re-Optimization with LLM Guidance](https://openreview.net/pdf?id=xbyebbS1ZF) || `MILP` | *Under Review* | Algorithm |\n| 2025.11 | [Experience-Guided Reflective Co-Evolution of Prompts and Heuristics for Automatic Algorithm Design](https://openreview.net/pdf?id=oD9RwlFqEE) || `TSP, BPP` | *Under Review* | Algorithm |\n| 2025.11 | [Adversarial examples for heuristics in combinatorial optimization: An LLM based approach](https://openreview.net/pdf?id=fasU6t3hL4) || `KP,BPP` | *Under Review* | Algorithm |\n| 2025.11 | [Rethinking Code Similarity for Automated Algorithm Design with LLMs](https://openreview.net/pdf?id=HIUqeO9OOr) || `ASP,TSP,CPP` | *ICLR 2026* | Algorithm |\n| 2025.11 | [AutoMOAE: Multi-Objective Auto-Algorithm Evolution](https://openreview.net/pdf?id=G8tP1Z9dLy) || `GCP,TSP` | *Under Review* | Algorithm |\n| 2025.11 | [Fusing LLMs with Scientific Literature for Heuristic Discovery](https://openreview.net/pdf?id=lwqeXDYKWJ) || `TSP` | *Under Review* | Algorithm |\n| 2025.11 | [Cognitively Inspired Reflective Evolution: Interactive Multi-Turn LLM–EA Synthesis of Heuristics for Combinatorial Optimization](https://openreview.net/pdf?id=31VTD5pS2v) || `TSP,BPP` | *Under Review* | Algorithm |\n| 2025.11 | [Hierarchical Representations for Cross-task Automated Heuristic Design using LLMs](https://openreview.net/pdf?id=dgvx86qybJ) || `TSP,CVRP,FSSP, BPP,ASP` | *Under Review* | Algorithm |\n| 2025.11 | [ThetaEvolve: Test-time Learning on Open Problems](https://arxiv.org/abs/2511.23473) || `HadamardMatrix, CirclePacking` | *arxiv* | Algorithm |\n| 2025.11 | [Leveraging large language models for efficient scheduling in Human–Robot collaborative flexible manufacturing systems](https://doi.org/10.1038/s44334-025-00061-w) || `DFJSP` | *npj Adv. Manuf.* | Algorithm |\n| 2025.12 | [RoCo: Role-Based LLMs Collaboration for Automatic Heuristic Design](https://arxiv.org/pdf/2512.03762) || `TSP,OP,CVRP, MKP,offline BPP` | *arxiv* | Algorithm |\n| 2025.12 | [CogMCTS: A Novel Cognitive-Guided Monte Carlo Tree Search Framework for Iterative Heuristic Evolution with Large Language Models](https://arxiv.org/pdf/2512.08609) || `TSP,OP,CVRP, MKP,KP` | *arxiv* | Algorithm |\n| 2025.12 | [Behavior and Representation in Large Language Models for Combinatorial Optimization: From Feature Extraction to Algorithm Selection](https://arxiv.org/pdf/2512.13374) || `BP,GCP,JSP,KP` | *arxiv* | Analysis |\n| 2025.12 | [LAPPI: Interactive Optimization with LLM-Assisted Preference-Based Problem Instantiation](https://arxiv.org/pdf/2512.14138) || `TSP,OP` | *arxiv* | Formulation |\n| 2026.01 | [DRAGON: LLM-Driven Decomposition and Reconstruction Agents for Large-Scale Combinatorial Optimization](https://arxiv.org/pdf/2601.06502) || `TSP,CVRP, BPP,MKP` | *arxiv* | Algorithm |\n| 2026.01 | [LLM-Assisted Automatic Dispatching Rule Design for Dynamic Flexible Assembly Flow Shop Scheduling](https://arxiv.org/pdf/2601.15738) || `Dynamic FAFSP` | *arxiv* | Algorithm |\n| 2026.01 | [Evolving Interdependent Operators with Large Language Models for Multi-Objective Combinatorial Optimization](https://arxiv.org/pdf/2601.17899) || `MOCP` | *arxiv* | Algorithm |\n| 2026.01 | [Algorithmic Prompt-Augmentation for Efficient LLM-Based Heuristic Design for A* Search](https://arxiv.org/pdf/2601.19622) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/tb-git-tud/a-ceoh-evolution-of-heuristics)| `SP,ULPMP` | *arxiv* | Algorithm |\n| 2026.01 | [Rethinking LLM-Driven Heuristic Design: Generating Efficient and Specialized Solvers via Dynamics-Aware Optimization](https://arxiv.org/pdf/2601.20868) || `TSP,CVRP, BPP,MKP` | *arxiv* | Algorithm |\n| 2026.01 | [PathWise: Planning through World Model for Automated Heuristic Design via Self-Evolving LLMs](https://arxiv.org/pdf/2601.20539) || `TSP,KP,CVRP, MKP,OP,BPP` | *arxiv* | Algorithm |\n| 2026.01 | [LLaMEA-SAGE: Guiding Automated Algorithm Design with Structural Feedback from Explainable AI](https://arxiv.org/pdf/2601.21511) || `BBO` | *arxiv* | Algorithm |\n| 2026.01 | [Game-Theoretic Co-Evolution for LLM-Based Heuristic Discovery](https://arxiv.org/pdf/2601.22896) || `OBP,TSP,CVRP` | *arxiv* | Algorithm |\n| 2026.01 | [Beyond the Node: Clade-level Selection for Efficient MCTS in Automatic Heuristic Design](https://arxiv.org/pdf/2602.00549) || `TSP,KP,CVRP, MKP,BPP` | *arxiv* | Algorithm |\n| 2026.02 | [Hard Constraints Meet Soft Generation: Guaranteed Feasibility for LLM-based Combinatorial Optimization](https://arxiv.org/pdf/2602.01090) || `TSP,OP,CVRP,MIS, MVC,PFSP,JSSP` | *arxiv* | Solution |\n| 2026.02 | [Reasoning in a Combinatorial and Constrained World: Benchmarking LLMs on Natural-Language Combinatorial Optimization](https://arxiv.org/pdf/2602.02188) || `COP` | *arxiv* | Benchmark |\n| 2026.02 | [G-LNS: Generative Large Neighborhood Search for LLM-Based Automatic Heuristic Design](https://arxiv.org/pdf/2602.08253) |[![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/zboyn/G-LNS)| `TSP,CVRP,OVRP` | *arxiv* | Algorithm |\n----\n\n### Domain FMs for Combinatorial Optimization\n\nDeveloping a domain FM capable of solving a wide range of COPs presents an intriguing and formidable challenge. Recent efforts in this area aim towards this ambitious goal by creating a unified architecture or representation applicable across various COPs.\n\n|  Date   |                            Paper                             |                             Link                             |                 Problem                  |    Venue     |\n| :-----: | :----------------------------------------------------------: | :----------------------------------------------------------: | :--------------------------------------: | :----------: |\n| 2022.08 | [One Model, Any CSP: Graph Neural Networks as Fast Global Search Heuristics for Constraint Satisfaction](https://arxiv.org/pdf/2208.10227) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/toenshoff/ANYCSP) | `CSP` | *IJCAI 2023* |\n| 2023.05 | [Efficient Training of Multi-task Combinatorial Neural Solver with Multi-armed Bandits](https://arxiv.org/pdf/2305.06361) |                      \u0026emsp;\u0026emsp;\u0026emsp;                      |             `TSP,VRP,OP,KP`              |   *TMLR*    |\n| 2024.02 | [Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalization](https://arxiv.org/pdf/2402.16891) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/FeiLiu36/MTNCO) |                 `16VRPs`                 |  *KDD 2024*  |\n| 2024.03 | [Towards a Generic Representation of Combinatorial Problems for Learning-Based Approaches](https://arxiv.org/pdf/2403.06026) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/corail-research/learning-generic-csp) |             `SAT,TSP,COL,KP`             |   *CPAIOR 2024*    |\n| 2024.04 | [Cross-Problem Learning for Solving Vehicle Routing Problems](https://arxiv.org/pdf/2404.11677) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/Zhuoyi-Lin/Cross_problem_learning) |              `TSP,OP,PCTSP`              | *IJCAI 2024* |\n| 2024.05 | [MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts](https://arxiv.org/pdf/2405.01029) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/RoyalSkye/Routing-MVMoE) |                 `16VRPs`                 | *ICML 2024*  |\n| 2024.06 | [RouteFinder: Towards Foundation Models for Vehicle Routing Problems](https://arxiv.org/pdf/2406.15007) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/ai4co/routefinder) \u003cbr\u003e [![Project-Page](https://img.shields.io/badge/Page-74aa9c?style=for-the-badge)](https://ai4co.github.io/routefinder/) |                 `48VRPs`                 |    *TMLR*    |\n| 2024.06 | [GOAL: A Generalist Combinatorial Optimization Agent Learner](https://arxiv.org/pdf/2406.15079) |          [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/naver/goal-co)                                              | `(A)TSP,5VRPs,OP,JSSP, OSSP,UMSP,KP,MVC, MIS,MCLP,TRP,SOP` |   *ICLR 2025*   |\n| 2024.08 | [UNCO: Towards Unifying Neural Combinatorial Optimization through Large Language Model](https://arxiv.org/pdf/2408.12214) |                                                              |        `TSP,CVRP,KP, MVCP,SMTWTP`        |   *arXiv*    |\n| 2024.09 | [MAPF-GPT: Imitation Learning for Multi-Agent Pathfinding at Scale](https://arxiv.org/pdf/2409.00134) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/Cognitive-AI-Systems/MAPF-GPT) |                  `MAPF`                  |   *AAAI 2025*    |\n| 2024.10 | [Toward Learning Generalized Cross-Problem Solving Strategies for Combinatorial Optimization](https://openreview.net/forum?id=VnaJNW80pN) | |                  `TSP,VRP,SDVRP, OP,PCTSP,SPCTSP`                  |   *Under Review*   |\n| 2024.10 | [Learning General Representations Across Graph Combinatorial Optimization Problems](https://openreview.net/forum?id=elmTU101oS) | |                  `7GDPs`                  | *Under Review* |\n| 2024.10 | [Solving Diverse Combinatorial Optimization Problems with a Unified Model](https://openreview.net/forum?id=Kc3yoIL5oR) | |                  `(A)TSP,CVRP,OP,PCTSP, SPCTSP,KP,MIS,FFSP`                  | *Under Review* |\n| 2024.10 | [SHIELD: Multi-task Multi-distribution Vehicle Routing Solver with Sparsity \u0026 Hierarchy in Efficiently Layered Decoder](https://openreview.net/forum?id=AMbIvaD4Rr) | | `16VRPs` | *ICML 2025* |\n| 2024.10 | [Unified Neural Solvers for General TSP and Multiple Combinatorial Optimization Tasks via Problem Reduction and Matrix Encoding](https://openreview.net/forum?id=yEwakMNIex) | | `(A)TSP,DHCP,3SAT` | *ICLR 2025* |\n| 2024.10 | [Foundation Models for Boolean Logic](https://openreview.net/forum?id=qeY25DwmKO) | | `Boolean Logic` | *Under Review* |\n| 2024.11 | [CaDA: Cross-Problem Routing Solver with Constraint-Aware Dual-Attention](https://arxiv.org/pdf/2412.00346) | | `16VRPs` | *ICML 2025* |\n| 2024.12 | [Multi-task Representation Learning for Mixed Integer Linear Programming](https://arxiv.org/pdf/2412.14409) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/caidog1129/MILP_multitask) | `MILP` | *arXiv* |\n| 2025.05 | [A Mixed-Curvature based Pre-training Paradigm for Multi-Task Vehicle Routing Solver](https://openreview.net/pdf?id=JsPyLqCgks) | [![Code](https://img.shields.io/badge/Code-025E8C?style=for-the-badge)](https://github.com/lsyysl9711/Mixed_Curvature_VRPs) | `VRP` | *ICML 2025* |\n| 2025.07 | [LRM-1B: Towards Large Routing Model](https://www.arxiv.org/pdf/2507.03300) || `VRP` | *arxiv* |\n| 2025.08 | [FORGE: Foundational Optimization Representations from Graph Embeddings](https://arxiv.org/pdf/2508.20330) || `MIP` | *arxiv* |\n| 2025.09 | [Graph Foundation Models: Bridging Language Model Paradigms and Graph Optimization](https://arxiv.org/abs/2509.24256) || `OR` | *arxiv* |\n| 2025.11 | [Foundation Models for Industrial Scheduling Leveraging the Techniques from LLMs](https://openreview.net/pdf?id=qRjLjYrvMi) || `FJSP` | *Under Review* |\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fai4co%2Fawesome-fm4co","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fai4co%2Fawesome-fm4co","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fai4co%2Fawesome-fm4co/lists"}