├── .gitignore
├── LICENSE
└── README.md
/.gitignore:
--------------------------------------------------------------------------------
1 | # Byte-compiled / optimized / DLL files
2 | __pycache__/
3 | *.py[cod]
4 | *$py.class
5 |
6 | # macOS
7 | .DS_Store
8 |
9 | # Jupyter Notebook
10 | .ipynb_checkpoints
11 |
12 | .idea/
13 |
--------------------------------------------------------------------------------
/LICENSE:
--------------------------------------------------------------------------------
1 | MIT License
2 |
3 | Copyright (c) 2024 Jianan Zhou
4 |
5 | Permission is hereby granted, free of charge, to any person obtaining a copy
6 | of this software and associated documentation files (the "Software"), to deal
7 | in the Software without restriction, including without limitation the rights
8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 |
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 |
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
22 |
--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
1 | Foundation Models for Combinatorial Optimization
2 |
3 | FM4CO contains interesting research papers (1) using **Existing Large Language Models for Combinatorial Optimization**, and (2) building **Domain Foundation Models for Combinatorial Optimization**.
4 |
5 | ----
6 |
7 | ### LLMs for Combinatorial Optimization
8 |
9 | Most 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.
10 |
11 | | Date | Paper | Link | Problem | Venue | Remark* |
12 | | :-----: | :----------------------------------------------------------: | :----------------------------------------------------------: | :-------------------: | :------------: | :--------------: |
13 | | 2023.07 | [Large Language Models for Supply Chain Optimization](https://arxiv.org/pdf/2307.03875) | [](https://github.com/microsoft/OptiGuide) | `Supply_Chain` | *arXiv* | Algorithm w. Interpretability |
14 | | 2023.09 | [Can Language Models Solve Graph Problems in Natural Language?](https://arxiv.org/pdf/2305.10037) | [](https://github.com/Arthur-Heng/NLGraph) | `Graph` | *NeurIPS 2023* | Solution |
15 | | 2023.09 | [Large Language Models as Optimizers](https://arxiv.org/pdf/2309.03409) | [](https://github.com/google-deepmind/opro) | `TSP` | *ICLR 2024* | Solution |
16 | | 2023.10 | [Chain-of-Experts: When LLMs Meet Complex Operations Research Problems](https://openreview.net/pdf?id=HobyL1B9CZ) | [](https://github.com/xzymustbexzy/Chain-of-Experts) | `MILP` | *ICLR 2024* | Formulation |
17 | | 2023.10 | [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://arxiv.org/pdf/2402.10172) | [](https://github.com/teshnizi/OptiMUS) | `MILP` | *ICML 2024* | Formulation |
18 | | 2023.10 | [AI-Copilot for Business Optimisation: A Framework and A Case Study in Production Scheduling](https://arxiv.org/pdf/2309.13218) | [](https://github.com/pivithuruthejanamarasinghe/AI-Copilot-Data) | `JSSP` | *arXiv* | Formulation |
19 | | 2023.11 | [Large Language Models as Evolutionary Optimizers](https://arxiv.org/pdf/2310.19046) | [](https://github.com/cschen1205/LMEA) | `TSP` | *CEC 2024* | Solution |
20 | | 2023.11 | [Algorithm Evolution Using Large Language Model](https://arxiv.org/pdf/2311.15249) | | `TSP` | *arXiv* | Algorithm |
21 | | 2023.12 | [Mathematical discoveries from program search with large language models](https://www.nature.com/articles/s41586-023-06924-6) | [](https://github.com/google-deepmind/funsearch) | `BPP` | *Nature* | Algorithm |
22 | | 2023.12 | [NPHardEval: Dynamic Benchmark on Reasoning Ability of Large Language Models via Complexity Classes](https://arxiv.org/pdf/2312.14890) | [](https://github.com/casmlab/NPHardEval) | `TSP,KP, GCP,MSP` | *ACL 2024* | Benchmark |
23 | | 2024.02 | [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://arxiv.org/pdf/2402.01145) | [](https://github.com/ai4co/reevo)
[](https://github.com/ai4co/reevo) | `TSP,VRP,OP, MKP,BPP,EDA` | *NeurIPS 2024* | Algorithm |
24 | | 2024.02 | [AutoSAT: Automatically Optimize SAT Solvers via Large Language Models](https://arxiv.org/pdf/2402.10705) | | `SAT` | *arXiv* | Algorithm |
25 | | 2024.02 | [From Large Language Models and Optimization to Decision Optimization CoPilot: A Research Manifesto](https://arxiv.org/pdf/2402.16269) | | `MILP` | *arXiv* | Formulation |
26 | | 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 |
27 | | 2024.03 | [RouteExplainer: An Explanation Framework for Vehicle Routing Problem](https://arxiv.org/pdf/2403.03585.pdf) | [](https://github.com/ntt-dkiku/route-explainer)
[](https://ntt-dkiku.github.io/xai-vrp) | `VRP` | *PAKDD 2024* | Interpretability |
28 | | 2024.03 | [Can Large Language Models Solve Robot Routing?](https://arxiv.org/pdf/2403.10795) | [](https://github.com/Zhehui-Huang/LLM_Routing)
[](https://sites.google.com/view/words-to-routes) | `TSP,VRP` | *arXiv* | Algorithm |
29 | | 2024.05 | [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://arxiv.org/pdf/2401.02051) | [](https://github.com/FeiLiu36/EoH) | `TSP,BPP,FSSP` | *ICML 2024* | Algorithm |
30 | | 2024.05 | [ORLM: Training Large Language Models for Optimization Modeling](https://arxiv.org/pdf/2405.17743) | [](https://github.com/Cardinal-Operations/ORLM) | `General OPT` | *Operations Research* | Formulation |
31 | | 2024.05 | [Self-Guiding Exploration for Combinatorial Problems](https://arxiv.org/pdf/2405.17950) | [](https://github.com/Zangir/LLM-for-CP) | `TSP,VRP,BPP, AP,KP,JSSP` | *NeurIPS 2024* | Solution |
32 | | 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 |
33 | | 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) | [](https://github.com/ahmed-abdulhuy/Solving-TSP-and-mTSP-Combinatorial-Challenges-using-Visual-Reasoning-and-Multi-Agent-Approach-MLLMs-) | `TSP,mTSP` | *arXiv* | Solution |
34 | | 2024.07 | [Solving General Natural-Language-Description Optimization Problems with Large Language Models](https://arxiv.org/pdf/2407.07924) | [](https://opt.alibabacloud.com/chat) | `MILP` | *NAACL 2024* | Formulation |
35 | | 2024.08 | [Diagnosing Infeasible Optimization Problems Using Large Language Models](https://arxiv.org/pdf/2308.12923) | | `MILP` | *INFOR* | Formulation |
36 | | 2024.08 | [LLMs can Schedule](https://arxiv.org/pdf/2408.06993) | [](https://github.com/starjob42/datasetjsp) | `JSSP` | *arXiv* | Solution |
37 | | 2024.09 | [Multi-objective Evolution of Heuristic Using Large Language Model](https://arxiv.org/pdf/2409.16867) | | `TSP,BPP` | *AAAI 2025* | Algorithm |
38 | | 2024.10 | [Towards Foundation Models for Mixed Integer Linear Programming](https://arxiv.org/pdf/2410.08288) | | `MILP` | *ICLR 2025* | Formulation |
39 | | 2024.10 | [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://arxiv.org/pdf/2410.13213) | | `General OPT` | *ICLR 2025* | Formulation |
40 | | 2024.10 | [OptiBench: Benchmarking Large Language Models in Optimization Modeling with Equivalence-Detection Evaluation](https://openreview.net/forum?id=KD9F5Ap878) | | `MILP` | *Under Review* | Benchmark |
41 | | 2024.10 | [OptiBench Meets ReSocratic: Measure and Improve LLMs for Optimization Modeling](https://openreview.net/forum?id=fsDZwS49uY) | | `MILP` | *ICLR 2025* | Benchmark |
42 | | 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 |
43 | | 2024.10 | [STARJOB: Dataset for LLM-Driven Job Shop Scheduling](https://openreview.net/forum?id=t0fU6t3Skw) | | `JSSP` | *Under Review* | Solution |
44 | | 2024.10 | [LLM4Solver: Large Language Model for Efficient Algorithm Design of Combinatorial Optimization Solver](https://openreview.net/forum?id=XTxdDEFR6D) | | `MILP` | *Under Review* | Algorithm |
45 | | 2024.10 | [Unifying All Species: LLM-based Hyper-Heuristics for Multi-objective Optimization](https://openreview.net/forum?id=sUywd7UhFT) | | `TSP` | *Under Review* | Algorithm |
46 | | 2024.10 | [Evo-Step: Evolutionary Generation and Stepwise Validation for Optimizing LLMs in OR](https://openreview.net/forum?id=aapUBU9U0D) | | `MILP` | *Under Review* | Formulation |
47 | | 2024.10 | [Automatic programming via large language models with population self-evolution for dynamic job shop scheduling problem](https://arxiv.org/pdf/2410.22657) | | `DyJSSP` | *arXiv* | Algorithm |
48 | | 2024.11 | [Large Language Models for Combinatorial Optimization of Design Structure Matrix](https://arxiv.org/pdf/2411.12571) | | `DSM` | *arXiv* | Solution |
49 | | 2024.12 | [HSEvo: Elevating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMs](https://arxiv.org/pdf/2412.14995) |[](https://github.com/datphamvn/HSEvo) | `TSP,BPP,OP` | *AAAI 2025* | Algorithm |
50 | | 2024.12 | [Evaluating LLM Reasoning in the Operations Research Domain with ORQA](https://arxiv.org/pdf/2412.17874) |[](https://github.com/nl4opt/ORQA) | `General OR` | *AAAI 2025* | Benchmark |
51 | | 2024.12 | [QUBE: Enhancing Automatic Heuristic Design via Quality-Uncertainty Balanced Evolution](https://arxiv.org/pdf/2412.20694) |[](https://github.com/zzjchen/QUBE_code) | `OBP,TSP,CSP` | *arxiv* | Algorithm |
52 | | 2025.01 | [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://arxiv.org/pdf/2501.08603) |[](https://github.com/zz1358m/MCTS-AHD-master) | `TSP,CVRP,KP, BPP,MKP,ASP` | *ICML 2025* | Algorithm |
53 | | 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 |
54 | | 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 |
55 | | 2025.02 | [Improving Existing Optimization Algorithms with LLMs](https://arxiv.org/pdf/2502.08298) || `MIS` | *arXiv* | Algorithm |
56 | | 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 |
57 | | 2025.02 | [GraphThought: Graph Combinatorial Optimization with Thought Generation](https://arxiv.org/pdf/2502.11607) || `MIS,MVC,TSP` | *arXiv* | Algorithm |
58 | | 2025.02 | [EquivaMap: Leveraging LLMs for Automatic Equivalence Checking of Optimization Formulations](https://arxiv.org/pdf/2502.14760) |[](https://github.com/HumainLab/EquivaMap)| `MILP` | *arXiv* | Algorithm |
59 | | 2025.02 | [ARS: Automatic Routing Solver with Large Language Models](https://arxiv.org/pdf/2502.15359) |[](https://github.com/Ahalikai/ARS-Routbench)| `VRP` | *arXiv* | Benchmark & Algorithm |
60 | | 2025.02 | [Text2Zinc: A Cross-Domain Dataset for Modeling Optimization and Satisfaction Problems in MiniZinc](https://arxiv.org/pdf/2503.10642) | [](https://huggingface.co/datasets/skadio/text2zinc)| `LP,MIP,CP` | *arXiv* | Formulation (Dataset) |
61 | | 2025.02 | [GraphArena: Evaluating and Exploring Large Language Models on Graph Computation](https://openreview.net/pdf?id=Y1r9yCMzeA) | [](https://github.com/squareRoot3/GraphArena/tree/master) | `MVC,MIS,MCP, TSP,MCS,GED` | *ICLR 2025* | Benchmark & Dataset & Model|
62 | | 2025.03 | [Leveraging Large Language Models to Develop Heuristics for Emerging Optimization Problems](https://arxiv.org/pdf/2503.03350) |[](https://github.com/nico-koltermann/contextual-evolution-of-heuristics)| `UPMP` | *arXiv* | Algorithm |
63 | | 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) |[](https://github.com/bwz96sco/or_llm_agent)| `OP` | *arXiv* | Formulation |
64 | | 2025.03 | [Combinatorial Optimization for All: Using LLMs to Aid Non-Experts in Improving Optimization Algorithms](https://arxiv.org/pdf/2503.10968) | [](https://github.com/camilochs/comb-opt-for-all)
[](https://camilochs.github.io/comb-opt-for-all/)| `TSP` | *arXiv* | Algorithm |
65 | | 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` | *arXiv* | Formulation |
66 | | 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 |
67 | | 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 |
68 | | 2025.04 | [Algorithm Discovery With LLMs: Evolutionary Search Meets Reinforcement Learning](https://arxiv.org/pdf/2504.05108) || `BPP,TSP,FP` | *COLM 2025* | Algorithm |
69 | | 2025.04 | [OptimAI: Optimization from Natural Language Using LLM-Powered AI Agents](https://arxiv.org/pdf/2504.16918) || `MILP` | *arXiv* | Formulation |
70 | | 2025.04 | [Fitness Landscape of Large Language Model-Assisted Automated Algorithm Search](https://arxiv.org/pdf/2504.19636) || `OBP,TSP, CVRP,VRPTW` | *arXiv* | Benchmark & Interpretability |
71 | | 2025.04 | [Large Language Models powered Neural Solvers for Generalized Vehicle Routing Problems](https://openreview.net/pdf?id=EVqlVjvlt8) |[](https://github.com/Fsoft-AIC/NCO-LLM)| `VRP` | *ICLR 2025 Workshop AgenticAI* | Algorithm |
72 | | 2025.05 | [Efficient Heuristics Generation for Solving Combinatorial Optimization Problems Using Large Language Models](https://arxiv.org/pdf/2505.12627v1) |[](https://github.com/wuuu110/Hercules)| `TSP,CVRP,BPP, MKP,OP` | *KDD 2025* | Algorithm |
73 | | 2025.05 | [CALM: Co-evolution of Algorithms and Language Model for Automatic Heuristic Design](https://arxiv.org/pdf/2505.12285v1) || `TSP,KP,OBP,OP` | *arXiv* | Algorithm |
74 | | 2025.05 | [Know the Ropes: A Heuristic Strategy for LLM-based Multi-Agent System Design](https://arxiv.org/pdf/2505.16979) || `KP` | *arXiv* | Solution |
75 | | 2025.05 | [A Comprehensive Evaluation of Contemporary ML-Based Solvers for Combinatorial Optimization](https://arxiv.org/pdf/2505.16952) | [](https://huggingface.co/datasets/CO-Bench/FrontierCO)| `MIS,MDS, TSP,CVRP,CFLP, CPMP,FJSP,STP` | *ICML 2025 Workshop AI4Math* | Benchmark |
76 | | 2025.05 | [LLM-Meta-SR: In-Context Learning for Evolving Selection Operators in Symbolic Regression](https://arxiv.org/abs/2505.18602) || `SR` | *arXiv* | Algorithm |
77 | | 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 |
78 | | 2025.05 | [Generalizable Heuristic Generation Through Large Language Models with Meta-Optimization](https://arxiv.org/pdf/2505.20881) || `TSP,CVRP,BPP` | *arXiv* | Algorithm |
79 | | 2025.05 | [Large Language Model-driven Large Neighborhood Search for Large-Scale MILP Problems](https://openreview.net/pdf?id=teUg2pMrF0) | [](https://github.com/thuiar/LLM-LNS)| `MILP` | *ICML 2025* | Algorithm |
80 | | 2025.05 | [Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling](https://arxiv.org/pdf/2505.11792) | [](https://github.com/Cardinal-Operations/SIRL)| `General OPT` | *NeurIPS 2025* | Formulation |
81 | | 2025.06 | [LLM-Driven Instance-Specific Heuristic Generation and Selection](https://arxiv.org/pdf/2506.00490) || `OBPP,CVRP` | *arXiv* | Algorithm |
82 | | 2025.06 | [ORMind: A Cognitive-Inspired End-to-End Reasoning Framework for Operations Research](https://arxiv.org/pdf/2506.01326) |[](https://github.com/XiaoAI1989/ORMind)| `OR` | *ACL 2025* | Formulation |
83 | | 2025.06 | [EALG: Evolutionary Adversarial Generation of Language Model–Guided Generators for Combinatorial Optimization](https://arxiv.org/pdf/2506.02594) || `TSP,OP` | *arXiv* | Algorithm |
84 | | 2025.06 | [CP-Bench: Evaluating Large Language Models for Constraint Modelling](https://arxiv.org/pdf/2506.06052) || `CP` | *arXiv* | Benchmark |
85 | | 2025.06 | [REMoH: A Reflective Evolution of Multi-objective Heuristics approach via Large Language Models](https://arxiv.org/pdf/2506.07759) || `FJSSP` | *arXiv* | Algorithm |
86 | | 2025.06 | [HeuriGym: An Agentic Benchmark for LLM-Crafted Heuristics in Combinatorial Optimization](https://arxiv.org/pdf/2506.07972) |[](https://github.com/cornell-zhang/heurigym)| `TSP,SAT` | *arXiv* | Benchmark |
87 | | 2025.06 | [ALE-Bench: A Benchmark for Long-Horizon Objective-Driven Algorithm Engineering](https://arxiv.org/pdf/2506.09050) | [](https://github.com/SakanaAI/ALE-Bench)
[](https://huggingface.co/datasets/SakanaAI/ALE-Bench)| `General OPT` | *NeurIPS 2025 Datasets and Benchmarks Track* | Benchmark |
88 | | 2025.06 | [OPT-BENCH: Evaluating LLM Agent on Large-Scale Search Spaces Optimization Problems](https://arxiv.org/pdf/2506.10764) | [](https://huggingface.co/datasets/OPT-Bench/OPT-Bench)
[](https://github.com/OliverLeeXZ/OPT-BENCH)| `GCP,KP,MCP, MIS,SCP,TSP` | *arXiv* | Benchmark |
89 | | 2025.06 | [STRCMP: Integrating Graph Structural Priors with Language Models for Combinatorial Optimization](https://arxiv.org/pdf/2506.11057) || `SAT` | *NeurIPS 2025* | Solution |
90 | | 2025.06 | [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://arxiv.org/pdf/2506.13131) |[](https://colab.research.google.com/github/google-deepmind/alphaevolve_results/blob/master/mathematical_results.ipynb)| `OPT` | *arXiv* | Algorithm |
91 | | 2025.06 | [HeurAgenix: Leveraging LLMs for Solving Complex Combinatorial Optimization Challenges](https://arxiv.org/pdf/2506.15196) | [](https://github.com/microsoft/HeurAgenix)| `TSP,CVRP,JSSP, MaxCut,MKP` | *arXiv* | Algorithm |
92 | | 2025.07 | [Large Language Models for Combinatorial Optimization: A Systematic Review](https://arxiv.org/pdf/2507.03637) || `CO` | *arXiv* | Review |
93 | | 2025.07 | [Fine-tuning Large Language Model for Automated Algorithm Design](https://arxiv.org/pdf/2507.10614) || `ASP,TSP,CVRP` | *arXiv* | Algorithm |
94 | | 2025.07 | [DHEvo: Data-Algorithm Based Heuristic Evolution for Generalizable MILP Solving](https://arxiv.org/pdf/2507.15615) || `MILP` | *arXiv* | Algorithm |
95 | | 2025.07 | [MeLA: A Metacognitive LLM-Driven Architecture for Automatic Heuristic Design](https://arxiv.org/pdf/2507.20541) |[](https://github.com/Qzs1335/MeLA)| `TSP,BPP,ACS` | *arXiv* | Algorithm |
96 | | 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) |[](https://github.com/langkhachhoha/MPaGE)| `TSP,CVRP,KP` | *AAAI 2026* | Algorithm |
97 | | 2025.07 | [Automatically discovering heuristics in a complex SAT solver with large language models](https://arxiv.org/pdf/2507.22876) || `SAT` | *arXiv* | Algorithm |
98 | | 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 |
99 | | 2025.08 | [ReflecSched: Solving Dynamic Flexible Job-Shop Scheduling via LLM-Powered Hierarchical Reflection](https://arxiv.org/pdf/2508.01724) || `DFJSP` | *arxiv* | Solution |
100 | | 2025.08 | [OptiHive: Ensemble Selection for LLM-Based Optimization via Statistical Modeling](https://arxiv.org/pdf/2508.02503) || `MDVRP,WSCP` | *arxiv* | Formulation |
101 | | 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 |
102 | | 2025.08 | [X-evolve: Solution space evolution powered by large language models](https://arxiv.org/pdf/2508.07932) || `CSP,BPP, Shannon capacity` | *arxiv* | Algorithm |
103 | | 2025.08 | [EvoCut: Strengthening Integer Programs via Evolution-Guided Language Models](https://arxiv.org/pdf/2508.11850) |[](https://github.com/milad1378yz/EvoCut)| `MILP` | *arxiv* | Formulation |
104 | | 2025.08 | [HIFO-PROMPT: Prompting with Hindsight and Foresight For LLM-Based Automatic Heuristic Design](https://arxiv.org/pdf/2508.13333) || `TSP,OBP,FSSP` | *arxiv* | Algorithm |
105 | | 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 |
106 | | 2025.09 | [AutoPBO: LLM-powered Optimization for Local Search PBO Solvers](https://arxiv.org/pdf/2509.04007) || `PBO` | *arxiv* | Solution |
107 | | 2025.09 | [Autonomous Code Evolution MeetsNP-Completeness](https://arxiv.org/pdf/2509.07367) || `SAT` | *arxiv* | Solution |
108 | | 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 |
109 | | 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 |
110 | | 2025.09 | [DaSAThco: Data-Aware SAT Heuristics Combinations Optimization via Large Language Models](https://arxiv.org/pdf/2509.12602) || `SAT` | *arxiv* | Algorithm |
111 | | 2025.09 | [Large Language Models as End-to-end Combinatorial Optimization Solvers](https://arxiv.org/pdf/2509.16865) |[](https://github.com/Summer142857/LLMCoSolver)| `TSP,OP,CVRP, MIS,MVC,PFSP,JSSP` | *NeurIPS 2025* | Solution |
112 | | 2025.09 | [Large Language Models and Operations Research: A Structured Survey](https://arxiv.org/pdf/2509.18180) || `OR` | *arxiv* | Review |
113 | | 2025.09 | [ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolution](https://arxiv.org/pdf/2509.19349) |[](https://github.com/SakanaAI/ShinkaEvolve)| `OPT` | *arXiv* | Algorithm |
114 | | 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 |
115 | | 2025.09 | [OptiMind: Teaching LLMs to Think Like Optimization Experts](https://arxiv.org/pdf/2509.22979) || `MILP` | *arxiv* | Formulation |
116 | | 2025.09 | [AutoEP: LLMs-Driven Automation of Hyperparameter Evolution for Metaheuristic Algorithms](https://arxiv.org/pdf/2509.23189) || `TSP,CVRP,FSSP` | *arxiv* | Algorithm |
117 | | 2025.09 | [ViTSP: A Vision Language Models Guided Framework for Large-Scale Traveling Salesman Problems](https://arxiv.org/pdf/2509.23465) || `TSP` | *arxiv* | Algorithm |
118 | | 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 |
119 | | 2025.10 | [EvoSpeak: Large Language Models for Interpretable Genetic Programming-Evolved Heuristics](https://arxiv.org/pdf/2510.02686) || `DFJSS` | *arxiv* | Algorithm |
120 | | 2025.10 | [VRPAgent: LLM-Driven Discovery of Heuristic Operators for Vehicle Routing Problems](https://arxiv.org/pdf/2510.07073) |[](https://github.com/ai4co/vrpagent)| `VRP` | *arxiv* | Algorithm |
121 | | 2025.10 | [Refining Hybrid Genetic Search for CVRP via Reinforcement Learning-Finetuned LLM](https://arxiv.org/pdf/2510.11121) || `CVRP` | *arxiv* | Algorithm |
122 | | 2025.10 | [An Agentic Framework with LLMs for Solving Complex Vehicle Routing Problems](https://arxiv.org/pdf/2510.16701) || `VRP` | *arxiv* | Formulation |
123 | | 2025.10 | [OptiTree: Hierarchical Thoughts Generation with Tree Search for LLM Optimization Modeling](https://arxiv.org/pdf/2510.22192) |[](https://github.com/MIRALab-USTC/OptiTree)| `OR` | *NeurIPS 2025* | Formulation |
124 | | 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 |
125 | | 2025.11 | [Bridging Synthetic and Real Routing Problems via LLM-Guided Instance Generation and Progressive Adaptation](https://arxiv.org/pdf/2511.10233) |[](https://github.com/HenryZhu1029/EvoReal)| `TSP,CVRP` | *AAAI 2026* | Algorithm |
126 | | 2025.11 | [LLM4EO: Large Language Model for Evolutionary Optimization in Flexible Job Shop Scheduling](https://arxiv.org/pdf/2511.16485) || `FJSP` | *arxiv* | Algorithm |
127 | | 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 & Benchmark |
128 | | 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 |
129 | | 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 |
130 | | 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 |
131 | | 2025.11 | [Large Language Model Guided Dynamic Branching Rule Scheduling in Branch-and-Bound](https://openreview.net/pdf?id=8LCdjf7uIk) || `MILP` | *Under Review* | Algorithm |
132 | | 2025.11 | [Online Algorithm Configuration for MILP Re-Optimization with LLM Guidance](https://openreview.net/pdf?id=xbyebbS1ZF) || `MILP` | *Under Review* | Algorithm |
133 | | 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 |
134 | | 2025.11 | [Adversarial examples for heuristics in combinatorial optimization: An LLM based approach](https://openreview.net/pdf?id=fasU6t3hL4) || `KP,BPP` | *Under Review* | Algorithm |
135 | | 2025.11 | [Rethinking Code Similarity for Automated Algorithm Design with LLMs](https://openreview.net/pdf?id=HIUqeO9OOr) || `ASP,TSP,CPP` | *Under Review* | Algorithm |
136 | | 2025.11 | [AutoMOAE: Multi-Objective Auto-Algorithm Evolution](https://openreview.net/pdf?id=G8tP1Z9dLy) || `GCP,TSP` | *Under Review* | Algorithm |
137 | | 2025.11 | [Fusing LLMs with Scientific Literature for Heuristic Discovery](https://openreview.net/pdf?id=lwqeXDYKWJ) || `TSP` | *Under Review* | Algorithm |
138 | | 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 |
139 | | 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 |
140 | | 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 |
141 | | 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 |
142 | | 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 |
143 | | 2025.12 | [LAPPI: Interactive Optimization with LLM-Assisted Preference-Based Problem Instantiation](https://arxiv.org/pdf/2512.14138) || `TSP,OP` | *arxiv* | Formulation |
144 |
145 | ----
146 |
147 | ### Domain FMs for Combinatorial Optimization
148 |
149 | Developing 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.
150 |
151 | | Date | Paper | Link | Problem | Venue |
152 | | :-----: | :----------------------------------------------------------: | :----------------------------------------------------------: | :--------------------------------------: | :----------: |
153 | | 2022.08 | [One Model, Any CSP: Graph Neural Networks as Fast Global Search Heuristics for Constraint Satisfaction](https://arxiv.org/pdf/2208.10227) | [](https://github.com/toenshoff/ANYCSP) | `CSP` | *IJCAI 2023* |
154 | | 2023.05 | [Efficient Training of Multi-task Combinatorial Neural Solver with Multi-armed Bandits](https://arxiv.org/pdf/2305.06361) | | `TSP,VRP,OP,KP` | *TMLR* |
155 | | 2024.02 | [Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalization](https://arxiv.org/pdf/2402.16891) | [](https://github.com/FeiLiu36/MTNCO) | `16VRPs` | *KDD 2024* |
156 | | 2024.03 | [Towards a Generic Representation of Combinatorial Problems for Learning-Based Approaches](https://arxiv.org/pdf/2403.06026) | [](https://github.com/corail-research/learning-generic-csp) | `SAT,TSP,COL,KP` | *CPAIOR 2024* |
157 | | 2024.04 | [Cross-Problem Learning for Solving Vehicle Routing Problems](https://arxiv.org/pdf/2404.11677) | [](https://github.com/Zhuoyi-Lin/Cross_problem_learning) | `TSP,OP,PCTSP` | *IJCAI 2024* |
158 | | 2024.05 | [MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts](https://arxiv.org/pdf/2405.01029) | [](https://github.com/RoyalSkye/Routing-MVMoE) | `16VRPs` | *ICML 2024* |
159 | | 2024.06 | [RouteFinder: Towards Foundation Models for Vehicle Routing Problems](https://arxiv.org/pdf/2406.15007) | [](https://github.com/ai4co/routefinder)
[](https://ai4co.github.io/routefinder/) | `48VRPs` | *TMLR* |
160 | | 2024.06 | [GOAL: A Generalist Combinatorial Optimization Agent Learner](https://arxiv.org/pdf/2406.15079) | [](https://github.com/naver/goal-co) | `(A)TSP,5VRPs,OP,JSSP, OSSP,UMSP,KP,MVC, MIS,MCLP,TRP,SOP` | *ICLR 2025* |
161 | | 2024.08 | [UNCO: Towards Unifying Neural Combinatorial Optimization through Large Language Model](https://arxiv.org/pdf/2408.12214) | | `TSP,CVRP,KP, MVCP,SMTWTP` | *arXiv* |
162 | | 2024.09 | [MAPF-GPT: Imitation Learning for Multi-Agent Pathfinding at Scale](https://arxiv.org/pdf/2409.00134) | [](https://github.com/Cognitive-AI-Systems/MAPF-GPT) | `MAPF` | *AAAI 2025* |
163 | | 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* |
164 | | 2024.10 | [Learning General Representations Across Graph Combinatorial Optimization Problems](https://openreview.net/forum?id=elmTU101oS) | | `7GDPs` | *Under Review* |
165 | | 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* |
166 | | 2024.10 | [SHIELD: Multi-task Multi-distribution Vehicle Routing Solver with Sparsity & Hierarchy in Efficiently Layered Decoder](https://openreview.net/forum?id=AMbIvaD4Rr) | | `16VRPs` | *ICML 2025* |
167 | | 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* |
168 | | 2024.10 | [Foundation Models for Boolean Logic](https://openreview.net/forum?id=qeY25DwmKO) | | `Boolean Logic` | *Under Review* |
169 | | 2024.11 | [CaDA: Cross-Problem Routing Solver with Constraint-Aware Dual-Attention](https://arxiv.org/pdf/2412.00346) | | `16VRPs` | *ICML 2025* |
170 | | 2024.12 | [Multi-task Representation Learning for Mixed Integer Linear Programming](https://arxiv.org/pdf/2412.14409) | [](https://github.com/caidog1129/MILP_multitask) | `MILP` | *arXiv* |
171 | | 2025.05 | [A Mixed-Curvature based Pre-training Paradigm for Multi-Task Vehicle Routing Solver](https://openreview.net/pdf?id=JsPyLqCgks) | [](https://github.com/lsyysl9711/Mixed_Curvature_VRPs) | `VRP` | *ICML 2025* |
172 | | 2025.07 | [LRM-1B: Towards Large Routing Model](https://www.arxiv.org/pdf/2507.03300) || `VRP` | *arxiv* |
173 | | 2025.08 | [FORGE: Foundational Optimization Representations from Graph Embeddings](https://arxiv.org/pdf/2508.20330) || `MIP` | *arxiv* |
174 | | 2025.09 | [Graph Foundation Models: Bridging Language Model Paradigms and Graph Optimization](https://arxiv.org/abs/2509.24256) || `OR` | *arxiv* |
175 | | 2025.11 | [Foundation Models for Industrial Scheduling Leveraging the Techniques from LLMs](https://openreview.net/pdf?id=qRjLjYrvMi) || `FJSP` | *Under Review* |
--------------------------------------------------------------------------------