FM4CO contains interesting research papers (1) using Existing Large Language Models for Combinatorial Optimization, and (2) building Domain Foundation Models for Combinatorial Optimization.

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.

Date	Paper	Link	Problem	Venue	Remark*
2023.07	Large Language Models for Supply Chain Optimization		Supply_Chain	arXiv	Algorithm w. Interpretability
2023.09	Can Language Models Solve Graph Problems in Natural Language?		Graph	NeurIPS 2023	Solution
2023.09	Large Language Models as Optimizers		TSP	ICLR 2024	Solution
2023.10	Chain-of-Experts: When LLMs Meet Complex Operations Research Problems		MILP	ICLR 2024	Formulation
2023.10	OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models		MILP	ICML 2024	Formulation
2023.10	AI-Copilot for Business Optimisation: A Framework and A Case Study in Production Scheduling		JSSP	arXiv	Formulation
2023.11	Large Language Models as Evolutionary Optimizers		TSP	CEC 2024	Solution
2023.11	Algorithm Evolution Using Large Language Model		TSP	arXiv	Algorithm
2023.12	Mathematical discoveries from program search with large language models		BPP	Nature	Algorithm
2023.12	NPHardEval: Dynamic Benchmark on Reasoning Ability of Large Language Models via Complexity Classes		TSP,KP, GCP,MSP	ACL 2024	Benchmark
2024.02	ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution		TSP,VRP,OP, MKP,BPP,EDA	NeurIPS 2024	Algorithm
2024.02	AutoSAT: Automatically Optimize SAT Solvers via Large Language Models		SAT	arXiv	Algorithm
2024.02	From Large Language Models and Optimization to Decision Optimization CoPilot: A Research Manifesto		MILP	arXiv	Formulation
2024.03	How Multimodal Integration Boost the Performance of LLM for Optimization: Case Study on Capacitated Vehicle Routing Problems		VRP	arXiv	Solution
2024.03	RouteExplainer: An Explanation Framework for Vehicle Routing Problem		VRP	PAKDD 2024	Interpretability
2024.03	Can Large Language Models Solve Robot Routing?		TSP,VRP	arXiv	Algorithm
2024.05	Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model		TSP,BPP,FSSP	ICML 2024	Algorithm
2024.05	ORLM: Training Large Language Models for Optimization Modeling		General OPT	Operations Research	Formulation
2024.05	Self-Guiding Exploration for Combinatorial Problems		TSP,VRP,BPP, AP,KP,JSSP	NeurIPS 2024	Solution
2024.06	Eyeballing Combinatorial Problems: A Case Study of Using Multimodal Large Language Models to Solve Traveling Salesman Problems		TSP	ISBCom 2024	Solution
2024.07	Visual Reasoning and Multi-Agent Approach in Multimodal Large Language Models (MLLMs): Solving TSP and mTSP Combinatorial Challenges		TSP,mTSP	arXiv	Solution
2024.07	Solving General Natural-Language-Description Optimization Problems with Large Language Models		MILP	NAACL 2024	Formulation
2024.08	Diagnosing Infeasible Optimization Problems Using Large Language Models		MILP	INFOR	Formulation
2024.08	LLMs can Schedule		JSSP	arXiv	Solution
2024.09	Multi-objective Evolution of Heuristic Using Large Language Model		TSP,BPP	AAAI 2025	Algorithm
2024.10	Towards Foundation Models for Mixed Integer Linear Programming		MILP	ICLR 2025	Formulation
2024.10	LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch		General OPT	ICLR 2025	Formulation
2024.10	OptiBench: Benchmarking Large Language Models in Optimization Modeling with Equivalence-Detection Evaluation		MILP	Under Review	Benchmark
2024.10	OptiBench Meets ReSocratic: Measure and Improve LLMs for Optimization Modeling		MILP	ICLR 2025	Benchmark
2024.10	DRoC: Elevating Large Language Models for Complex Vehicle Routing via Decomposed Retrieval of Constraints		48VRPs	ICLR 2025	Formulation
2024.10	STARJOB: Dataset for LLM-Driven Job Shop Scheduling		JSSP	Under Review	Solution
2024.10	LLM4Solver: Large Language Model for Efficient Algorithm Design of Combinatorial Optimization Solver		MILP	Under Review	Algorithm
2024.10	Unifying All Species: LLM-based Hyper-Heuristics for Multi-objective Optimization		TSP	Under Review	Algorithm
2024.10	Evo-Step: Evolutionary Generation and Stepwise Validation for Optimizing LLMs in OR		MILP	Under Review	Formulation
2024.10	Automatic programming via large language models with population self-evolution for dynamic job shop scheduling problem		DyJSSP	arXiv	Algorithm
2024.11	Large Language Models for Combinatorial Optimization of Design Structure Matrix		DSM	arXiv	Solution
2024.12	HSEvo: Elevating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMs		TSP,BPP,OP	AAAI 2025	Algorithm
2024.12	Evaluating LLM Reasoning in the Operations Research Domain with ORQA		General OR	AAAI 2025	Benchmark
2024.12	QUBE: Enhancing Automatic Heuristic Design via Quality-Uncertainty Balanced Evolution		OBP,TSP,CSP	arxiv	Algorithm
2025.01	Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design		TSP,CVRP,KP, BPP,MKP,ASP	ICML 2025	Algorithm
2025.01	Bridging Visualization and Optimization: Multimodal Large Language Models on Graph-Structured Combinatorial Optimization		Influence Maximization, Network Dismantling	arXiv	Algorithm
2025.01	Can Large Language Models Be Trusted as Black-Box Evolutionary Optimizers for Combinatorial Problems?		Influence Maximization	arXiv	Algorithm
2025.02	Improving Existing Optimization Algorithms with LLMs		MIS	arXiv	Algorithm
2025.02	Planning of Heuristics: Strategic Planning on Large Language Models with Monte Carlo Tree Search for Automating Heuristic Optimization		TSP,FSSP	arXiv	Algorithm
2025.02	GraphThought: Graph Combinatorial Optimization with Thought Generation		MIS,MVC,TSP	arXiv	Algorithm
2025.02	EquivaMap: Leveraging LLMs for Automatic Equivalence Checking of Optimization Formulations		MILP	arXiv	Algorithm
2025.02	ARS: Automatic Routing Solver with Large Language Models		VRP	arXiv	Benchmark & Algorithm
2025.02	Text2Zinc: A Cross-Domain Dataset for Modeling Optimization and Satisfaction Problems in MiniZinc		LP,MIP,CP	arXiv	Formulation (Dataset)
2025.02	GraphArena: Evaluating and Exploring Large Language Models on Graph Computation		MVC,MIS,MCP, TSP,MCS,GED	ICLR 2025	Benchmark & Dataset & Model
2025.03	Leveraging Large Language Models to Develop Heuristics for Emerging Optimization Problems		UPMP	arXiv	Algorithm
2025.03	OR-LLM-Agent: Automating Modeling and Solving of Operations Research Optimization Problem with Reasoning Large Language Model		OP	arXiv	Formulation
2025.03	Combinatorial Optimization for All: Using LLMs to Aid Non-Experts in Improving Optimization Algorithms		TSP	arXiv	Algorithm
2025.03	Automatic MILP Model Construction for Multi-Robot Task Allocation and Scheduling Based on Large Language Models		MILP	arXiv	Formulation
2025.03	Code Evolution Graphs: Understanding Large Language Model Driven Design of Algorithms		BBO,TSP,BPP	GECCO 2025	Interpretability
2025.04	CO-Bench: Benchmarking Language Model Agents in Algorithm Search for Combinatorial Optimization		General COP	AAAI 2026	Benchmark
2025.04	Algorithm Discovery With LLMs: Evolutionary Search Meets Reinforcement Learning		BPP,TSP,FP	COLM 2025	Algorithm
2025.04	OptimAI: Optimization from Natural Language Using LLM-Powered AI Agents		MILP	arXiv	Formulation
2025.04	Fitness Landscape of Large Language Model-Assisted Automated Algorithm Search		OBP,TSP, CVRP,VRPTW	arXiv	Benchmark & Interpretability
2025.04	Large Language Models powered Neural Solvers for Generalized Vehicle Routing Problems		VRP	ICLR 2025 Workshop AgenticAI	Algorithm
2025.05	Efficient Heuristics Generation for Solving Combinatorial Optimization Problems Using Large Language Models		TSP,CVRP,BPP, MKP,OP	KDD 2025	Algorithm
2025.05	CALM: Co-evolution of Algorithms and Language Model for Automatic Heuristic Design		TSP,KP,OBP,OP	arXiv	Algorithm
2025.05	Know the Ropes: A Heuristic Strategy for LLM-based Multi-Agent System Design		KP	arXiv	Solution
2025.05	A Comprehensive Evaluation of Contemporary ML-Based Solvers for Combinatorial Optimization		MIS,MDS, TSP,CVRP,CFLP, CPMP,FJSP,STP	ICML 2025 Workshop AI4Math	Benchmark
2025.05	LLM-Meta-SR: In-Context Learning for Evolving Selection Operators in Symbolic Regression		SR	arXiv	Algorithm
2025.05	RedAHD: Reduction-Based End-to-End Automatic Heuristic Design with Large Language Models		TSP,CVRP, KP,BPP,MKP	arXiv	Algorithm
2025.05	Generalizable Heuristic Generation Through Large Language Models with Meta-Optimization		TSP,CVRP,BPP	arXiv	Algorithm
2025.05	Large Language Model-driven Large Neighborhood Search for Large-Scale MILP Problems		MILP	ICML 2025	Algorithm
2025.05	Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling		General OPT	NeurIPS 2025	Formulation
2025.06	LLM-Driven Instance-Specific Heuristic Generation and Selection		OBPP,CVRP	arXiv	Algorithm
2025.06	ORMind: A Cognitive-Inspired End-to-End Reasoning Framework for Operations Research		OR	ACL 2025	Formulation
2025.06	EALG: Evolutionary Adversarial Generation of Language Model–Guided Generators for Combinatorial Optimization		TSP,OP	arXiv	Algorithm
2025.06	CP-Bench: Evaluating Large Language Models for Constraint Modelling		CP	arXiv	Benchmark
2025.06	REMoH: A Reflective Evolution of Multi-objective Heuristics approach via Large Language Models		FJSSP	arXiv	Algorithm
2025.06	HeuriGym: An Agentic Benchmark for LLM-Crafted Heuristics in Combinatorial Optimization		TSP,SAT	arXiv	Benchmark
2025.06	ALE-Bench: A Benchmark for Long-Horizon Objective-Driven Algorithm Engineering		General OPT	NeurIPS 2025 Datasets and Benchmarks Track	Benchmark
2025.06	OPT-BENCH: Evaluating LLM Agent on Large-Scale Search Spaces Optimization Problems		GCP,KP,MCP, MIS,SCP,TSP	arXiv	Benchmark
2025.06	STRCMP: Integrating Graph Structural Priors with Language Models for Combinatorial Optimization		SAT	NeurIPS 2025	Solution
2025.06	AlphaEvolve: A coding agent for scientific and algorithmic discovery		OPT	arXiv	Algorithm
2025.06	HeurAgenix: Leveraging LLMs for Solving Complex Combinatorial Optimization Challenges		TSP,CVRP,JSSP, MaxCut,MKP	arXiv	Algorithm
2025.07	Large Language Models for Combinatorial Optimization: A Systematic Review		CO	arXiv	Review
2025.07	Fine-tuning Large Language Model for Automated Algorithm Design		ASP,TSP,CVRP	arXiv	Algorithm
2025.07	DHEvo: Data-Algorithm Based Heuristic Evolution for Generalizable MILP Solving		MILP	arXiv	Algorithm
2025.07	MeLA: A Metacognitive LLM-Driven Architecture for Automatic Heuristic Design		TSP,BPP,ACS	arXiv	Algorithm
2025.07	Pareto-Grid-Guided Large Language Models for Fast and High-Quality Heuristics Design in Multi-Objective Combinatorial Optimization		TSP,CVRP,KP	AAAI 2026	Algorithm
2025.07	Automatically discovering heuristics in a complex SAT solver with large language models		SAT	arXiv	Algorithm
2025.07	Nested-Refinement Metamorphosis: Reflective Evolution for Efficient Optimization of Networking Problems		TSP,MKP,CVRP	ACL 2025	Algorithm
2025.08	ReflecSched: Solving Dynamic Flexible Job-Shop Scheduling via LLM-Powered Hierarchical Reflection		DFJSP	arxiv	Solution
2025.08	OptiHive: Ensemble Selection for LLM-Based Optimization via Statistical Modeling		MDVRP,WSCP	arxiv	Formulation
2025.08	EoH-S: Evolution of Heuristic Set using LLMs for Automated Heuristic Design		OBP,TSP,CVRP	AAAI 2026	Algorithm
2025.08	X-evolve: Solution space evolution powered by large language models		CSP,BPP, Shannon capacity	arxiv	Algorithm
2025.08	EvoCut: Strengthening Integer Programs via Evolution-Guided Language Models		MILP	arxiv	Formulation
2025.08	HIFO-PROMPT: Prompting with Hindsight and Foresight For LLM-Based Automatic Heuristic Design		TSP,OBP,FSSP	arxiv	Algorithm
2025.09	LLM-QUBO: An End-to-End Framework for Automated QUBO Transformation from Natural Language Problem Descriptions		MILP	arxiv	Formulation
2025.09	AutoPBO: LLM-powered Optimization for Local Search PBO Solvers		PBO	arxiv	Solution
2025.09	Autonomous Code Evolution MeetsNP-Completeness		SAT	arxiv	Solution
2025.09	LLM-based Instance-driven Heuristic Bias in the Context of a Biased Random Key Genetic Algorithm		LRS	arxiv	Algorithm
2025.09	Learn to Relax with Large Language Models: Solving Nonlinear Combinatorial Optimization Problems via Bidirectional Coevolution		MDD,SFL,TSPTW	arxiv	Algorithm
2025.09	DaSAThco: Data-Aware SAT Heuristics Combinations Optimization via Large Language Models		SAT	arxiv	Algorithm
2025.09	Large Language Models as End-to-end Combinatorial Optimization Solvers		TSP,OP,CVRP, MIS,MVC,PFSP,JSSP	NeurIPS 2025	Solution
2025.09	Large Language Models and Operations Research: A Structured Survey		OR	arxiv	Review
2025.09	ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolution		OPT	arXiv	Algorithm
2025.09	StepORLM: A Self-Evolving Framework With Generative Process Supervision For Operations Research Language Models		OR	arxiv	Formulation
2025.09	OptiMind: Teaching LLMs to Think Like Optimization Experts		MILP	arxiv	Formulation
2025.09	AutoEP: LLMs-Driven Automation of Hyperparameter Evolution for Metaheuristic Algorithms		TSP,CVRP,FSSP	arxiv	Algorithm
2025.09	ViTSP: A Vision Language Models Guided Framework for Large-Scale Traveling Salesman Problems		TSP	arxiv	Algorithm
2025.09	Experience-guided reflective co-evolution of prompts and heuristics for automatic algorithm design		TSP,BPP	arxiv	Algorithm
2025.10	EvoSpeak: Large Language Models for Interpretable Genetic Programming-Evolved Heuristics		DFJSS	arxiv	Algorithm
2025.10	VRPAgent: LLM-Driven Discovery of Heuristic Operators for Vehicle Routing Problems		VRP	arxiv	Algorithm
2025.10	Refining Hybrid Genetic Search for CVRP via Reinforcement Learning-Finetuned LLM		CVRP	arxiv	Algorithm
2025.10	An Agentic Framework with LLMs for Solving Complex Vehicle Routing Problems		VRP	arxiv	Formulation
2025.10	OptiTree: Hierarchical Thoughts Generation with Tree Search for LLM Optimization Modeling		OR	NeurIPS 2025	Formulation
2025.11	Bridging Synthetic and Real Routing Problems via LLM-Guided Instance Generation and Progressive Adaptation		TSP,CVRP	AAAI 2026	Algorithm
2025.11	LLM4EO: Large Language Model for Evolutionary Optimization in Flexible Job Shop Scheduling		FJSP	arxiv	Algorithm
2025.11	ACCORD: Autoregressive Constraint-satisfying Generation for COmbinatorial Optimization with Routing and Dynamic attention		FSSP,JSSP,BPP, KP,TSP,VRP	Under Review	Solution & Benchmark
2025.11	AutoFloorplan: Evolving Heuristics for Chip Floorplanning with Large Language Models and Textual Gradient-Guided Repair		Floorplanning	Under Review	Algorithm
2025.11	TPD-AHD: Textual Preference Differentiation for LLM-Based Automatic Heuristic Design		TSP,CVRP,JSSP, MKP, VRP,MASP,CFLP	Under Review	Algorithm
2025.11	ALIGNING LLMS WITH GRAPH NEURAL SOLVERS FOR COMBINATORIAL OPTIMIZATION		TSP,CVRP,KP, MVCP,MISP	Under Review	Algorithm
2025.11	Large Language Model Guided Dynamic Branching Rule Scheduling in Branch-and-Bound		MILP	Under Review	Algorithm
2025.11	Online Algorithm Configuration for MILP Re-Optimization with LLM Guidance		MILP	Under Review	Algorithm
2025.11	Experience-Guided Reflective Co-Evolution of Prompts and Heuristics for Automatic Algorithm Design		TSP, BPP	Under Review	Algorithm
2025.11	Adversarial examples for heuristics in combinatorial optimization: An LLM based approach		KP,BPP	Under Review	Algorithm
2025.11	Rethinking Code Similarity for Automated Algorithm Design with LLMs		ASP,TSP,CPP	Under Review	Algorithm
2025.11	AutoMOAE: Multi-Objective Auto-Algorithm Evolution		GCP,TSP	Under Review	Algorithm
2025.11	Fusing LLMs with Scientific Literature for Heuristic Discovery		TSP	Under Review	Algorithm
2025.11	Cognitively Inspired Reflective Evolution: Interactive Multi-Turn LLM–EA Synthesis of Heuristics for Combinatorial Optimization		TSP,BPP	Under Review	Algorithm
2025.11	Hierarchical Representations for Cross-task Automated Heuristic Design using LLMs		TSP,CVRP,FSSP, BPP,ASP	Under Review	Algorithm
2025.12	RoCo: Role-Based LLMs Collaboration for Automatic Heuristic Design		TSP,OP,CVRP, MKP,offline BPP	arxiv	Algorithm
2025.12	CogMCTS: A Novel Cognitive-Guided Monte Carlo Tree Search Framework for Iterative Heuristic Evolution with Large Language Models		TSP,OP,CVRP, MKP,KP	arxiv	Algorithm
2025.12	Behavior and Representation in Large Language Models for Combinatorial Optimization: From Feature Extraction to Algorithm Selection		BP,GCP,JSP,KP	arxiv	Analysis
2025.12	LAPPI: Interactive Optimization with LLM-Assisted Preference-Based Problem Instantiation		TSP,OP	arxiv	Formulation

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.

Date	Paper	Link	Problem	Venue
2022.08	One Model, Any CSP: Graph Neural Networks as Fast Global Search Heuristics for Constraint Satisfaction		CSP	IJCAI 2023
2023.05	Efficient Training of Multi-task Combinatorial Neural Solver with Multi-armed Bandits		TSP,VRP,OP,KP	TMLR
2024.02	Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalization		16VRPs	KDD 2024
2024.03	Towards a Generic Representation of Combinatorial Problems for Learning-Based Approaches		SAT,TSP,COL,KP	CPAIOR 2024
2024.04	Cross-Problem Learning for Solving Vehicle Routing Problems		TSP,OP,PCTSP	IJCAI 2024
2024.05	MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts		16VRPs	ICML 2024
2024.06	RouteFinder: Towards Foundation Models for Vehicle Routing Problems		48VRPs	TMLR
2024.06	GOAL: A Generalist Combinatorial Optimization Agent Learner		(A)TSP,5VRPs,OP,JSSP, OSSP,UMSP,KP,MVC, MIS,MCLP,TRP,SOP	ICLR 2025
2024.08	UNCO: Towards Unifying Neural Combinatorial Optimization through Large Language Model		TSP,CVRP,KP, MVCP,SMTWTP	arXiv
2024.09	MAPF-GPT: Imitation Learning for Multi-Agent Pathfinding at Scale		MAPF	AAAI 2025
2024.10	Toward Learning Generalized Cross-Problem Solving Strategies for Combinatorial Optimization		TSP,VRP,SDVRP, OP,PCTSP,SPCTSP	Under Review
2024.10	Learning General Representations Across Graph Combinatorial Optimization Problems		7GDPs	Under Review
2024.10	Solving Diverse Combinatorial Optimization Problems with a Unified Model		(A)TSP,CVRP,OP,PCTSP, SPCTSP,KP,MIS,FFSP	Under Review
2024.10	SHIELD: Multi-task Multi-distribution Vehicle Routing Solver with Sparsity & Hierarchy in Efficiently Layered Decoder		16VRPs	ICML 2025
2024.10	Unified Neural Solvers for General TSP and Multiple Combinatorial Optimization Tasks via Problem Reduction and Matrix Encoding		(A)TSP,DHCP,3SAT	ICLR 2025
2024.10	Foundation Models for Boolean Logic		Boolean Logic	Under Review
2024.11	CaDA: Cross-Problem Routing Solver with Constraint-Aware Dual-Attention		16VRPs	ICML 2025
2024.12	Multi-task Representation Learning for Mixed Integer Linear Programming		MILP	arXiv
2025.05	A Mixed-Curvature based Pre-training Paradigm for Multi-Task Vehicle Routing Solver		VRP	ICML 2025
2025.07	LRM-1B: Towards Large Routing Model		VRP	arxiv
2025.08	FORGE: Foundational Optimization Representations from Graph Embeddings		MIP	arxiv
2025.09	Graph Foundation Models: Bridging Language Model Paradigms and Graph Optimization		OR	arxiv
2025.11	Foundation Models for Industrial Scheduling Leveraging the Techniques from LLMs		FJSP	Under Review