Foundation Models for Combinatorial Optimization
FM4CO contains interesting research papers (1) using Existing Large Language Models for Combinatorial Optimization , and (2) building Domain Foundation Models for Combinatorial Optimization .
LLMs 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
Automation
2023.10
OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models
MILP
ICML 2024
Automation
2023.10
AI-Copilot for Business Optimisation: A Framework and A Case Study in Production Scheduling
JSSP
arXiv
Automation
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
2024.02
Large Language Models as Hyper-Heuristics for Combinatorial Optimization
TSP,VRP,OP, MKP,BPP,EDA
arXiv
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
Automation
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
From Words to Routes: Applying Large Language Models to Vehicle Routing
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
arXiv
Automation
2024.05
Self-Guiding Exploration for Combinatorial Problems
TSP,VRP,BPP, AP,KP,JSSP
arXiv
Solution
2024.06
Eyeballing Combinatorial Problems: A Case Study of Using Multimodal Large Language Models to Solve Traveling Salesman Problems
TSP
arXiv
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
Domain FMs for Combinatorial Optimization
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
2023.05
Efficient Training of Multi-task Combinatorial Neural Solver with Multi-armed Bandits
TSP,VRP,OP,KP
arXiv
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
arXiv
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
24VRPs
arXiv
2024.06
GOAL: A Generalist Combinatorial Optimization Agent Learner
(A)TSP,4VRPs, OP,JSSP,UMSP, KP,MVC,MIS
arXiv