mlsanityData to 7 Oct 2026

GOAL: A Generalist Combinatorial Optimization Agent Learner

arXiv 2406.15079 ↗First posted 21 Jun 2024cs.LGcited by 39

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Abstract (arXiv)

Machine Learning-based heuristics have recently shown impressive performance in solving a variety of hard combinatorial optimization problems (COPs). However, they generally rely on a separate neural model, specialized and trained for each single problem. Any variation of a problem requires adjustment of its model and re-training from scratch. In this paper, we propose GOAL (for Generalist combinatorial Optimization Agent Learner), a generalist model capable of efficiently solving multiple COPs and which can be fine-tuned to solve new COPs. GOAL consists of a single backbone plus light-weight problem-specific adapters for input and output processing. The backbone is based on a new form of mixed-attention blocks which allows to handle problems defined on graphs with arbitrary combinations of node, edge and instance-level features. Additionally, problems which involve heterogeneous types of nodes or edges are handled through a novel multi-type transformer architecture, where the attention blocks are duplicated to attend the meaningful combinations of types while relying on the same shared parameters. We train GOAL on a set of routing, scheduling and classic graph problems and show that it is only slightly inferior to the specialized baselines while being the first multi-task model that solves a wide range of COPs. Finally we showcase the strong transfer learning capacity of GOAL by fine-tuning it on several new problems. Our code is available at https://github.com/naver/goal-co/.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). Builds on 52 of its 68 references that are in the map. First posted on arXiv 21 Jun 2024.

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52 of 68 references.

References · 52

  1. 2017Attention Is All You Needcited by 59,932
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38 more
  1. 2020ReZero is All You Need: Fast Convergence at Large Depthcited by 260
  2. 2017Thinking Fast and Slow with Deep Learning and Tree Searchcited by 245
  3. 2019Simple, Scalable Adaptation for Neural Machine Translationcited by 239
  4. 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 216
  5. 2020Random Features Strengthen Graph Neural Networkscited by 184
  6. 2018Learning to Perform Local Rewriting for Combinatorial Optimizationcited by 183
  7. 2019Learning Improvement Heuristics for Solving Routing Problemscited by 162
  8. 2020Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instancescited by 161
  9. 2020Learning to Dispatch for Job Shop Scheduling via Deep Reinforcement Learningcited by 139
  10. 2022DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problemscited by 127
  11. 2020Hybrid Genetic Search for the CVRP: Open-Source Implementation and SWAP* Neighborhoodcited by 122
  12. 2022Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimizationcited by 118
  13. 2019Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problemcited by 117
  14. 2021Learning to Delegate for Large-scale Vehicle Routingcited by 108
  15. 2021Learning to Iteratively Solve Routing Problems with Dual-Aspect Collaborative Transformercited by 108
  16. 2020Multi-Decoder Attention Model with Embedding Glimpse for Solving Vehicle Routing Problemscited by 100
  17. 2021Efficient Active Search for Combinatorial Optimization Problemscited by 99
  18. 2020Learning the Travelling Salesperson Problem Requires Rethinking Generalizationcited by 96
  19. 2021Deep Policy Dynamic Programming for Vehicle Routing Problemscited by 94
  20. 2021Matrix Encoding Networks for Neural Combinatorial Optimizationcited by 89
  21. 2022Simulation-guided Beam Search for Neural Combinatorial Optimizationcited by 84
  22. 2015Parallelizing the dual revised simplex methodcited by 83
  23. 2023BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimizationcited by 80
  24. 2024MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Expertscited by 69
  25. 2023Towards Omni-generalizable Neural Methods for Vehicle Routing Problemscited by 68
  26. 2022Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillationcited by 61
  27. 2022A Generalist Neural Algorithmic Learnercited by 58
  28. 2023SMART: Self-supervised Multi-task pretrAining with contRol Transformerscited by 44
  29. 2023H-TSP: Hierarchically Solving the Large-Scale Travelling Salesman Problemcited by 43
  30. 2021Independent Prototype Propagation for Zero-Shot Compositionalitycited by 42
  31. 2023Combinatorial Optimization with Policy Adaptation using Latent Space Searchcited by 41
  32. 2024Self-Improvement for Neural Combinatorial Optimization: Sample without Replacement, but Improvementcited by 32
  33. 2020Learning to Solve Vehicle Routing Problems with Time Windows through Joint Attentioncited by 29
  34. 2024Self-Improved Learning for Scalable Neural Combinatorial Optimizationcited by 29
  35. 2022On the Generalization of Neural Combinatorial Optimization Heuristicscited by 24
  36. 2024Cross-Problem Learning for Solving Vehicle Routing Problemscited by 24
  37. 2023Meta-SAGE: Scale Meta-Learning Scheduled Adaptation with Guided Exploration for Mitigating Scale Shift on Combinatorial Optimizationcited by 23
  38. 2024Self-Labeling the Job Shop Scheduling Problemcited by 23

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Citing papers per year: 2024: 3; 2025: 16; 2026: 20.

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  1. 2025Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Designcited by 100
  2. 2025Rethinking Light Decoder-based Solvers for Vehicle Routing Problemscited by 36
  3. 2025Large Language Models as End-to-end Combinatorial Optimization Solverscited by 27
  4. 2025Heterogeneous Swarms: Jointly Optimizing Model Roles and Weights for Multi-LLM Systemscited by 22
  5. 2025Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learningcited by 12
  6. 2025RRNCO: Towards Real-World Routing with Neural Combinatorial Optimizationcited by 10
  7. 2025Learning to Insert for Constructive Neural Vehicle Routing Solvercited by 10
  8. 2024Collaboration! Towards Robust Neural Methods for Routing Problemscited by 9
  9. 2025GraphThought: Graph Combinatorial Optimization with Thought Generationcited by 9
  10. 2024A GREAT Architecture for Edge-Based Graph Problems Like TSPcited by 7
  11. 2025Generalizable Heuristic Generation Through LLMs with Meta-Optimizationcited by 7
  12. 2025URS: A Unified Neural Routing Solver for Cross-Problem Zero-Shot Generalizationcited by 7
27 more
  1. 2025Multi-Task Vehicle Routing Solver via Mixture of Specialized Experts under State-Decomposable MDPcited by 7
  2. 2026RADAR: Learning to Route with Asymmetry-aware DistAnce Representationscited by 7
  3. 2026LUMINA: Foundation Models for Topology Transferable ACOPFcited by 7
  4. 2024Multi-task Representation Learning for Mixed Integer Linear Programmingcited by 6
  5. 2025RoME: Domain-Robust Mixture-of-Experts for MILP Solution Prediction across Domainscited by 3
  6. 2025Beyond Simple Graphs: Neural Multi-Objective Routing on Multigraphscited by 2
  7. 2026Chain-of-Context Learning: Dynamic Constraint Understanding for Multi-Task VRPscited by 2
  8. 2025Recurrent State Encoders for Efficient Neural Combinatorial Optimizationcited by 1
  9. 2025Lifelong Learning with Behavior Consolidation for Vehicle Routingcited by 1
  10. 2026Efficient Decoder Scaling Strategy for Neural Routing Solverscited by 1
  11. 2026Aligning LLMs with Graph Neural Solvers for Combinatorial Optimizationcited by 1
  12. 2026BEAM: Bi-level Memory-adaptive Algorithmic Evolution for LLM-Powered Heuristic Designcited by 1
  13. 2026Towards Systematic Generalization for Power Grid Optimization Problemscited by 1
  14. 2026SPACE: Unifying Symmetric and Asymmetric Routing Problems for Generalist Neural Solvercited by 1
  15. 2026Vision-Assisted Foundation Model for Solving Multi-Task Vehicle Routing Problemscited by 1
  16. 2025ARC: Leveraging Compositional Representations for Cross-Problem Learning on VRPscited by 0
  17. 2026Enterprise Resource Planning Using Multi-type Transformers in Ferro-Titanium Industrycited by 0
  18. 2026Keep Rehearsing and Refining: Lifelong Learning Vehicle Routing under Continually Drifting Taskscited by 0
  19. 2026Beyond Solving: Prescriptive Probing for Neural Routing Solverscited by 0
  20. 2026UniHetCO: A Unified Heterogeneous Representation for Multi-Problem Learning in Unsupervised Neural Combinatorial Optimizationcited by 0
  21. 2026Two-Stage Learned Decomposition for Scalable Routing on Multigraphscited by 0
  22. 2026A Unified Knowledge Embedded Reinforcement Learning-based Framework for Generalized Capacitated Vehicle Routing Problemscited by 0
  23. 2026Learning to Solve Compositional Geometry Routing Problemscited by 0
  24. 2026TSP with Predictions: Heatmap to Tour with Provable Guaranteescited by 0
  25. 2026LaT: LLM-as-Trainer for Multi-Task Vehicle Routing Solverscited by 0
  26. 2026Compute Time Scaling with Recursive Models for Combinatorial Optimizationcited by 0
  27. 2026SimpleEvol: An Agent-Loop Framework for LLM-Driven Automated Heuristic Design with Minimal Human Priorscited by 0