mlsanityData to 14 Oct 2026

Moco: A Learnable Meta Optimizer for Combinatorial Optimization

arXiv 2402.04915 ↗First posted 7 Feb 2024cs.LGcited by 5

Not on the map. Why?

Abstract (arXiv)

Relevant combinatorial optimization problems (COPs) are often NP-hard. While they have been tackled mainly via handcrafted heuristics in the past, advances in neural networks have motivated the development of general methods to learn heuristics from data. Many approaches utilize a neural network to directly construct a solution, but are limited in further improving based on already constructed solutions at inference time. Our approach, Moco, defines a lightweight solution construction procedure, guided by a single continuous vector θ (called heatmap) and learns a neural network to update θ for a single instance of a COP at inference time. The update is based on various features of the current search state. The training procedure is budget aware, targeting the overall best solution found during the entire search. Moco is a fully learnable meta optimizer not utilizing problem specific heuristics or requiring optimal solutions for training. We test Moco on the Traveling Salesman Problem (TSP) and Maximum Independent Set (MIS) and show that it significantly improves over other heatmap based methods.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 40 of its 53 references that are in the map. First posted on arXiv 7 Feb 2024.

Builds on

40 of 53 references.

References · 40

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2017Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networkscited by 4,897
  3. 2018Relational inductive biases, deep learning, and graph networkscited by 1,360
  4. 2018Attention, Learn to Solve Routing Problems!cited by 656
  5. 2016Learning to learn by gradient descent by gradient descentcited by 620
  6. 2016Neural Combinatorial Optimization with Reinforcement Learningcited by 608
  7. 2017Evolution Strategies as a Scalable Alternative to Reinforcement Learningcited by 574
  8. 2020POMO: Policy Optimization with Multiple Optima for Reinforcement Learningcited by 348
  9. 2019An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problemcited by 269
  10. 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 221
  11. 2021Learning to Optimize: A Primer and A Benchmarkcited by 208
  12. 2018Combinatorial Optimization with Graph Convolutional Networks and Guided Tree Searchcited by 183
28 more
  1. 2020Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instancescited by 162
  2. 2023Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalizationcited by 142
  3. 2022DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problemscited by 129
  4. 2022Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimizationcited by 119
  5. 2019Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problemcited by 117
  6. 2021Learning to Delegate for Large-scale Vehicle Routingcited by 109
  7. 2021Efficient Active Search for Combinatorial Optimization Problemscited by 100
  8. 2018Understanding and correcting pathologies in the training of learned optimizerscited by 97
  9. 2021Deep Policy Dynamic Programming for Vehicle Routing Problemscited by 94
  10. 2022Simulation-guided Beam Search for Neural Combinatorial Optimizationcited by 84
  11. 2023BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimizationcited by 82
  12. 2023DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimizationcited by 78
  13. 2023Towards Omni-generalizable Neural Methods for Vehicle Routing Problemscited by 69
  14. 2020Tasks, stability, architecture, and compute: Training more effective learned optimizers, and using them to train themselvescited by 58
  15. 2022Winner Takes It All: Training Performant RL Populations for Combinatorial Optimizationcited by 58
  16. 2023Unsupervised Learning for Solving the Travelling Salesman Problemcited by 58
  17. 2022VeLO: Training Versatile Learned Optimizers by Scaling Upcited by 57
  18. 2020Learning What to Defer for Maximum Independent Setscited by 54
  19. 2021Unbiased Gradient Estimation in Unrolled Computation Graphs with Persistent Evolution Strategiescited by 52
  20. 2023Pointerformer: Deep Reinforced Multi-Pointer Transformer for the Traveling Salesman Problemcited by 50
  21. 2022What's Wrong with Deep Learning in Tree Search for Combinatorial Optimizationcited by 37
  22. 2015Finding Near-Optimal Independent Sets at Scalecited by 33
  23. 2023Meta-SAGE: Scale Meta-Learning Scheduled Adaptation with Guided Exploration for Mitigating Scale Shift on Combinatorial Optimizationcited by 23
  24. 2023Efficient Meta Neural Heuristic for Multi-Objective Combinatorial Optimizationcited by 21
  25. 2023Variational Annealing on Graphs for Combinatorial Optimizationcited by 21
  26. 2022Learning to Control Local Search for Combinatorial Optimizationcited by 18
  27. 2023Low-Variance Gradient Estimation in Unrolled Computation Graphs with ES-Singlecited by 7
  28. 2023Too Big, so Fail? -- Enabling Neural Construction Methods to Solve Large-Scale Routing Problemscited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 2; 2025: 0; 2026: 3.

5 papers.

  1. 2024Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectivescited by 23
  2. 2024Memory-Enhanced Neural Solvers for Routing Problemscited by 4
  3. 2026CADO: From Imitation to Cost Minimization for Heatmap-based Solvers in Combinatorial Optimizationcited by 2
  4. 2026A Unified Knowledge Embedded Reinforcement Learning-based Framework for Generalized Capacitated Vehicle Routing Problemscited by 0
  5. 2026Compute Time Scaling with Recursive Models for Combinatorial Optimizationcited by 0