Efficient Active Search for Combinatorial Optimization Problems
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Abstract (arXiv)
Recently numerous machine learning based methods for combinatorial optimization problems have been proposed that learn to construct solutions in a sequential decision process via reinforcement learning. While these methods can be easily combined with search strategies like sampling and beam search, it is not straightforward to integrate them into a high-level search procedure offering strong search guidance. Bello et al. (2016) propose active search, which adjusts the weights of a (trained) model with respect to a single instance at test time using reinforcement learning. While active search is simple to implement, it is not competitive with state-of-the-art methods because adjusting all model weights for each test instance is very time and memory intensive. Instead of updating all model weights, we propose and evaluate three efficient active search strategies that only update a subset of parameters during the search. The proposed methods offer a simple way to significantly improve the search performance of a given model and outperform state-of-the-art machine learning based methods on combinatorial problems, even surpassing the well-known heuristic solver LKH3 on the capacitated vehicle routing problem. Finally, we show that (efficient) active search enables learned models to effectively solve instances that are much larger than those seen during training.
Key facts. Cited by 99 papers in the map (data through 7 Oct 2026). Builds on 21 of its 34 references that are in the map. First posted on arXiv 9 Jun 2021.
Builds on
21 of 34 references.
References · 21
- 2017Attention Is All You Needcited by 59,932
- 2014Adam: A Method for Stochastic Optimizationcited by 36,960
- 2015Pointer Networkscited by 882
- 2018Attention, Learn to Solve Routing Problems!cited by 646
- 2016Neural Combinatorial Optimization with Reinforcement Learningcited by 600
- 2017Learning Combinatorial Optimization Algorithms over Graphscited by 557
- 2020POMO: Policy Optimization with Multiple Optima for Reinforcement Learningcited by 341
- 2018Reinforcement Learning for Solving the Vehicle Routing Problemcited by 327
- 2019An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problemcited by 265
- 2018Learning to Perform Local Rewriting for Combinatorial Optimizationcited by 183
- 2018Combinatorial Optimization with Graph Convolutional Networks and Guided Tree Searchcited by 182
- 2019Learning Improvement Heuristics for Solving Routing Problemscited by 162
9 more
- 2020Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instancescited by 161
- 2020Learning to Dispatch for Job Shop Scheduling via Deep Reinforcement Learningcited by 139
- 2019Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problemcited by 117
- 2020Learning 2-opt Heuristics for the Traveling Salesman Problem via Deep Reinforcement Learningcited by 100
- 2021Deep Policy Dynamic Programming for Vehicle Routing Problemscited by 94
- 2020Learning Combinatorial Optimization on Graphs: A Survey with Applications to Networkingcited by 70
- 2020A Deep Reinforcement Learning Algorithm Using Dynamic Attention Model for Vehicle Routing Problemscited by 30
- 2020Learning to Solve Vehicle Routing Problems with Time Windows through Joint Attentioncited by 29
- 2017Deep Learning Assisted Heuristic Tree Search for the Container Pre-marshalling Problemcited by 18
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Citing papers per year: 2021: 3; 2022: 10; 2023: 16; 2024: 27; 2025: 22; 2026: 21.
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- 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 216
- 2023Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalizationcited by 140
- 2022DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problemscited by 127
- 2022Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimizationcited by 118
- 2021Matrix Encoding Networks for Neural Combinatorial Optimizationcited by 89
- 2022Simulation-guided Beam Search for Neural Combinatorial Optimizationcited by 84
- 2023Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Optcited by 81
- 2023DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimizationcited by 77
- 2023RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmarkcited by 70
- 2023Towards Omni-generalizable Neural Methods for Vehicle Routing Problemscited by 68
- 2022Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillationcited by 61
- 2022Winner Takes It All: Training Performant RL Populations for Combinatorial Optimizationcited by 57
38 more
- 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problemscited by 54
- 2024Ant Colony Sampling with GFlowNets for Combinatorial Optimizationcited by 53
- 2024INViT: A Generalizable Routing Problem Solver with Invariant Nested View Transformercited by 43
- 2025Fast T2T: Optimization Consistency Speeds Up Diffusion-Based Training-to-Testing Solving for Combinatorial Optimizationcited by 43
- 2023Combinatorial Optimization with Policy Adaptation using Latent Space Searchcited by 41
- 2024GOAL: A Generalist Combinatorial Optimization Agent Learnercited by 39
- 2024PolyNet: Learning Diverse Solution Strategies for Neural Combinatorial Optimizationcited by 35
- 2024Self-Improvement for Neural Combinatorial Optimization: Sample without Replacement, but Improvementcited by 32
- 2024Self-Improved Learning for Scalable Neural Combinatorial Optimizationcited by 29
- 2024Learning to Handle Complex Constraints for Vehicle Routing Problemscited by 29
- 2024Cross-Problem Learning for Solving Vehicle Routing Problemscited by 24
- 2023Meta-SAGE: Scale Meta-Learning Scheduled Adaptation with Guided Exploration for Mitigating Scale Shift on Combinatorial Optimizationcited by 23
- 2024Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectivescited by 23
- 2022Deep Reinforcement Learning Guided Improvement Heuristic for Job Shop Schedulingcited by 20
- 2022Learning to Control Local Search for Combinatorial Optimizationcited by 18
- 2021Guidelines for the Computational Testing of Machine Learning approaches to Vehicle Routing Problemscited by 16
- 2022Learning to Solve Vehicle Routing Problems: A Surveycited by 16
- 2023Equity-Transformer: Solving NP-hard Min-Max Routing Problems as Sequential Generation with Equity Contextcited by 16
- 2025Neural Deconstruction Search for Vehicle Routing Problemscited by 15
- 2025Learning to Reduce Search Space for Generalizable Neural Routing Solvercited by 14
- 2023Continuation Path Learning for Homotopy Optimizationcited by 12
- 2025Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learningcited by 12
- 2024DISCO: Efficient Diffusion Solver for Large-Scale Combinatorial Optimization Problemscited by 10
- 2025RRNCO: Towards Real-World Routing with Neural Combinatorial Optimizationcited by 10
- 2025Learning to Insert for Constructive Neural Vehicle Routing Solvercited by 10
- 2024Instance-Conditioned Adaptation for Large-scale Generalization of Neural Routing Solvercited by 9
- 2024Hierarchical Neural Constructive Solver for Real-world TSP Scenarioscited by 9
- 2024Collaboration! Towards Robust Neural Methods for Routing Problemscited by 9
- 2024Bridging Large Language Models and Optimization: A Unified Framework for Text-attributed Combinatorial Optimizationcited by 8
- 2024PARCO: Parallel AutoRegressive Models for Multi-Agent Combinatorial Optimizationcited by 7
- 2025Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degreescited by 7
- 2022Neural Combinatorial Optimization: a New Player in the Fieldcited by 6
- 2023Symmetric Replay Training: Enhancing Sample Efficiency in Deep Reinforcement Learning for Combinatorial Optimizationcited by 6
- 2023Too Big, so Fail? -- Enabling Neural Construction Methods to Solve Large-Scale Routing Problemscited by 6
- 2025Preference-Driven Multi-Objective Combinatorial Optimization with Conditional Computationcited by 6
- 2023Routing Arena: A Benchmark Suite for Neural Routing Solverscited by 5
- 2024Moco: A Learnable Meta Optimizer for Combinatorial Optimizationcited by 5
- 2024Learning Topological Representations with Bidirectional Graph Attention Network for Solving Job Shop Scheduling Problemcited by 5
50 most cited of 99 All 99 (JSON)
- 2026Depot-Closed Multi-Component Construction for Neural Vehicle Routing28 Sep 2026
- 2026GeoPAR: Large-Scale Multi-Agent Combinatorial Optimization with Geometry-Guided Parallel Autoregressive Learning1 Sep 2026
- 2026Drive, Pack, Fly: The Travelling Thief Problem with Drone17 Aug 2026
- 2026Interpreting Neural Combinatorial Optimization via Evolving Programmatic Bottlenecks18 Jun 2026
- 2026MViewRouter: Internalizing Geometric Equivariance via Multi-view Alternating Attention for Combinatorial Routing31 May 2026
- 2026COAgents: Multi-Agent Framework to Learn and Navigate Routing Problems Search Space20 May 2026
- 2026Learning with Foresight: Enhancing Neural Routing Policy via Multi-Node Lookahead Prediction19 May 2026
- 2026GOAL: Graph-based Objective-Aligned Diffusion Solvers for Dynamic Multi-Objective Optimization18 May 2026
- 2026Learning to Solve Compositional Geometry Routing Problems18 May 2026
- 2026An Amortized Efficiency Threshold for Comparing Neural and Heuristic Solvers in Combinatorial Optimization14 May 2026
- 2026Learning to Solve the Quadratic Assignment Problem with Warm-Started MCMC Finetuning22 Apr 2026
- 2026A First Guess is Rarely the Final Answer: Learning to Search in the Traveling Salesperson Problem8 Apr 2026
38 more
- 2026Aligning LLMs with Graph Neural Solvers for Combinatorial Optimization28 Mar 2026
- 2026Chain-of-Context Learning: Dynamic Constraint Understanding for Multi-Task VRPs2 Mar 2026
- 2026Efficient Decoder Scaling Strategy for Neural Routing Solvers28 Feb 2026
- 2026Survey on Neural Routing Solvers25 Feb 2026
- 2026CADO: From Imitation to Cost Minimization for Heatmap-based Solvers in Combinatorial Optimization9 Feb 2026
- 2026Small Shifts, Large Gains: Unlocking Traditional TSP Heuristic Guided-Sampling via Unsupervised Neural Instance Modification31 Jan 2026
- 2026Test-Time Adaptation for Unsupervised Combinatorial Optimization28 Jan 2026
- 2026HeatACO: A Heatmap-Guided Max--Min Ant System for Large-Scale Travelling Salesman Problems26 Jan 2026
- 2026Generating Diverse TSP Tours via a Combination of Graph Pointer Network and Dispersion3 Jan 2026
- 2025Enhancing the Cross-Size Generalization for Solving Vehicle Routing Problems via Continual Learning11 Oct 2025
- 2025Recurrent State Encoders for Efficient Neural Combinatorial Optimization5 Sep 2025
- 2025On Distributional Dependent Performance of Classical and Neural Routing Solvers4 Aug 2025
- 2025Learning to Segment for Vehicle Routing Problems22 Jun 2025
- 2025EFormer: An Effective Edge-based Transformer for Vehicle Routing Problems19 Jun 2025
- 2025Synergizing Reinforcement Learning and Genetic Algorithms for Neural Combinatorial Optimization11 Jun 2025
- 2025Preference-Driven Multi-Objective Combinatorial Optimization with Conditional Computation10 Jun 2025
- 2025Latent Guided Sampling for Combinatorial Optimization4 Jun 2025
- 2025Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learning3 Jun 2025
- 2025RsGCN: Subgraph-Based Rescaling Enhances Generalization of GCNs for Solving Traveling Salesman Problems31 May 2025
- 2025Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degrees30 May 2025
- 2025Breaking the Performance Ceiling in Reinforcement Learning requires Inference Strategies27 May 2025
- 2025LMask: Learn to Solve Constrained Routing Problems with Lazy Masking23 May 2025
- 2025Learning to Insert for Constructive Neural Vehicle Routing Solver20 May 2025
- 2025USPR: Learning a Unified Solver for Profiled Routing8 May 2025
- 2025ABCDWaveNet: Advancing Robust Road Ponding Detection in Fog through Dynamic Frequency-Spatial Synergy7 Apr 2025
- 2025RRNCO: Towards Real-World Routing with Neural Combinatorial Optimization20 Mar 2025
- 2025Learning to Reduce Search Space for Generalizable Neural Routing Solver5 Mar 2025
- 2025Navigating Demand Uncertainty in Container Shipping: Deep Reinforcement Learning for Enabling Adaptive and Feasible Master Stowage Planning18 Feb 2025
- 2025Neural Genetic Search in Discrete Spaces9 Feb 2025
- 2025Fast T2T: Optimization Consistency Speeds Up Diffusion-Based Training-to-Testing Solving for Combinatorial Optimization5 Feb 2025
- 2025Neural Deconstruction Search for Vehicle Routing Problems7 Jan 2025
- 2024Enhancing Large-scale UAV Route Planing with Global and Local Features via Reinforcement Graph Fusion20 Dec 2024
- 2024Scaling Combinatorial Optimization Neural Improvement Heuristics with Online Search and Adaptation13 Dec 2024
- 2024Beyond the Heatmap: A Rigorous Evaluation of Component Impact in MCTS-Based TSP Solvers14 Nov 2024
- 2024Learning to Handle Complex Constraints for Vehicle Routing Problems28 Oct 2024
- 2024Collaboration! Towards Robust Neural Methods for Routing Problems7 Oct 2024
- 2024PARCO: Parallel AutoRegressive Models for Multi-Agent Combinatorial Optimization5 Sep 2024
- 2024Bridging Large Language Models and Optimization: A Unified Framework for Text-attributed Combinatorial Optimization22 Aug 2024
50 newest of 99 All 99 (JSON)
- 2023Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalizationcited by 140
- 2022DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problemscited by 127
- 2022Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimizationcited by 118
- 2021Matrix Encoding Networks for Neural Combinatorial Optimizationcited by 89
- 2022Simulation-guided Beam Search for Neural Combinatorial Optimizationcited by 84
- 2023Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Optcited by 81
- 2023DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimizationcited by 77
- 2023RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmarkcited by 70
- 2023Towards Omni-generalizable Neural Methods for Vehicle Routing Problemscited by 68
- 2022Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillationcited by 61
- 2022Winner Takes It All: Training Performant RL Populations for Combinatorial Optimizationcited by 57
- 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problemscited by 54
12 most cited of 97 All 97 (JSON)
- 2026Depot-Closed Multi-Component Construction for Neural Vehicle Routing28 Sep 2026
- 2026GeoPAR: Large-Scale Multi-Agent Combinatorial Optimization with Geometry-Guided Parallel Autoregressive Learning1 Sep 2026
- 2026Drive, Pack, Fly: The Travelling Thief Problem with Drone17 Aug 2026
- 2026Interpreting Neural Combinatorial Optimization via Evolving Programmatic Bottlenecks18 Jun 2026
- 2026MViewRouter: Internalizing Geometric Equivariance via Multi-view Alternating Attention for Combinatorial Routing31 May 2026
- 2026COAgents: Multi-Agent Framework to Learn and Navigate Routing Problems Search Space20 May 2026
- 2026Learning with Foresight: Enhancing Neural Routing Policy via Multi-Node Lookahead Prediction19 May 2026
- 2026GOAL: Graph-based Objective-Aligned Diffusion Solvers for Dynamic Multi-Objective Optimization18 May 2026
- 2026Learning to Solve Compositional Geometry Routing Problems18 May 2026
- 2026An Amortized Efficiency Threshold for Comparing Neural and Heuristic Solvers in Combinatorial Optimization14 May 2026
- 2026Learning to Solve the Quadratic Assignment Problem with Warm-Started MCMC Finetuning22 Apr 2026
- 2026A First Guess is Rarely the Final Answer: Learning to Search in the Traveling Salesperson Problem8 Apr 2026
12 newest of 97 All 97 (JSON)