RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmark
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Abstract (arXiv)
Combinatorial optimization (CO) is fundamental to several real-world applications, from logistics and scheduling to hardware design and resource allocation. Deep reinforcement learning (RL) has recently shown significant benefits in solving CO problems, reducing reliance on domain expertise and improving computational efficiency. However, the absence of a unified benchmarking framework leads to inconsistent evaluations, limits reproducibility, and increases engineering overhead, raising barriers to adoption for new researchers. To address these challenges, we introduce RL4CO, a unified and extensive benchmark with in-depth library coverage of 27 CO problem environments and 23 state-of-the-art baselines. Built on efficient software libraries and best practices in implementation, RL4CO features modularized implementation and flexible configurations of diverse environments, policy architectures, RL algorithms, and utilities with extensive documentation. RL4CO helps researchers build on existing successes while exploring and developing their own designs, facilitating the entire research process by decoupling science from heavy engineering. We finally provide extensive benchmark studies to inspire new insights and future work. RL4CO has already attracted numerous researchers in the community and is open-sourced at https://github.com/ai4co/rl4co.
Key facts. Cited by 71 papers in the map (data through 14 Oct 2026). Builds on 72 of its 166 references that are in the map. First posted on arXiv 29 Jun 2023.
Builds on
72 of 166 references.
References · 72
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- 2014Recurrent Models of Visual Attentioncited by 349
- 2020POMO: Policy Optimization with Multiple Optima for Reinforcement Learningcited by 348
- 2018Reinforcement Learning for Solving the Vehicle Routing Problemcited by 333
- 2019An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problemcited by 269
- 2020Reinforcement Learning for Combinatorial Optimization: A Surveycited by 236
- 2019Differentiation of Blackbox Combinatorial Solverscited by 226
- 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 221
- 2019Stochastic Beams and Where to Find Them: The Gumbel-Top-k Trick for Sampling Sequences Without Replacementcited by 211
- 2018Learning to Perform Local Rewriting for Combinatorial Optimizationcited by 185
- 2018Combinatorial Optimization with Graph Convolutional Networks and Guided Tree Searchcited by 183
- 2019Learning Improvement Heuristics for Solving Routing Problemscited by 164
- 2020Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instancescited by 162
- 2021Tianshou: a Highly Modularized Deep Reinforcement Learning Librarycited by 143
- 2020Learning to Dispatch for Job Shop Scheduling via Deep Reinforcement Learningcited by 140
- 2022DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problemscited by 129
- 2020Hybrid Genetic Search for the CVRP: Open-Source Implementation and SWAP* Neighborhoodcited by 125
- 2022Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimizationcited by 119
- 2019Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problemcited by 117
- 2021Learning to Delegate for Large-scale Vehicle Routingcited by 109
- 2021Learning to Iteratively Solve Routing Problems with Dual-Aspect Collaborative Transformercited by 108
- 2021NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problemcited by 103
- 2020Learning 2-opt Heuristics for the Traveling Salesman Problem via Deep Reinforcement Learningcited by 100
- 2020Multi-Decoder Attention Model with Embedding Glimpse for Solving Vehicle Routing Problemscited by 100
- 2021Efficient Active Search for Combinatorial Optimization Problemscited by 100
- 2021Deep Policy Dynamic Programming for Vehicle Routing Problemscited by 94
- 2021Matrix Encoding Networks for Neural Combinatorial Optimizationcited by 91
- 2021Learning Collaborative Policies to Solve NP-hard Routing Problemscited by 86
- 2022Simulation-guided Beam Search for Neural Combinatorial Optimizationcited by 84
- 2019Exploratory Combinatorial Optimization with Reinforcement Learningcited by 82
- 2019Combinatorial Optimization by Graph Pointer Networks and Hierarchical Reinforcement Learningcited by 78
- 2021Graph Neural Network Guided Local Search for the Traveling Salesperson Problemcited by 70
- 2022Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillationcited by 62
- 2023TorchRL: A data-driven decision-making library for PyTorchcited by 60
- 2023Jumanji: a Diverse Suite of Scalable Reinforcement Learning Environments in JAXcited by 58
50 most cited of 72 All 72 (JSON)
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Citing papers per year: 2023: 3; 2024: 12; 2025: 34; 2026: 22.
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- 2023GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-timecited by 85
- 2023DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimizationcited by 78
- 2024MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Expertscited by 70
- 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problemscited by 55
- 2025Rethinking Light Decoder-based Solvers for Vehicle Routing Problemscited by 37
- 2024PolyNet: Learning Diverse Solution Strategies for Neural Combinatorial Optimizationcited by 35
- 2024Learning to Handle Complex Constraints for Vehicle Routing Problemscited by 29
- 2025Large Language Models as End-to-end Combinatorial Optimization Solverscited by 28
- 2025Neural Deconstruction Search for Vehicle Routing Problemscited by 15
- 2024ACEGEN: Reinforcement learning of generative chemical agents for drug discoverycited by 14
- 2025RRNCO: Towards Real-World Routing with Neural Combinatorial Optimizationcited by 11
- 2025FrontierCO: Real-World and Large-Scale Evaluation of Machine Learning Solvers for Combinatorial Optimizationcited by 11
38 more
- 2024Collaboration! Towards Robust Neural Methods for Routing Problemscited by 9
- 2025Generalizable Heuristic Generation Through LLMs with Meta-Optimizationcited by 9
- 2024Ensembling Prioritized Hybrid Policies for Multi-agent Pathfindingcited by 7
- 2024Tackling Prevalent Conditions in Unsupervised Combinatorial Optimization: Cardinality, Minimum, Covering, and Morecited by 7
- 2024PARCO: Parallel AutoRegressive Models for Multi-Agent Combinatorial Optimizationcited by 7
- 2025VRPAgent: LLM-Driven Discovery of Heuristic Operators for Vehicle Routing Problemscited by 7
- 2025Preference-Driven Multi-Objective Combinatorial Optimization with Conditional Computationcited by 6
- 2025Fine-tuning Large Language Model for Automated Algorithm Designcited by 6
- 2024Neural Solver Selection for Combinatorial Optimizationcited by 5
- 2025Reinforcement learning with combinatorial actions for coupled restless banditscited by 5
- 2025Learning to Segment for Vehicle Routing Problemscited by 5
- 2025An Agentic Framework with LLMs for Solving Complex Vehicle Routing Problemscited by 5
- 2025Learning to Partially Defer for Sequencescited by 4
- 2025Learning Constraints-Based Adaptive Hypergraph Neural Networks for Solving Vehicle Routing Problemscited by 3
- 2025LMask: Learn to Solve Constrained Routing Problems with Lazy Maskingcited by 3
- 2025Mechanistic Interpretability for Neural TSP Solverscited by 3
- 2026Towards Efficient Constraint Handling in Neural Solvers for Routing Problemscited by 3
- 2023Learning Efficient Surrogate Dynamic Models with Graph Spline Networkscited by 2
- 2025Learning to Solve the Min-Max Mixed-Shelves Picker-Routing Problem via Hierarchical and Parallel Decodingcited by 2
- 2025Accelerating Vehicle Routing via AI-Initialized Genetic Algorithmscited by 2
- 2025Planning in Branch-and-Bound: Model-Based Reinforcement Learning for Exact Combinatorial Optimizationcited by 2
- 2025USPR: Learning a Unified Solver for Profiled Routingcited by 1
- 2025Recurrent State Encoders for Efficient Neural Combinatorial Optimizationcited by 1
- 2025Learn to Relax with Large Language Models: Solving Constraint Optimization Problems via Bidirectional Coevolutioncited by 1
- 2025ViTSP: A Vision Language Models Guided Framework for Solving Large-Scale Traveling Salesman Problemscited by 1
- 2026Baseline-Free Policy Optimization for Neural Combinatorial Optimizationcited by 1
- 2026HyCO: A Hybrid Neural Solver for Combinatorial Optimizationcited by 1
- 2024Learn to Solve Vehicle Routing Problems ASAP: A Neural Optimization Approach for Time-Constrained Vehicle Routing Problems with Finite Vehicle Fleetcited by 0
- 2024Multi-Agent Environments for Vehicle Routing Problemscited by 0
- 2025TransPlace: Transferable Circuit Global Placement via Graph Neural Networkcited by 0
- 2025SED2AM: Solving Multi-Trip Time-Dependent Vehicle Routing Problem using Deep Reinforcement Learningcited by 0
- 2025Onboard Mission Replanning for Adaptive Cooperative Multi-Robot Systemscited by 0
- 2025On Training-Test (Mis)alignment in Unsupervised Combinatorial Optimization: Observation, Empirical Exploration, and Analysiscited by 0
- 2025POMO+: Leveraging starting nodes in POMO for solving Capacitated Vehicle Routing Problemcited by 0
- 2025NeuFACO: Neural Focused Ant Colony Optimization for Traveling Salesman Problemcited by 0
- 2025Tackling GNARLy Problems: Graph Neural Algorithmic Reasoning Reimagined through Reinforcement Learningcited by 0
- 2025A Unified Deep Reinforcement Learning Approach for Close Enough Traveling Salesman Problemcited by 0
- 2025Multi-Action Self-Improvement for Neural Combinatorial Optimizationcited by 0
50 most cited of 71 All 71 (JSON)
- 2026RELAGRAM: Recursive Latent Graph Model for the Capacitated Vehicle Routing Problem10 Oct 2026
- 2026VLM Fine-Tuning for End-to-End Combinatorial Optimization29 Sep 2026
- 2026Self-Supervised Combinatorial Optimization with Constraints via Frank-Wolfe22 Sep 2026
- 2026HyCO: A Hybrid Neural Solver for Combinatorial Optimization7 Sep 2026
- 2026Two Black Boxes, One Solver: Encoder Probing and Decoder Attribution for Neural Multi-Attribute VRP under Hard-Mask and Recourse Decoders5 Jul 2026
- 2026SkillChain-Gym: A Benchmark for Reskilling-Aware Production-Inventory Control under Disruptions15 Jun 2026
- 2026Geometry-Aware Reinforcement Learning for 2D Irregular Nesting9 Jun 2026
- 2026Baseline-Free Policy Optimization for Neural Combinatorial Optimization9 Jun 2026
- 2026Beyond Static Priors: Dynamic Neural Guidance for Large-Scale Ant Colony Optimization2 Jun 2026
- 2026SQARL: A Size-Agnostic Reinforcement Learning approach for Circuit Allocation in Distributed Quantum Architectures26 May 2026
- 2026Constraint-Anchored Attribution: Feasibility-Certified Counterfactuals and Bonferroni-PAC Sufficient Subsets for Neural CO Policies24 May 2026
- 2026MVR-cache: Optimizing Semantic Caching via Multi-Vector Retrieval and Learned Prompt Segmentation24 May 2026
38 more
- 2026Learning to Solve Compositional Geometry Routing Problems18 May 2026
- 2026An Amortized Efficiency Threshold for Comparing Neural and Heuristic Solvers in Combinatorial Optimization14 May 2026
- 2026CO-MAP: A Reinforcement Learning Approach to the Qubit Allocation Problem13 May 2026
- 2026LINC: Decoupling Local Consequence Scoring from Hidden Matching in Constructive Neural Routing7 May 2026
- 2026Benchmarking Classical Coverage Path Planning Heuristics on Irregular Hexagonal Grids for Maritime Coverage Scenarios16 Apr 2026
- 2026Critic-Free Deep Reinforcement Learning for Maritime Coverage Path Planning on Irregular Hexagonal Grids30 Mar 2026
- 2026Decoupling Numerical and Structural Parameters: An Empirical Study on Adaptive Genetic Algorithms via Deep Reinforcement Learning for the Large-Scale TSP21 Mar 2026
- 2026UniHetCO: A Unified Heterogeneous Representation for Multi-Problem Learning in Unsupervised Neural Combinatorial Optimization12 Mar 2026
- 2026Learning to Solve Orienteering Problem with Time Windows and Variable Profits6 Mar 2026
- 2026Towards Efficient Constraint Handling in Neural Solvers for Routing Problems17 Feb 2026
- 2025Deep Reinforcement Learning for Solving the Fleet Size and Mix Vehicle Routing Problem30 Dec 2025
- 2025Planning in Branch-and-Bound: Model-Based Reinforcement Learning for Exact Combinatorial Optimization12 Nov 2025
- 2025Mechanistic Interpretability for Neural TSP Solvers24 Oct 2025
- 2025A Markov Decision Process for Variable Selection in Branch & Bound22 Oct 2025
- 2025An Agentic Framework with LLMs for Solving Complex Vehicle Routing Problems19 Oct 2025
- 2025Multi-Action Self-Improvement for Neural Combinatorial Optimization14 Oct 2025
- 2025VRPAgent: LLM-Driven Discovery of Heuristic Operators for Vehicle Routing Problems8 Oct 2025
- 2025A Unified Deep Reinforcement Learning Approach for Close Enough Traveling Salesman Problem3 Oct 2025
- 2025ViTSP: A Vision Language Models Guided Framework for Solving Large-Scale Traveling Salesman Problems27 Sep 2025
- 2025Tackling GNARLy Problems: Graph Neural Algorithmic Reasoning Reimagined through Reinforcement Learning23 Sep 2025
- 2025NeuFACO: Neural Focused Ant Colony Optimization for Traveling Salesman Problem21 Sep 2025
- 2025Large Language Models as End-to-end Combinatorial Optimization Solvers21 Sep 2025
- 2025Learn to Relax with Large Language Models: Solving Constraint Optimization Problems via Bidirectional Coevolution16 Sep 2025
- 2025Recurrent State Encoders for Efficient Neural Combinatorial Optimization5 Sep 2025
- 2025POMO+: Leveraging starting nodes in POMO for solving Capacitated Vehicle Routing Problem11 Aug 2025
- 2025Fine-tuning Large Language Model for Automated Algorithm Design13 Jul 2025
- 2025Learning to Segment for Vehicle Routing Problems22 Jun 2025
- 2025On Training-Test (Mis)alignment in Unsupervised Combinatorial Optimization: Observation, Empirical Exploration, and Analysis20 Jun 2025
- 2025Preference-Driven Multi-Objective Combinatorial Optimization with Conditional Computation10 Jun 2025
- 2025Onboard Mission Replanning for Adaptive Cooperative Multi-Robot Systems6 Jun 2025
- 2025Generalizable Heuristic Generation Through LLMs with Meta-Optimization27 May 2025
- 2025LMask: Learn to Solve Constrained Routing Problems with Lazy Masking23 May 2025
- 2025FrontierCO: Real-World and Large-Scale Evaluation of Machine Learning Solvers for Combinatorial Optimization22 May 2025
- 2025USPR: Learning a Unified Solver for Profiled Routing8 May 2025
- 2025Accelerating Vehicle Routing via AI-Initialized Genetic Algorithms8 Apr 2025
- 2025RRNCO: Towards Real-World Routing with Neural Combinatorial Optimization20 Mar 2025
- 2025Learning Constraints-Based Adaptive Hypergraph Neural Networks for Solving Vehicle Routing Problems13 Mar 2025
- 2025SED2AM: Solving Multi-Trip Time-Dependent Vehicle Routing Problem using Deep Reinforcement Learning6 Mar 2025
50 newest of 71 All 71 (JSON)
- 2025Rethinking Light Decoder-based Solvers for Vehicle Routing Problemscited by 37
- 2024PolyNet: Learning Diverse Solution Strategies for Neural Combinatorial Optimizationcited by 35
- 2024ACEGEN: Reinforcement learning of generative chemical agents for drug discoverycited by 14
- 2025Preference-Driven Multi-Objective Combinatorial Optimization with Conditional Computationcited by 6
- 2025Reinforcement learning with combinatorial actions for coupled restless banditscited by 5
- 2025Learning Constraints-Based Adaptive Hypergraph Neural Networks for Solving Vehicle Routing Problemscited by 3
- 2025Accelerating Vehicle Routing via AI-Initialized Genetic Algorithmscited by 2
- 2025Planning in Branch-and-Bound: Model-Based Reinforcement Learning for Exact Combinatorial Optimizationcited by 2
- 2025SED2AM: Solving Multi-Trip Time-Dependent Vehicle Routing Problem using Deep Reinforcement Learningcited by 0
- 2025POMO+: Leveraging starting nodes in POMO for solving Capacitated Vehicle Routing Problemcited by 0
- 2025NeuFACO: Neural Focused Ant Colony Optimization for Traveling Salesman Problemcited by 0
- 2025A Unified Deep Reinforcement Learning Approach for Close Enough Traveling Salesman Problemcited by 0
12 most cited of 18 All 18 (JSON)
- 2026Geometry-Aware Reinforcement Learning for 2D Irregular Nesting9 Jun 2026
- 2026SQARL: A Size-Agnostic Reinforcement Learning approach for Circuit Allocation in Distributed Quantum Architectures26 May 2026
- 2026CO-MAP: A Reinforcement Learning Approach to the Qubit Allocation Problem13 May 2026
- 2026Critic-Free Deep Reinforcement Learning for Maritime Coverage Path Planning on Irregular Hexagonal Grids30 Mar 2026
- 2026Decoupling Numerical and Structural Parameters: An Empirical Study on Adaptive Genetic Algorithms via Deep Reinforcement Learning for the Large-Scale TSP21 Mar 2026
- 2025Deep Reinforcement Learning for Solving the Fleet Size and Mix Vehicle Routing Problem30 Dec 2025
- 2025Planning in Branch-and-Bound: Model-Based Reinforcement Learning for Exact Combinatorial Optimization12 Nov 2025
- 2025A Unified Deep Reinforcement Learning Approach for Close Enough Traveling Salesman Problem3 Oct 2025
- 2025NeuFACO: Neural Focused Ant Colony Optimization for Traveling Salesman Problem21 Sep 2025
- 2025POMO+: Leveraging starting nodes in POMO for solving Capacitated Vehicle Routing Problem11 Aug 2025
- 2025Preference-Driven Multi-Objective Combinatorial Optimization with Conditional Computation10 Jun 2025
- 2025Accelerating Vehicle Routing via AI-Initialized Genetic Algorithms8 Apr 2025
12 newest of 18 All 18 (JSON)
- 2025Mechanistic Interpretability for Neural TSP Solverscited by 3
- 2025Mechanistic Interpretability for Neural TSP Solvers24 Oct 2025
- 2023GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-timecited by 85
- 2023DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimizationcited by 78
- 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problemscited by 55
- 2024Learning to Handle Complex Constraints for Vehicle Routing Problemscited by 29
- 2025Large Language Models as End-to-end Combinatorial Optimization Solverscited by 28
- 2025Neural Deconstruction Search for Vehicle Routing Problemscited by 15
- 2025RRNCO: Towards Real-World Routing with Neural Combinatorial Optimizationcited by 11
- 2025FrontierCO: Real-World and Large-Scale Evaluation of Machine Learning Solvers for Combinatorial Optimizationcited by 11
- 2024Collaboration! Towards Robust Neural Methods for Routing Problemscited by 9
- 2025Generalizable Heuristic Generation Through LLMs with Meta-Optimizationcited by 9
- 2024Ensembling Prioritized Hybrid Policies for Multi-agent Pathfindingcited by 7
- 2024Tackling Prevalent Conditions in Unsupervised Combinatorial Optimization: Cardinality, Minimum, Covering, and Morecited by 7
12 most cited of 47 All 47 (JSON)
- 2026RELAGRAM: Recursive Latent Graph Model for the Capacitated Vehicle Routing Problem10 Oct 2026
- 2026VLM Fine-Tuning for End-to-End Combinatorial Optimization29 Sep 2026
- 2026Self-Supervised Combinatorial Optimization with Constraints via Frank-Wolfe22 Sep 2026
- 2026Two Black Boxes, One Solver: Encoder Probing and Decoder Attribution for Neural Multi-Attribute VRP under Hard-Mask and Recourse Decoders5 Jul 2026
- 2026SkillChain-Gym: A Benchmark for Reskilling-Aware Production-Inventory Control under Disruptions15 Jun 2026
- 2026Beyond Static Priors: Dynamic Neural Guidance for Large-Scale Ant Colony Optimization2 Jun 2026
- 2026Constraint-Anchored Attribution: Feasibility-Certified Counterfactuals and Bonferroni-PAC Sufficient Subsets for Neural CO Policies24 May 2026
- 2026MVR-cache: Optimizing Semantic Caching via Multi-Vector Retrieval and Learned Prompt Segmentation24 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
- 2026LINC: Decoupling Local Consequence Scoring from Hidden Matching in Constructive Neural Routing7 May 2026
- 2026Benchmarking Classical Coverage Path Planning Heuristics on Irregular Hexagonal Grids for Maritime Coverage Scenarios16 Apr 2026
12 newest of 47 All 47 (JSON)