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arxiv: 2605.18094 · v1 · pith:U5QVZC4Bnew · submitted 2026-05-18 · 💻 cs.AI

Learning to Solve Compositional Geometry Routing Problems

Mingfeng Fan , Jianan Zhou , Jiaqi Cheng , Yifeng Zhang , Jie Zhang , Guillaume Adrien Sartoretti This is my paper

Pith reviewed 2026-05-20 10:58 UTC · model grok-4.3

classification 💻 cs.AI
keywords compositional geometry routingdifferential attentioncontrastive learningrouting problemsgeneralizationvehicle routingreinforcement learningattention mechanism
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The pith

A solver with differential attention and double-level contrastive learning handles routing problems that mix points, lines, and areas.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to establish that a single plug-and-play method can solve a broad family of routing problems whose tasks include visiting points, traversing lines, covering areas, or any combination of these. Real-world routing often mixes these geometries, creating asymmetric routes and many irrelevant action choices that standard point-based solvers struggle with. DiCon addresses the issues by using differential attention to lower the chance of selecting weak candidate moves and by applying contrastive learning at both the full-instance level and the geometry-task level to build transferable representations. If the approach works as claimed, it would allow one model to perform well across many different task mixes without retraining or redesign for each new composition.

Core claim

The authors introduce DiCon as a differential attention-assisted solver with contrastive learning. The differential attention mechanism suppresses probability mass on less competitive candidate actions, while the double-level contrastive objective promotes robust global instance representations and regularizes geometry-aware task representations. Extensive experiments show that this framework delivers strong performance, broad versatility, and superior generalization on CGRP instances spanning point-only, line-only, area-only, and arbitrary hybrid compositions.

What carries the argument

DiCon, a framework that pairs a differential attention mechanism for down-weighting irrelevant actions with a double-level contrastive learning objective for geometry-aware representations.

If this is right

  • Routing solvers can now address asymmetric problems where routes are tightly coupled to the intrinsic paths of lines or areas.
  • The enlarged action space of hybrid tasks becomes manageable by actively reducing focus on poor candidate moves.
  • A single trained model can be applied to many different task compositions without retraining or architectural changes.
  • The plug-and-play design allows the attention and contrastive components to be added to existing routing solvers.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same attention-plus-contrastive pattern may transfer to other combinatorial problems that feature variable action spaces and geometric constraints.
  • Logistics and robotics planning systems could reduce the need for separate models when tasks shift between point visits, line traversals, and area coverage.
  • Integration with classical optimization techniques might further improve solution quality on very large hybrid instances.

Load-bearing premise

The differential attention and double-level contrastive objective will consistently suppress irrelevant actions and produce representations that transfer across arbitrary mixes of point, line, and area tasks without any task-specific tuning.

What would settle it

If DiCon is tested on a held-out set of CGRP instances that use previously unseen task compositions, such as heavy mixtures of area-covering tasks, and its solution quality or generalization gap falls below that of standard routing baselines, the central claim would be falsified.

Figures

Figures reproduced from arXiv: 2605.18094 by Guillaume Adrien Sartoretti, Jianan Zhou, Jiaqi Cheng, Jie Zhang, Mingfeng Fan, Yifeng Zhang.

Figure 1
Figure 1. Figure 1: The characteristics of CGRP. line tasks, area tasks, or arbitrary combinations of them [18, 60]. Treating these cases as separate routing problems limits the flexibility of solver design and often requires geometry-specific adaptation. To provide a common abstraction for homogeneous and mixed-geometry routing, we study the Compositional Geometry Routing Problem (CGRP), a unified formulation over point, lin… view at source ↗
Figure 2
Figure 2. Figure 2: An overview of DiCon. DiCon incorporates two mechanisms: 1) a multi-head differential [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Ablation study. To assess the contribution of key components in DiCon, we progressively remove the intra-task (IT) CL, instance-level (IL) CL, and DA modules from DiCon-P, yielding DiCon-P w/o IT, DiCon-P w/o IT+IL, and the backbone POMO, respectively. The results on CGRP100 and Area20+Line30 are visualized in [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Visualization results on a real-world urban monitoring instance in Hangzhou, where area [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Visualization results on a real-world electric power inspection instance in Jiaxing, where the [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The visualizations of randomly selected CGRP instances. [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparative results on large problem sizes. [PITH_FULL_IMAGE:figures/full_fig_p021_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The visualization results on extreme and highly imbalanced task mixtures. (1) Clustered [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Performance comparison on DCCGRP . node from each cluster while optimizing the tour. The results are reported in [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Entropy comparison between MHA and MHDA. [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗
read the original abstract

We study the Compositional Geometry Routing Problem (CGRP), a unified superclass of traditional routing problems that covers point-only, line-only, area-only, and arbitrary hybrid task geometries, providing a broad abstraction for real-world routing scenarios. Beyond standard point-based routing, CGRP with non-point tasks can be inherently asymmetric, tightly coupled travel routes with the intrinsic path, and enlarges the action space with numerous feasible yet often irrelevant options, thereby posing significant challenges for both representation learning and decision-making. To address these challenges, we propose DiCon, a differential attention-assisted solver with contrastive learning, as a plug-and-play framework that tackles the problem from two complementary angles. First, we introduce a differential attention mechanism that actively suppresses the probability mass on less competitive candidate actions. Second, we design a double-level contrastive learning objective to promote robust global instance representations and regularize geometry-aware task representations. Extensive experiments demonstrate that DiCon achieves strong performance, broad versatility, and superior generalization across diverse CGRP instances with different compositions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript defines the Compositional Geometry Routing Problem (CGRP) as a unified superclass encompassing point-only, line-only, area-only, and arbitrary hybrid routing tasks. It introduces DiCon, a plug-and-play neural solver that combines a differential attention mechanism to suppress probability mass on less competitive actions with a double-level contrastive learning objective for learning global instance representations and geometry-aware task representations. The central claim is that DiCon delivers strong performance, broad versatility, and superior generalization across diverse CGRP instances with varying compositions.

Significance. If the performance and generalization results hold under rigorous cross-composition testing, the work would make a useful contribution to learning-based solvers for combinatorial optimization by extending them to asymmetric, geometry-coupled problems with expanded action spaces. The CGRP abstraction itself provides a coherent way to unify previously separate routing variants, and the contrastive components offer a plausible route to transferable representations. These elements could inform practical routing systems that mix point, line, and area tasks.

major comments (2)
  1. [Section 4] Section 4 (Experiments): The generalization claim that DiCon succeeds on arbitrary hybrids rests on test instances whose composition distribution is not shown to be disjoint from training. Without explicit hold-out protocols that evaluate on novel point/line/area mixes absent from the training set, it remains possible that reported gains arise from memorization of seen mixtures rather than the differential attention or double-level contrastive objective. This is load-bearing for the central claim of composition-agnostic transfer.
  2. [Abstract and Section 5] Abstract and Section 5 (Results): The abstract asserts positive experimental outcomes yet supplies no numerical metrics, optimality gaps, runtime comparisons, or ablation tables. If the full manuscript's tables and figures do not report concrete baselines (e.g., OR-Tools, standard attention-based solvers) and component ablations on the same CGRP instances, the magnitude and reliability of the claimed improvements cannot be assessed.
minor comments (2)
  1. [Section 3.1] Section 3.1: The precise implementation of how differential attention modifies the policy logits (e.g., the scaling factor or masking threshold) should be stated explicitly, preferably with an equation or short algorithm box.
  2. [Section 3.2] Notation: The two levels of the contrastive objective are described in prose; adding a compact equation for the combined loss (with temperature and weighting hyperparameters) would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our work. We address each major comment below, providing clarifications on our experimental design and committing to revisions that improve the clarity and rigor of the presentation without altering the core claims.

read point-by-point responses

  1. Referee: [Section 4] Section 4 (Experiments): The generalization claim that DiCon succeeds on arbitrary hybrids rests on test instances whose composition distribution is not shown to be disjoint from training. Without explicit hold-out protocols that evaluate on novel point/line/area mixes absent from the training set, it remains possible that reported gains arise from memorization of seen mixtures rather than the differential attention or double-level contrastive objective. This is load-bearing for the central claim of composition-agnostic transfer.

    Authors: We agree that explicit documentation of the composition distributions is essential to substantiate the generalization claim. Our training instances were generated from a fixed set of compositions (point-only, line-only, area-only, and a limited set of predefined hybrids), while test instances were drawn from arbitrary hybrid compositions explicitly excluded from the training distribution. In the revised manuscript, we will add a table and accompanying text in Section 4 detailing the exact composition counts and the hold-out protocol used to ensure no overlap in mixture types. This revision will make the composition-agnostic transfer explicit and address the concern directly. revision: yes

  2. Referee: [Abstract and Section 5] Abstract and Section 5 (Results): The abstract asserts positive experimental outcomes yet supplies no numerical metrics, optimality gaps, runtime comparisons, or ablation tables. If the full manuscript's tables and figures do not report concrete baselines (e.g., OR-Tools, standard attention-based solvers) and component ablations on the same CGRP instances, the magnitude and reliability of the claimed improvements cannot be assessed.

    Authors: We concur that the abstract would be strengthened by including key quantitative indicators. The full manuscript already contains, in Section 5 and the associated tables, direct comparisons of DiCon against OR-Tools and standard attention-based solvers, together with ablation results isolating the differential attention and double-level contrastive components, all evaluated on identical CGRP instances. We will revise the abstract to report representative metrics such as average optimality gaps and runtime improvements relative to these baselines. revision: yes

Circularity Check

0 steps flagged

No circularity in claimed method or results

full rationale

The paper proposes DiCon as a new neural solver architecture and training objective for the defined CGRP class. All load-bearing elements (differential attention, double-level contrastive loss, and reported performance) are introduced as design choices and then evaluated on held-out test instances. No equation or claim reduces by construction to a fitted parameter, self-citation, or renamed input; the derivation chain consists of standard encoder-decoder components plus two explicitly motivated regularizers whose effectiveness is measured against external instance distributions rather than being tautological with the training data.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the untested assumption that differential attention plus contrastive objectives will generalize across arbitrary geometry compositions; no free parameters are explicitly listed in the abstract, but neural network weights and contrastive temperature are implicit fitted quantities.

free parameters (1)
  • contrastive temperature and loss weights
    Typical hyperparameters in contrastive objectives that are tuned on the training distribution of CGRP instances.
axioms (1)
  • domain assumption The action space enlargement and asymmetry in non-point CGRP tasks can be mitigated by attention suppression and representation regularization.
    Stated in the abstract as the core challenges the method addresses.

pith-pipeline@v0.9.0 · 5714 in / 1235 out tokens · 22401 ms · 2026-05-20T10:58:20.438104+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
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    Relation between the paper passage and the cited Recognition theorem.

    We introduce a differential attention mechanism that actively suppresses the probability mass on less competitive candidate actions... double-level contrastive learning objective to promote robust global instance representations and regularize geometry-aware task representations.

What do these tags mean?
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supports
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Reference graph

Works this paper leans on

61 extracted references · 61 canonical work pages

  1. [1]

    Line coverage with multiple robots: algorithms and experiments

    Saurav Agarwal and Srinivas Akella. Line coverage with multiple robots: algorithms and experiments. IEEE Transactions on Robotics, 40:1664–1683, 2024

    work page 2024

  2. [2]

    Multi-robot persistent monitoring: Minimizing latency and number of robots with recharging constraints.IEEE Transactions on Robotics, 2024

    Ahmad Bilal Asghar, Shreyas Sundaram, and Stephen L Smith. Multi-robot persistent monitoring: Minimizing latency and number of robots with recharging constraints.IEEE Transactions on Robotics, 2024

    work page 2024

  3. [3]

    Revisiting boustrophedon coverage path planning as a generalized traveling salesman problem

    Rik Bähnemann, Nicholas Lawrance, Jen Jen Chung, Michael Pantic, Roland Siegwart, and Juan Nieto. Revisiting boustrophedon coverage path planning as a generalized traveling salesman problem. InField and Service Robotics: Results of the 12th International Conference, pages 277–290. Springer, 2021

    work page 2021

  4. [4]

    Neural combinatorial optimization with reinforcement learning

    Irwan Bello, Hieu Pham, Quoc V Le, Mohammad Norouzi, and Samy Bengio. Neural combinatorial optimization with reinforcement learning. InInternational Conference on Learning Representations (Workshop), 2017

    work page 2017

  5. [5]

    Rl4co: an extensive reinforcement learning for combi- natorial optimization benchmark

    Federico Berto, Chuanbo Hua, Junyoung Park, Laurin Luttmann, Yining Ma, Fanchen Bu, Jiarui Wang, Haoran Ye, Minsu Kim, Sanghyeok Choi, et al. Rl4co: an extensive reinforcement learning for combi- natorial optimization benchmark. InProceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V . 2, pages 5278–5289, 2025

    work page 2025

  6. [6]

    RouteFinder: Towards foundation models for vehicle routing problems.Transactions on Machine Learning Research, 2025

    Federico Berto, Chuanbo Hua, Nayeli Gast Zepeda, André Hottung, Niels Wouda, Leon Lan, Junyoung Park, Kevin Tierney, and Jinkyoo Park. RouteFinder: Towards foundation models for vehicle routing problems.Transactions on Machine Learning Research, 2025

    work page 2025

  7. [7]

    Learning generalizable models for vehicle routing problems via knowledge distillation.Advances in Neural Information Processing Systems, 35:31226–31238, 2022

    Jieyi Bi, Yining Ma, Jiahai Wang, Zhiguang Cao, Jinbiao Chen, Yuan Sun, and Yeow Meng Chee. Learning generalizable models for vehicle routing problems via knowledge distillation.Advances in Neural Information Processing Systems, 35:31226–31238, 2022

    work page 2022

  8. [8]

    Exploring simple siamese representation learning

    Xinlei Chen and Kaiming He. Exploring simple siamese representation learning. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15750–15758, 2021

    work page 2021

  9. [9]

    Multimodal fused learning for solving the generalized traveling salesman problem in robotic task planning

    Jiaqi Cheng, Mingfeng Fan, Xuefeng Zhang, Jingsong Liang, Yuhong Cao, Guohua Wu, and Guil- laume Adrien Sartoretti. Multimodal fused learning for solving the generalized traveling salesman problem in robotic task planning. In Joseph Lim, Shuran Song, and Hae-Won Park, editors,Proceedings of The 9th Conference on Robot Learning, volume 305 ofProceedings of...

    work page 2025

  10. [10]

    Debiased contrastive learning.Advances in Neural Information Processing systems, 33:8765–8775, 2020

    Ching-Yao Chuang, Joshua Robinson, Yen-Chen Lin, Antonio Torralba, and Stefanie Jegelka. Debiased contrastive learning.Advances in Neural Information Processing systems, 33:8765–8775, 2020

    work page 2020

  11. [11]

    Ant colony system: a cooperative learning approach to the traveling salesman problem.IEEE Transactions on Evolutionary Computation, 1(1):53–66, 2002

    Marco Dorigo and Luca Maria Gambardella. Ant colony system: a cooperative learning approach to the traveling salesman problem.IEEE Transactions on Evolutionary Computation, 1(1):53–66, 2002

    work page 2002

  12. [12]

    GOAL: A generalist combinatorial optimization agent learner

    Darko Drakulic, Sofia Michel, and Jean-Marc Andreoli. GOAL: A generalist combinatorial optimization agent learner. InThe Thirteenth International Conference on Learning Representations, 2025

    work page 2025

  13. [13]

    Bq-nco: Bisimulation quotienting for efficient neural combinatorial optimization.Advances in Neural Information Processing Systems, 36:77416–77429, 2023

    Darko Drakulic, Sofia Michel, Florian Mai, Arnaud Sors, and Jean-Marc Andreoli. Bq-nco: Bisimulation quotienting for efficient neural combinatorial optimization.Advances in Neural Information Processing Systems, 36:77416–77429, 2023. 10

    work page 2023

  14. [14]

    Augment with care: Contrastive learning for combinatorial problems

    Haonan Duan, Pashootan Vaezipoor, Max B Paulus, Yangjun Ruan, and Chris Maddison. Augment with care: Contrastive learning for combinatorial problems. InInternational Conference on Machine Learning, pages 5627–5642. PMLR, 2022

    work page 2022

  15. [15]

    The traveling-salesman problem.Operations Research, 4(1):61–75, 1956

    Merrill M Flood. The traveling-salesman problem.Operations Research, 4(1):61–75, 1956

    work page 1956

  16. [16]

    OR-Tools Routing Library version v9.15

    Vincent Furnon and Laurent Perron. OR-Tools Routing Library version v9.15. https://developers. google.com/optimization/routing/, 2026

    work page 2026

  17. [17]

    Towards generalizable neural solvers for vehicle routing problems via ensemble with transferrable local policy

    Chengrui Gao, Haopu Shang, Ke Xue, Dong Li, and Chao Qian. Towards generalizable neural solvers for vehicle routing problems via ensemble with transferrable local policy. InProceedings of the Thirty-First International Joint Conference on Artificial Intelligence, 2024

    work page 2024

  18. [18]

    Multi-UA V reconnaissance task allocation for heterogeneous targets using grouping ant colony optimization algorithm.Soft Computing, 25(10):7155–7167, 2021

    Sheng Gao, Jiazheng Wu, and Jianliang Ai. Multi-UA V reconnaissance task allocation for heterogeneous targets using grouping ant colony optimization algorithm.Soft Computing, 25(10):7155–7167, 2021

    work page 2021

  19. [19]

    DeCLUTR: Deep contrastive learning for unsupervised textual representations

    John Giorgi, Osvald Nitski, Bo Wang, and Gary Bader. DeCLUTR: Deep contrastive learning for unsupervised textual representations. InProceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, pages 879–895, 2021

    work page 2021

  20. [20]

    Winner takes it all: Training performant RL populations for combinatorial optimization

    Nathan Grinsztajn, Daniel Furelos-Blanco, Shikha Surana, Clément Bonnet, and Thomas D Barrett. Winner takes it all: Training performant RL populations for combinatorial optimization. InAdvances in Neural Information Processing Systems, 2023

    work page 2023

  21. [21]

    ConRep4CO: Contrastive representation learning of combinatorial optimization instances across types

    Ziao Guo, Yang Li, Shiyue Wang, and Junchi Yan. ConRep4CO: Contrastive representation learning of combinatorial optimization instances across types. InThe Fourteenth International Conference on Learning Representations, 2026

    work page 2026

  22. [22]

    Momentum contrast for unsupervised visual representation learning

    Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross Girshick. Momentum contrast for unsupervised visual representation learning. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9729–9738, 2020

    work page 2020

  23. [23]

    An effective implementation of the Lin–Kernighan traveling salesman heuristic.European Journal of Operational Research, 126(1):106–130, 2000

    Keld Helsgaun. An effective implementation of the Lin–Kernighan traveling salesman heuristic.European Journal of Operational Research, 126(1):106–130, 2000

    work page 2000

  24. [24]

    LKH-3 version 3.0.7.http://webhotel4.ruc.dk/~keld/research/LKH-3/, 2017

    Keld Helsgaun. LKH-3 version 3.0.7.http://webhotel4.ruc.dk/~keld/research/LKH-3/, 2017

    work page 2017

  25. [25]

    Efficient active search for combinatorial optimization problems

    André Hottung, Yeong-Dae Kwon, and Kevin Tierney. Efficient active search for combinatorial optimization problems. InInternational Conference on Learning Representations, 2022, Virtual Event, April 25-29, 2022, 2022

    work page 2022

  26. [26]

    Generalize learned heuristics to solve large-scale vehicle routing problems in real-time

    Qingchun Hou, Jingwei Yang, Yiqiang Su, Xiaoqing Wang, and Yuming Deng. Generalize learned heuristics to solve large-scale vehicle routing problems in real-time. InInternational Conference on Learning Representations, 2023

    work page 2023

  27. [27]

    Contrastive predict-and-search for mixed integer linear programs

    Taoan Huang, Aaron M Ferber, Arman Zharmagambetov, Yuandong Tian, and Bistra Dilkina. Contrastive predict-and-search for mixed integer linear programs. InInternational Conference on Machine Learning, 2024

    work page 2024

  28. [28]

    Rethinking light decoder-based solvers for vehicle routing problems

    Ziwei Huang, Jianan Zhou, Zhiguang Cao, and Yixin Xu. Rethinking light decoder-based solvers for vehicle routing problems. InThe Thirteenth International Conference on Learning Representations, 2025

    work page 2025

  29. [29]

    A neural solver with traversal-based feature representation and adjacent attention for capacitated arc routing problem.IEEE Transactions on Intelligent Transportation Systems, 2025

    Ya-Hui Jia, Qiquan Zheng, Yang Wang, Yi Mei, Wei-Neng Chen, and Zhenhong Lin. A neural solver with traversal-based feature representation and adjacent attention for capacitated arc routing problem.IEEE Transactions on Intelligent Transportation Systems, 2025

    work page 2025

  30. [30]

    Multi-view graph contrastive learning for solving vehicle routing problems

    Yuan Jiang, Zhiguang Cao, Yaoxin Wu, and Jie Zhang. Multi-view graph contrastive learning for solving vehicle routing problems. InUncertainty in Artificial Intelligence, pages 984–994. PMLR, 2023

    work page 2023

  31. [31]

    Lin–Kernighan heuristic adaptations for the generalized traveling salesman problem.European Journal of Operational Research, 208(3):221–232, 2011

    Daniel Karapetyan and Gregory Gutin. Lin–Kernighan heuristic adaptations for the generalized traveling salesman problem.European Journal of Operational Research, 208(3):221–232, 2011

    work page 2011

  32. [32]

    Sym-nco: Leveraging symmetricity for neural combinatorial optimization

    Minsu Kim, Junyoung Park, and Jinkyoo Park. Sym-nco: Leveraging symmetricity for neural combinatorial optimization. InAdvances in Neural Information Processing Systems, 2022

    work page 2022

  33. [33]

    Attention, learn to solve routing problems

    Wouter Kool, Herke Van Hoof, and Max Welling. Attention, learn to solve routing problems. In International Conference on Learning Representations, 2018. 11

    work page 2018

  34. [34]

    Pomo: Policy optimization with multiple optima for reinforcement learning.Advances in Neural Information Processing Systems, 33:21188–21198, 2020

    Yeong-Dae Kwon, Jinho Choo, Byoungjip Kim, Iljoo Yoon, Youngjune Gwon, and Seungjai Min. Pomo: Policy optimization with multiple optima for reinforcement learning.Advances in Neural Information Processing Systems, 33:21188–21198, 2020

    work page 2020

  35. [35]

    Matrix encoding networks for neural combinatorial optimization.Advances in Neural Information Processing Systems, 34:5138–5149, 2021

    Yeong-Dae Kwon, Jinho Choo, Iljoo Yoon, Minah Park, Duwon Park, and Youngjune Gwon. Matrix encoding networks for neural combinatorial optimization.Advances in Neural Information Processing Systems, 34:5138–5149, 2021

    work page 2021

  36. [36]

    Heterogeneous attention-based graph convolutional network for solving asymmetric pickup and delivery problem.IEEE Transactions on Automation Science and Engineering, 2025

    Jiayi Li, Guohua Wu, Mingfeng Fan, Zhiguang Cao, and Yalin Wang. Heterogeneous attention-based graph convolutional network for solving asymmetric pickup and delivery problem.IEEE Transactions on Automation Science and Engineering, 2025

    work page 2025

  37. [37]

    Learning to delegate for large-scale vehicle routing.Advances in Neural Information Processing Systems, 34:26198–26211, 2021

    Sirui Li, Zhongxia Yan, and Cathy Wu. Learning to delegate for large-scale vehicle routing.Advances in Neural Information Processing Systems, 34:26198–26211, 2021

    work page 2021

  38. [38]

    An effective heuristic algorithm for the traveling-salesman problem

    Shen Lin and Brian W Kernighan. An effective heuristic algorithm for the traveling-salesman problem. Operations Research, 21(2):498–516, 1973

    work page 1973

  39. [39]

    Neural combinatorial optimization with heavy decoder: Toward large scale generalization.Advances in Neural Information Processing Systems, 36:8845–8864, 2023

    Fu Luo, Xi Lin, Fei Liu, Qingfu Zhang, and Zhenkun Wang. Neural combinatorial optimization with heavy decoder: Toward large scale generalization.Advances in Neural Information Processing Systems, 36:8845–8864, 2023

    work page 2023

  40. [40]

    Boosting neural combinatorial optimization for large-scale vehicle routing problems

    Fu Luo, Xi Lin, Yaoxin Wu, Zhenkun Wang, Tong Xialiang, Mingxuan Yuan, and Qingfu Zhang. Boosting neural combinatorial optimization for large-scale vehicle routing problems. InThe Thirteenth International Conference on Learning Representations, 2025

    work page 2025

  41. [41]

    Distributed representations of words and phrases and their compositionality.Advances in Neural Information Processing Systems, 26, 2013

    Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean. Distributed representations of words and phrases and their compositionality.Advances in Neural Information Processing Systems, 26, 2013

    work page 2013

  42. [42]

    Multi-tour set traveling salesman problem in planning power transmission line inspection.IEEE Robotics and Automation Letters, 6(4):6196–6203, 2021

    František Nekováˇr, Jan Faigl, and Martin Saska. Multi-tour set traveling salesman problem in planning power transmission line inspection.IEEE Robotics and Automation Letters, 6(4):6196–6203, 2021

    work page 2021

  43. [43]

    Jonathan Pirnay and Dominik G. Grimm. Self-improvement for neural combinatorial optimization: Sample without replacement, but improvement.Transactions on Machine Learning Research, 2024

    work page 2024

  44. [44]

    Path planning for spot spraying with UA Vs combining TSP and area coverages.Smart Agricultural Technology, page 100965, 2025

    Mogens Plessen. Path planning for spot spraying with UA Vs combining TSP and area coverages.Smart Agricultural Technology, page 100965, 2025

    work page 2025

  45. [45]

    GLNS: An effective large neighborhood search heuristic for the generalized traveling salesman problem.Computers & Operations Research, 87:1–19, 2017

    Stephen L Smith and Frank Imeson. GLNS: An effective large neighborhood search heuristic for the generalized traveling salesman problem.Computers & Operations Research, 87:1–19, 2017

    work page 2017

  46. [46]

    Contrastive multiview coding

    Yonglong Tian, Dilip Krishnan, and Phillip Isola. Contrastive multiview coding. InEuropean Conference on Computer Vision, pages 776–794. Springer, 2020

    work page 2020

  47. [47]

    The pickup and delivery traveling salesman problem with handling costs.European Journal of Operational Research, 257(1):118– 132, 2017

    Marjolein Veenstra, Kees Jan Roodbergen, Iris FA Vis, and Leandro C Coelho. The pickup and delivery traveling salesman problem with handling costs.European Journal of Operational Research, 257(1):118– 132, 2017

    work page 2017

  48. [48]

    Complete and near-optimal robotic crack coverage and filling in civil infrastructure.IEEE Transactions on Robotics, 40:2850–2867, 2024

    Vishnu Veeraraghavan, Kyle Hunte, Jingang Yi, and Kaiyan Yu. Complete and near-optimal robotic crack coverage and filling in civil infrastructure.IEEE Transactions on Robotics, 40:2850–2867, 2024

    work page 2024

  49. [49]

    Pointer networks

    Oriol Vinyals, Meire Fortunato, and Navdeep Jaitly. Pointer networks. InAdvances in Neural Information Processing Systems, volume 28, pages 2692–2700, 2015

    work page 2015

  50. [50]

    Xinyu Wang, Tsan-Ming Choi, Haikuo Liu, and Xiaohang Yue. A novel hybrid ant colony optimization algorithm for emergency transportation problems during post-disaster scenarios.IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48(4):545–556, 2016

    work page 2016

  51. [51]

    Simple statistical gradient-following algorithms for connectionist reinforcement learning.Machine Learning, 8(3):229–256, 1992

    Ronald J Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning.Machine Learning, 8(3):229–256, 1992

    work page 1992

  52. [52]

    L., and Zhou, Y

    Xuan Wu, Di Wang, Lijie Wen, Yubin Xiao, Chunguo Wu, Yuesong Wu, Chaoyu Yu, Douglas L Maskell, and You Zhou. Neural combinatorial optimization algorithms for solving vehicle routing problems: A comprehensive survey with perspectives.arXiv preprint arXiv:2406.00415, 2024

    work page arXiv 2024

  53. [53]

    Glop: Learning global partition and local construction for solving large-scale routing problems in real-time

    Haoran Ye, Jiarui Wang, Helan Liang, Zhiguang Cao, Yong Li, and Fanzhang Li. Glop: Learning global partition and local construction for solving large-scale routing problems in real-time. InProceedings of the AAAI Conference on Artificial Intelligence, 2024. 12

    work page 2024

  54. [54]

    Differential transformer

    Tianzhu Ye, Li Dong, Yuqing Xia, Yutao Sun, Yi Zhu, Gao Huang, and Furu Wei. Differential transformer. InInternational Conference on Learning Representations, 2025

    work page 2025

  55. [55]

    OPTFM: A scalable multi-view graph transformer for hierarchical pre-training in combinatorial optimization

    Hao Yuan, Wenli Ouyang, Changwen Zhang, Congrui Li, and Yong Sun. OPTFM: A scalable multi-view graph transformer for hierarchical pre-training in combinatorial optimization. InThe Thirty-ninth Annual Conference on Neural Information Processing Systems, 2025

    work page 2025

  56. [56]

    Zhongju Yuan, Genghui Li, Zhenkun Wang, Jianyong Sun, and Ran Cheng. RL-CSL: A combinatorial opti- mization method using reinforcement learning and contrastive self-supervised learning.IEEE Transactions on Emerging Topics in Computational Intelligence, 7(4):1010–1024, 2022

    work page 2022

  57. [57]

    Multi-region joint coverage for environmental monitoring using energy-constrained UA Vs.IEEE Transactions on Instrumentation and Measurement, 2025

    Changming Zhang, Caiyue Xu, Xu Cheng, Xin Li, Gang Li, and Bin He. Multi-region joint coverage for environmental monitoring using energy-constrained UA Vs.IEEE Transactions on Instrumentation and Measurement, 2025

    work page 2025

  58. [58]

    UDC: A unified neural divide-and-conquer framework for large-scale combinatorial optimization problems.Advances in Neural Information Processing Systems, 37:6081–6125, 2024

    Zhi Zheng, Changliang Zhou, Tong Xialiang, Mingxuan Yuan, and Zhenkun Wang. UDC: A unified neural divide-and-conquer framework for large-scale combinatorial optimization problems.Advances in Neural Information Processing Systems, 37:6081–6125, 2024

    work page 2024

  59. [59]

    MVMoE: Multi- task vehicle routing solver with mixture-of-experts

    Jianan Zhou, Zhiguang Cao, Yaoxin Wu, Wen Song, Yining Ma, Jie Zhang, and Xu Chi. MVMoE: Multi- task vehicle routing solver with mixture-of-experts. InInternational Conference on Machine Learning, 2024

    work page 2024

  60. [60]

    Wang Zhu, Liu Li, Long Teng, and Wen Yonglu. Multi-UA V reconnaissance task allocation for heteroge- neous targets using an opposition-based genetic algorithm with double-chromosome encoding.Chinese Journal of Aeronautics, 31(2):339–350, 2018

    work page 2018

  61. [61]

    Rbg: Hierarchically solving large-scale routing problems in logistic systems via reinforcement learning

    Zefang Zong, Hansen Wang, Jingwei Wang, Meng Zheng, and Yong Li. Rbg: Hierarchically solving large-scale routing problems in logistic systems via reinforcement learning. InProceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 4648–4658, 2022. 13 A Related Work A.1 Neural Routing Solver Pointer Networks [ 49] pioneered...

    work page arXiv 2022