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arxiv: 2604.10652 · v1 · submitted 2026-04-12 · 💻 cs.AI · cs.LG

Enhancing Cross-Problem Vehicle Routing via Federated Learning

Xiangchi Meng , Jianan Zhou , Jie Gao , Yifan Lu , Yaoxin Wu , Gonglin Yuan , Yaqing Hou This is my paper

Pith reviewed 2026-05-10 15:34 UTC · model grok-4.3

classification 💻 cs.AI cs.LG
keywords vehicle routing problemsfederated learningneural combinatorial optimizationcross-problem learningpre-trainingfine-tuninggeneralizationlogistics optimization
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The pith

A federated learning framework that pre-trains across multiple vehicle routing problems then fine-tunes per problem improves performance and generalization to new constraint sets.

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

The paper introduces a Multi-problem Pre-train then Single-problem Fine-tune framework with Federated Learning, called MPSF-FL, to address performance drops when neural solvers move from simple vehicle routing variants to ones with added complex constraints. It uses a shared global model built through federated averaging so that each local model keeps broad routing knowledge while adapting to its own target problem. A reader would care because vehicle routing sits at the center of logistics efficiency, and reliable transfer across constraint types could reduce the need to rebuild solvers from scratch for every new real-world rule set. Experiments reported in the work show gains both on known problem families and on problems held out during training.

Core claim

The central claim is that federated averaging of local models pre-trained on diverse vehicle routing instances produces a global model whose common VRP knowledge can be retained by local models during single-problem fine-tuning, allowing effective adaptation to downstream problems that carry heterogeneous complex constraints without the usual transfer degradation.

What carries the argument

The MPSF-FL framework, in which a federated global model aggregates common VRP knowledge from multiple pre-training problems and supplies it to local models that then fine-tune on single downstream problems with their own constraints.

If this is right

  • Local models achieve higher solution quality on their target vehicle routing problems.
  • Performance remains stable when moving from simple to complex constraint variants.
  • Generalization improves on vehicle routing problems never encountered during pre-training.
  • Knowledge sharing across problems occurs without requiring full retraining for each new constraint set.

Where Pith is reading between the lines

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

  • The same pre-train then federated fine-tune pattern might reduce data requirements when applying neural solvers to other combinatorial problems that share underlying structure.
  • In deployed logistics systems the global model could be updated periodically from new route data collected across clients while each client keeps its local fine-tuning private.
  • Testing the framework on larger-scale instances or on problems whose constraints combine multiple new features at once would clarify the limits of the retained common knowledge.

Load-bearing premise

Averaging the parameters of local models creates a global model whose shared routing knowledge transfers to new problems with different complex constraints without causing performance loss.

What would settle it

Apply the full MPSF-FL pipeline to a collection of simple VRPs, then evaluate the fine-tuned models on a held-out VRP family whose constraints differ markedly in type and complexity; if solution quality or generalization metrics fall below those of non-federated baselines, the transfer benefit does not hold.

Figures

Figures reproduced from arXiv: 2604.10652 by Gonglin Yuan, Jianan Zhou, Jie Gao, Xiangchi Meng, Yaoxin Wu, Yaqing Hou, Yifan Lu.

Figure 1
Figure 1. Figure 1: Performance comparison of CPL. Neural solvers (with [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Generalization performance decay when a pre-trained uni [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Our “Multi-problem Pre-train, then Single-problem Fine-tune” framework with Federated Learning (MPSF-FL) for VRPs, taking [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Vehicle routing problems (VRPs) constitute a core optimization challenge in modern logistics and supply chain management. The recent neural combinatorial optimization (NCO) has demonstrated superior efficiency over some traditional algorithms. While serving as a primary NCO approach for solving general VRPs, current cross-problem learning paradigms are still subject to performance degradation and generalizability decay, when transferring from simple VRP variants to those involving different and complex constraints. To strengthen the paradigms, this paper offers an innovative "Multi-problem Pre-train, then Single-problem Fine-tune" framework with Federated Learning (MPSF-FL). This framework exploits the common knowledge of a federated global model to foster efficient cross-problem knowledge sharing and transfer among local models for single-problem fine-tuning. In this way, local models effectively retain common VRP knowledge from up-to-date global model, while being efficiently adapted to downstream VRPs with heterogeneous complex constraints. Experimental results demonstrate that our framework not only enhances the performance in diverse VRPs, but also improves the generalizability in unseen problems.

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

0 major / 3 minor

Summary. The paper introduces the MPSF-FL framework, which performs multi-problem pre-training via federated averaging to build a global model capturing common VRP knowledge, followed by single-problem fine-tuning of local models on downstream VRPs with heterogeneous constraints. The central claim, supported by experimental results, is that this yields improved performance on diverse VRPs and better generalization to unseen problems compared to standard cross-problem learning paradigms.

Significance. If the empirical results hold, the work offers a meaningful advance in neural combinatorial optimization by demonstrating how federated learning can enable effective knowledge sharing and transfer across VRP variants without data centralization. This addresses a key limitation of performance degradation when moving from simple to complex constraints and has practical value for privacy-sensitive logistics applications. The empirical validation on both in-distribution and out-of-distribution cases is a strength.

minor comments (3)
  1. [Abstract] The abstract asserts performance gains and better generalization yet provides no quantitative results, baselines, dataset details, or ablation studies. Adding at least one key metric or reference to the experimental section would improve immediate readability.
  2. [§3] In the methods description of the fine-tuning stage, explicitly state how the global model parameters are used to initialize or regularize the local models and whether any additional loss terms are introduced to retain common knowledge.
  3. [Figures] Figure captions and legends should more clearly distinguish the different VRP variants and constraint types used in the experiments.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary of our MPSF-FL framework and for recognizing its potential contribution to neural combinatorial optimization through federated learning for cross-problem VRP solving. The recommendation for minor revision is noted, and we will address any minor points in the revised manuscript.

Circularity Check

0 steps flagged

No significant circularity in derivation or claims

full rationale

The paper introduces the MPSF-FL framework as a high-level architectural approach combining multi-problem pre-training with federated averaging and single-problem fine-tuning for VRPs. All performance claims are grounded in experimental results on in-distribution and out-of-distribution instances rather than any mathematical derivation, prediction step, or first-principles result. No equations appear that could reduce a claimed improvement to a fitted parameter or self-referential quantity, and no self-citation load-bearing uniqueness theorems or ansatzes are invoked. The argument is therefore self-contained as an empirical proposal whose validity can be assessed directly from the reported benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are stated in the provided text.

pith-pipeline@v0.9.0 · 5491 in / 993 out tokens · 24004 ms · 2026-05-10T15:34:54.264751+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

44 extracted references · 44 canonical work pages

  1. [1]

    Le, Mohammad Norouzi, and Samy Bengio

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

    work page 2017

  2. [2]

    RouteFinder: Towards Foundation Models for Vehicle Routing Problems

    Federico Berto, Chuanbo Hua, Nayeli Gast Zepeda, Andr \'e 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

  3. [3]

    Learning to handle complex constraints for vehicle routing problems

    Jieyi Bi, Yining Ma, Jianan Zhou, Wen Song, Zhiguang Cao, Yaoxin Wu, and Jie Zhang. Learning to handle complex constraints for vehicle routing problems. In Advances in Neural Information Processing Systems , 2024

    work page 2024

  4. [4]

    Vehicle routing problems for city logistics

    Diego Cattaruzza, Nabil Absi, Dominique Feillet, and Jes \'u s Gonz \'a lez-Feliu. Vehicle routing problems for city logistics. EURO Journal on Transportation and Logistics , 6(1):51--79, 2017

    work page 2017

  5. [5]

    Personalized federated learning with theoretical guarantees: A model-agnostic meta-learning approach

    Alireza Fallah, Aryan Mokhtari, and Asuman Ozdaglar. Personalized federated learning with theoretical guarantees: A model-agnostic meta-learning approach. Advances in neural information processing systems , 33:3557--3568, 2020

    work page 2020

  6. [6]

    Or-tools routing library, 2023

    Vincent Furnon and Laurent Perron. Or-tools routing library, 2023

    work page 2023

  7. [7]

    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. In Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence , pages 6914--6922, 2024

    work page 2024

  8. [8]

    Shield: Multi-task multi-distribution vehicle routing solver with sparsity and hierarchy

    Yong Liang Goh, Zhiguang Cao, Yining Ma, Jianan Zhou, Mohammed Haroon Dupty, and Wee Sun Lee. Shield: Multi-task multi-distribution vehicle routing solver with sparsity and hierarchy. In Aarti Singh, Maryam Fazel, Daniel Hsu, Simon Lacoste-Julien, Felix Berkenkamp, Tegan Maharaj, Kiri Wagstaff, and Jerry Zhu, editors, Proceedings of the 42nd International...

    work page 2025

  9. [9]

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

    Nathan Grinsztajn, Daniel Furelos-Blanco, Shikha Surana, Cl \'e ment Bonnet, and Tom Barrett. Winner takes it all: Training performant rl populations for combinatorial optimization. Advances in Neural Information Processing Systems , 36:48485--48509, 2023

    work page 2023

  10. [10]

    Polynet: Learning diverse solution strategies for neural combinatorial optimization

    Andr \'e Hottung, Mridul Mahajan, and Kevin Tierney. Polynet: Learning diverse solution strategies for neural combinatorial optimization. In The Thirteenth International Conference on Learning Representations , 2025

    work page 2025

  11. [11]

    Fft-moe: Efficient federated fine-tuning for foundation models via large-scale sparse moe under heterogeneous edge

    Gang Hu, Yinglei Teng, Pengfei Wu, and Nan Wang. Fft-moe: Efficient federated fine-tuning for foundation models via large-scale sparse moe under heterogeneous edge. arXiv preprint arXiv:2508.18663 , 2025

    work page arXiv 2025

  12. [12]

    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. In International Conference on Learning Representations , 2025

    work page 2025

  13. [13]

    Editing models with task arithmetic

    Gabriel Ilharco, Marco Tulio Ribeiro, Mitchell Wortsman, Ludwig Schmidt, Hannaneh Hajishirzi, and Ali Farhadi. Editing models with task arithmetic. In The Eleventh International Conference on Learning Representations , 2023

    work page 2023

  14. [14]

    Sym-nco: Leveraging symmetricity for neural combinatorial optimization

    Minsu Kim, Junyoung Park, and Jinkyoo Park. Sym-nco: Leveraging symmetricity for neural combinatorial optimization. Advances in Neural Information Processing Systems , 35:1936--1949, 2022

    work page 1936

  15. [15]

    Vehicle routing problem and related algorithms for logistics distribution: A literature review and classification

    Grigorios D Konstantakopoulos, Sotiris P Gayialis, and Evripidis P Kechagias. Vehicle routing problem and related algorithms for logistics distribution: A literature review and classification. Operational research , 22(3):2033--2062, 2022

    work page 2033

  16. [16]

    Attention, learn to solve routing problems! In International Conference on Learning Representations , 2019

    Wouter Kool, Herke van Hoof, and Max Welling. Attention, learn to solve routing problems! In International Conference on Learning Representations , 2019

    work page 2019

  17. [17]

    Pomo: Policy optimization with multiple optima for reinforcement learning

    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

  18. [18]

    Matrix encoding networks for neural combinatorial optimization

    Yeong-Dae Kwon, Jinho Choo, Iljoo Yoon, Minah Park, Duwon Park, and Youngjune Gwon. Matrix encoding networks for neural combinatorial optimization. In A. Beygelzimer, Y. Dauphin, P. Liang, and J. Wortman Vaughan, editors, Advances in Neural Information Processing Systems , 2021

    work page 2021

  19. [19]

    Federated optimization in heterogeneous networks

    Tian Li, Anit Kumar Sahu, Manzil Zaheer, Maziar Sanjabi, Ameet Talwalkar, and Virginia Smith. Federated optimization in heterogeneous networks. In I. Dhillon, D. Papailiopoulos, and V. Sze, editors, Proceedings of Machine Learning and Systems , volume 2, pages 429--450, 2020

    work page 2020

  20. [20]

    Learning to delegate for large-scale vehicle routing

    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

  21. [21]

    Ca DA : Cross-problem routing solver with constraint-aware dual-attention

    Han Li, Fei Liu, Zhi Zheng, Yu Zhang, and Zhenkun Wang. Ca DA : Cross-problem routing solver with constraint-aware dual-attention. In Forty-second International Conference on Machine Learning , 2025

    work page 2025

  22. [22]

    Bopo: Neural combinatorial optimization via best-anchored and objective-guided preference optimization

    Zijun Liao, Jinbiao Chen, Debing Wang, Zizhen Zhang, and Jiahai Wang. Bopo: Neural combinatorial optimization via best-anchored and objective-guided preference optimization. In International Conference on Machine Learning , 2025

    work page 2025

  23. [23]

    Cross-problem learning for solving vehicle routing problems

    Zhuoyi Lin, Yaoxin Wu, Bangjian Zhou, Zhiguang Cao, Wen Song, Yingqian Zhang, and Senthilnath Jayavelu. Cross-problem learning for solving vehicle routing problems. In Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence , pages 6958--6966, 2024

    work page 2024

  24. [24]

    Multi-task learning for routing problem with cross-problem zero-shot generalization

    Fei Liu, Xi Lin, Zhenkun Wang, Qingfu Zhang, Tong Xialiang, and Mingxuan Yuan. Multi-task learning for routing problem with cross-problem zero-shot generalization. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining , pages 1898--1908, 2024

    work page 1908

  25. [25]

    Decoupled weight decay regularization

    Ilya Loshchilov and Frank Hutter. Decoupled weight decay regularization. In International Conference on Learning Representations , 2017

    work page 2017

  26. [26]

    Neural combinatorial optimization with heavy decoder: Toward large scale generalization

    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

  27. [27]

    COE xpander: Adaptive solution expansion for combinatorial optimization

    Jiale Ma, Wenzheng Pan, Yang Li, and Junchi Yan. COE xpander: Adaptive solution expansion for combinatorial optimization. In Forty-second International Conference on Machine Learning , 2025

    work page 2025

  28. [28]

    Communication-efficient learning of deep networks from decentralized data

    Brendan McMahan, Eider Moore, Daniel Ramage, Seth Hampson, and Blaise Aguera y Arcas. Communication-efficient learning of deep networks from decentralized data. In Artificial intelligence and statistics , pages 1273--1282. PMLR, 2017

    work page 2017

  29. [29]

    Flis: Clustered federated learning via inference similarity for non-iid data distribution

    Mahdi Morafah, Saeed Vahidian, Weijia Wang, and Bill Lin. Flis: Clustered federated learning via inference similarity for non-iid data distribution. IEEE Open Journal of the Computer Society , 4:109--120, 2023

    work page 2023

  30. [30]

    Reinforcement learning for solving the vehicle routing problem

    Mohammadreza Nazari, Afshin Oroojlooy, Lawrence Snyder, and Martin Tak \'a c. Reinforcement learning for solving the vehicle routing problem. In Advances in Neural Information Processing Systems , page 9861–9871, 2018

    work page 2018

  31. [31]

    Multi-task vehicle routing solver via mixture of specialized experts under state-decomposable mdp

    Yuxin Pan, Zhiguang Cao, Liu Liu, Peilin Zhao, Yize Chen, Fangzhen Lin, et al. Multi-task vehicle routing solver via mixture of specialized experts under state-decomposable mdp. In The Thirty-ninth Annual Conference on Neural Information Processing Systems , 2015

    work page 2015

  32. [32]

    Clustered federated learning: Model-agnostic distributed multitask optimization under privacy constraints

    Felix Sattler, Klaus-Robert M \"u ller, and Wojciech Samek. Clustered federated learning: Model-agnostic distributed multitask optimization under privacy constraints. IEEE transactions on neural networks and learning systems , 32(8):3710--3722, 2020

    work page 2020

  33. [33]

    Federated multi-task learning

    Virginia Smith, Chao-Kai Chiang, Maziar Sanjabi, and Ameet S Talwalkar. Federated multi-task learning. Advances in neural information processing systems , 30, 2017

    work page 2017

  34. [34]

    Hybrid genetic search for the cvrp: Open-source implementation and swap* neighborhood

    Thibaut Vidal. Hybrid genetic search for the cvrp: Open-source implementation and swap* neighborhood. Computers & Operations Research , 140:105643, 2022

    work page 2022

  35. [35]

    Pointer networks

    Oriol Vinyals, Meire Fortunato, and Navdeep Jaitly. Pointer networks. Advances in neural information processing systems , 28, 2015

    work page 2015

  36. [36]

    Fedftha: A fine-tuning and head aggregation method in federated learning

    Yansong Wang, Hui Xu, Waqar Ali, Miaobo Li, Xiangmin Zhou, and Jie Shao. Fedftha: A fine-tuning and head aggregation method in federated learning. IEEE Internet of Things Journal , 10(14):12749--12762, 2023

    work page 2023

  37. [37]

    Flora: Federated fine-tuning large language models with heterogeneous low-rank adaptations

    Ziyao Wang, Zheyu Shen, Yexiao He, Guoheng Sun, Hongyi Wang, Lingjuan Lyu, and Ang Li. Flora: Federated fine-tuning large language models with heterogeneous low-rank adaptations. Advances in Neural Information Processing Systems , 37:22513--22533, 2024

    work page 2024

  38. [38]

    Simple statistical gradient-following algorithms for connectionist reinforcement learning

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

    work page 1992

  39. [39]

    Pyvrp: A high-performance vrp solver package

    Niels A Wouda, Leon Lan, and Wouter Kool. Pyvrp: A high-performance vrp solver package. INFORMS Journal on Computing , 36(4):943--955, 2024

    work page 2024

  40. [40]

    TIES -merging: Resolving interference when merging models

    Prateek Yadav, Derek Tam, Leshem Choshen, Colin Raffel, and Mohit Bansal. TIES -merging: Resolving interference when merging models. In Thirty-seventh Conference on Neural Information Processing Systems , 2023

    work page 2023

  41. [41]

    Language models are super mario: Absorbing abilities from homologous models as a free lunch

    Le Yu, Bowen Yu, Haiyang Yu, Fei Huang, and Yongbin Li. Language models are super mario: Absorbing abilities from homologous models as a free lunch. In Forty-first International Conference on Machine Learning , 2024

    work page 2024

  42. [42]

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

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

    work page 2024

  43. [43]

    Federated cinn clustering for accurate clustered federated learning

    Yuhao Zhou, Minjia Shi, Yuxin Tian, Yuanxi Li, Qing Ye, and Jiancheng Lv. Federated cinn clustering for accurate clustered federated learning. In ICASSP 2024-2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) , pages 5590--5594. IEEE, 2024

    work page 2024

  44. [44]

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