Pith. sign in

REVIEW 3 major objections 7 minor 83 references

CAMP: Collaborative Attention Model with Profiles for Vehicle Routing Problems

T0 review · 3 major / 7 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read CAMP, a collaborative attention model with profiles, is claimed to be the first learning-based solver for the Profiled Vehicle Routing Problem, beating existing neural baselines on both preference and zone-constrained variants.

desk verdict CAMP is a plausible and well-engineered solution to a newly named problem, but the central 'consistently outperforms' claim rests on single-seed numbers and the reward indexing looks wrong. read the letter →

arxiv 2501.02977 v2 pith:JYHXIHKS submitted 2025-01-06 cs.MA cs.AI

Chuanbo Hua , Federico Berto , Jiwoo Son , Seunghyun Kang , Changhyun Kwon , Jinkyoo Park This is my paper · ORCID
classification cs.MAcs.AI
keywords profiledvehicleroutingproblemmulti-agentreinforcementlearningattentionmodelneuralcombinatorialoptimizationheterogeneousfleetpreferenceconstraintsparalleldecodingrouteconstruction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper introduces the Profiled Vehicle Routing Problem (PVRP), where each vehicle has client-specific preferences or constraints, and proposes CAMP, a multi-agent reinforcement learning solver that constructs routes for all vehicles in parallel. The paper claims CAMP is the first learning method for PVRP and that it consistently outperforms all neural solver baselines on both PVRP with preferences and PVRP with zone constraints, across all tested client and vehicle counts, while running in well under a second. A sympathetic reader would care because real fleets are heterogeneous: vehicles differ in access rights, driver familiarity, and regulatory permissions, and a learned solver that respects those profiles in real time could replace hand-tuned heuristics for routing.

What carries the argument

CAMP's core mechanism is a profile embedding that concatenates vehicle, client, and preference features into a combined representation for every vehicle-client pair, processed by multi-head attention. A bipartite graph message-passing step then lets vehicle and client embeddings exchange information across all profiles, so each vehicle's representation reflects the whole instance. During decoding, a transformer-based communication layer performs self-attention among vehicle queries at every step, and a multiple pointer mechanism produces logits for every vehicle-node pair in parallel; conflicts are resolved by prioritizing the vehicle with the highest action probability. This machinery is what allows heterogeneous vehicle profiles to be encoded and decoded jointly rather than sequentially.

What would settle it

Inspect the released code's reward calculation: if the preference term $\alpha p_{ik}$ in Eq. (21) is computed with $i$ equal to the current node on each route edge rather than the destination client $j$, then the reported PVRP-P rewards do not match the stated objective, and a corrected implementation would change both training and evaluation results.

Watch

Extended reading notes

Core claim

The central claim is that CAMP consistently outperforms all other neural solver baselines in experiments across all client and vehicle sizes for both PVRP-P and PVRP-ZC, while also beating a classical constraint-programming solver in solution quality and achieving inference times under a second. The paper further claims that no learning method existed for the PVRP before CAMP, making it the first learned approach to handle vehicle profiles on a per-client basis. The gains are attributed to three design choices: vehicle-specific profile embeddings in the encoder, a communication layer that lets agents share decisions during decoding, and a batched pointer mechanism that evaluates all vehicle actions in parallel.

Load-bearing premise

The reward function used to train and evaluate the model is assumed to implement the PVRP objective correctly; if the preference term $p_{ik}$ on each edge $(i,j)$ rewards the departure node rather than the served client, the learned policy optimizes a different objective.

Editorial extensions

If this is right

  • CAMP constructs routes for all vehicles in parallel, so inference time stays near-constant as fleet size grows, enabling real-time re-routing in dynamic settings.
  • Because the encoder embeds each vehicle profile separately, the same trained model can handle fleets of different sizes and client-specific preference patterns without retraining on fixed vehicle counts.
  • On the zone-constrained variant, invalid actions are masked in the environment, so the learned policy never proposes a route where a vehicle serves a prohibited client.
  • The reward-balancing scheme lets one policy handle multiple preference distributions, such as random, angle-based, cluster-based, and zone-based preferences, without favoring one reward scale.
  • If the empirical results hold, a learned construction method can outperform a classical constraint-programming solver in quality while running in fractions of a second, though a stronger heuristic solver that takes minutes per instance still has the best reported solutions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural extension implied by the paper is testing whether the profile-embedding communication layer transfers to other heterogeneous combinatorial optimization problems, such as vehicle routing with time windows, skills, or compatibility constraints.
  • The reported gains are shown on synthetic preference distributions; a stronger test would evaluate zero-shot generalization to instance sizes and preference patterns not seen during training.
  • The reward function in Eq. (21) credits the departure node's preference on each edge; if the intended preference is for the served client, the trained policy may be optimizing a slightly different objective, and re-running with the destination-client preference would settle whether the quality comparison is robust.
  • The conflict-resolution rule that chooses the highest-probability vehicle is a fixed heuristic; learning a non-greedy conflict handler or adding an improvement step after construction could close the remaining gap to the best heuristic solver.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 7 minor

Summary. The paper introduces the Profiled Vehicle Routing Problem (PVRP), a generalization of the heterogeneous capacitated VRP in which each vehicle k carries a per-client profile p_i^k that either adds a soft preference term (PVRP-P) or imposes a hard zone constraint (PVRP-ZC). The authors give an ILP formulation (Eqs. 1-11), an MDP reformulation (Section 4.1), and propose CAMP, an attention-based construction method that maintains a separate client embedding per vehicle profile, refines them with bipartite-graph message passing in the encoder, lets agents exchange messages at each decoding step through a transformer communication layer, and emits actions for all vehicles in parallel via a batched pointer with priority-based conflict resolution. Training uses REINFORCE with a SymNCO-style shared baseline and a reward-balancing normalization across preference distributions. The method is benchmarked on PVRP-P and PVRP-ZC at N=60/80/100 with m=3/5/7 vehicles against OR-Tools, HGS-PyVRP, and four neural baselines (ET, DPN, 2D-Ptr, PARCO). Section 5.2 claims CAMP consistently outperforms all neural baselines at every configuration; the reported inference times are sub-second (0.17-0.54 s), with a roughly 3-5% gap to HGS-PyVRP.

Significance. If the headline empirical claim holds, CAMP is a solid first learner for a practical VRP variant: it is, to the best of the paper's own survey, the first construction method designed for per-client vehicle profiles, it reaches about 3-5% gap to a state-of-the-art heuristic (HGS-PyVRP) in sub-second inference while beating OR-Tools under time limits, and the four ablations give credible evidence that the profile-specific embeddings, encoder communication, and reward balancing each contribute. The paper earns credit for matched training budgets across baselines, an external anchor in OR-Tools/HGS-PyVRP (which prevents the benchmark from being entirely self-defined), honest reporting that HGS remains superior, and a public code release. The principal weakness is statistical: the central claim is supported only by single point estimates per model, with the decisive margins often near 1-2.4%; two table cells even show the full model slightly worse than its own ablation. The contribution's value for the community depends on whether the headline margin exceeds training noise, so the empirical claim needs variance or significance evidence before the comparison can be taken at face value.

major comments (3)
  1. [Table 1 / Section 5.2] The central claim that 'CAMP consistently outperforms all other neural solver baselines in experiments across all client and vehicle sizes' is based on single point estimates: no number of training seeds, no standard deviation, and no significance test are reported anywhere in Section 5. I verified that at the point-estimate level CAMP (both greedy and sampling) beats ET, DPN, 2D-Ptr, and PARCO in every one of the 18 size/vehicle configurations, but several margins are small (e.g., PVRP-P N=80 m=5 sampling: 8.57 vs 8.66, about 1%; PVRP-ZC N=100 m=5 sampling: 19.26 vs 19.72, about 2.4%). Two cells in Table 1 go the other way against the paper's own ablation CAMP(-EC): PVRP-ZC N=60 m=3 sampling (CAMP 12.54 vs CAMP(-EC) 12.49) and PVRP-ZC N=60 m=7 greedy (CAMP 13.14 vs CAMP(-EC) 13.05), which shows that differences at the reported precision are comparable to training noise. Since the headline claim is the paper's main empirical contribution, the authors should report the number of seeds and mean plus/minus standard deviation for the main models (or provide paired significance tests), or explicitly soften the claim to the level of evidence actually provided.
  2. [Section 5.1] The aggregation that produces the PVRP-P numbers in Table 1 and Figure 3 is under-specified. The text says results are averaged over 'settings of alpha ranging from 0.0 to 0.2' but does not state the alpha values or their count, does not say which preference distributions (Random, Angle, Cluster, and/or Zone) enter the average, and does not state whether the tabulated 'cost' is the combined objective (duration minus alpha times preference) or the duration component alone. Because the ILP objective (Eq. 1) and the reward (Eq. 21) are linear in alpha for a fixed route, the reported gaps to HGS-PyVRP and the Pareto curves in Figure 3 depend on this grid, and different plausible choices give different averages. The same paragraph must specify how OR-Tools and HGS-PyVRP were given the preference-dependent objective for each alpha (e.g., per-vehicle cost matrices) and how the reported 'Gap(%)' was computed for the PVRP-P rows.
  3. [Section 4.2.2-4.2.3] Several load-bearing pieces of the architecture are not defined precisely enough to reimplement from the text. The message-passing function Phi in the bipartite encoder is never defined, even though Eqs. (26)-(28) describe the rest of the encoder in detail. In Eq. (27), h^k_k and h^k_i are used without defining which index is the vehicle and which is the current node, and the notation is not time-indexed. In Eq. (30), the matrix L is said to be a projection of the node embeddings h, but h is defined as a list of m profile-specific tensors h^k in R^{(m+n) x d_h}; the dimensions do not line up for the batched pointer as written. Finally, the factorization in Eq. (25) conditions each vehicle's action only on its own history, while the decoder (Eqs. 27-28) uses cross-vehicle communication; the factorization and the procedure should be made consistent. The open-source release mitigates this, but a methods paper should be self-contained.
minor comments (7)
  1. [Eq. (21)] The reward in Eq. (21) (and the objective in Eqs. (1) and (12)) credits p_i^k on edge (i,j), i.e., the preference of the departure node, although p_i^k is defined as the preference for serving client i. I checked whether this is a substantive error and concluded it is not: in a closed route the sum of departure-node preferences over all edges equals the sum of the served-client preferences over all visited clients (the two sums contain the same terms, since each client appears exactly once as a departure node), provided p_0^k = 0 for the depot. The authors should still fix the notation, defining p_0^k = 0 and either re-indexing to the destination client or adding a sentence noting the equivalence, because as written the reward appears to credit the wrong node, and Eq. (19) correctly uses the destination index p_j^k for the zone constraint, making the inconsistency visible.
  2. [Eqs. (13) and (9)] Notation slips in the ILP: Eq. (13) writes y_ik without the trip and vehicle indices used in the definition y^r_ik in Section 3.1, and Eq. (9) uses a single subtour-elimination variable w_i per node although the constraint is imposed separately for each trip r; w should be indexed by r (or the trips removed) for the formulation to be correct.
  3. [Abstract] The abstract's claim that 'no learning method exists to solve the more practical and challenging PVRP' is stronger than what the paper demonstrates: Section 5 trains and benchmarks four learning baselines on PVRP instances, so the intended claim must be that no learning method has been proposed specifically for PVRP. The related-work section also omits the closest problem neighbors (e.g., colored TSP variants and other per-agent-node-constrained routing problems), which should be discussed to scope the novelty claim.
  4. [Table 2] Section 5.3 states that the '- Vehicle-specific Profile Embedding' ablation 'corresponds to PARCO,' but Table 2 reports a duration gap of 6.85% for this ablation on PVRP-P N=100, while Table 1 lists PARCO's average PVRP-P gaps as 13.21% (greedy) and 6.44% (sampling); neither value matches, so the basis of Table 2's gap numbers (and the definition of the 'preference gap' column) must be stated.
  5. [Eq. (32)] In the REINFORCE estimator, B is defined but the summation index L (presumably the number of augmented solutions or samples per instance) is not; the notation should be defined in the text.
  6. [Section 4.2.3] Minor wording issues: the communication layer in Eq. (28) is said to capture 'intra-vehicle dynamic relationships' but it operates between agents and should read 'inter-vehicle'; the encoder text uses 'client' and 'customer' interchangeably; and Eq. (12) drops the trip superscripts on x relative to Eq. (1).
  7. [Figure 3] The Pareto plot does not state the set of alpha values used, and the panel labeled 'Average Preference Distribution' is not defined; the axis quantities ('Duration Gap', 'Preference Gap') also need explicit definitions, as neither gap measure is defined in the text.

Circularity Check

0 steps flagged · score 0.0 of 10

Empirical benchmark paper with external solvers; no circular derivation; self-citations are not load-bearing.

full rationale

The paper's central claim is an empirical benchmark result, not a derivation from fitted parameters. Section 5.2 states 'CAMP consistently outperforms all other neural solver baselines,' and the support is Table 1, where CAMP is compared against OR-Tools, HGS-PyVRP, and several neural baselines on externally evaluable instances. The objective and reward equations (Eq. 1, Eq. 12, Eq. 21) define the problem and training signal; no fitted constant is renamed as a prediction. The reward-balancing EMA (Eq. 33) and the weight alpha are stated hyperparameters, not quantities fit to the benchmark values. Self-citations appear for architectural and training components (PARCO [4] for parallel autoregressive decoding and conflict handling, SymNCO [29] for the symmetric baseline, RouteFinder [5] for reward balancing), but these are implementation devices with released code, and PARCO itself is included as a baseline, so CAMP's advantage over it is measured empirically rather than assumed. The ablation statement that removing CAMP's contributed components 'corresponds to PARCO' is an architectural description, not an imported uniqueness theorem. The skeptical concern that Table 1 reports single-seed point estimates without variance, including one cell where CAMP(s.) is worse than CAMP(-EC)(s.), is a statistical-evidence weakness and a correctness risk, not circularity; it does not make any equation reduce to its own input. The conclusion's limitation statement about HGS is likewise honest and does not create circular reasoning.

Assumptions & free parameters 4 free parameters · 3 assumptions · 0 invented entities

The central claim is empirical; no theoretical derivation requires free parameters. The listed hyperparameters are standard NCO choices. The main axiom risk is the reward indexing and the parallel decoding approximation.

free parameters (4)
  • alpha (preference weight) = 0.0 to 0.2
    Balances travel cost and preference in the PVRP-P objective (Eq. 12). Chosen by the authors for evaluation; results are averaged over this range, which could mask behavior at extreme values.
  • beta (EMA smoothing factor) = not reported
    Used in reward balancing (Eq. 33) to normalize rewards across preference distributions; the value is not given, so exact reproduction is impossible without the code.
  • logit scale C = 10
    Pointer mechanism scale (Eq. 30), taken from Bello et al.; standard, not fitted.
  • encoder layers / embedding dim / heads / FF dim = 3 / 128 / 8 / 512
    Architecture hyperparameters from prior NCO models; they affect performance but are standard choices, not tuned to PVRP.
assumptions (3)
  • domain assumption The PVRP formulation (Eq. 1) is a faithful model of practical profiled routing.
    Used throughout as the optimization target; if real-world profiling differs (e.g., preference is not additive), the problem definition is not validated.
  • domain assumption The reward in Eq. (21) is assumed to correctly index the client being served.
    As written, p_i k is attached to edge (i,j), crediting the origin instead of the destination; the paper's results depend on this indexing being a typo rather than the actual implementation.
  • ad hoc to paper Parallel autoregressive sampling with conflict resolution is a valid policy for the sequential PVRP MDP.
    The decoder samples actions for all vehicles simultaneously and resolves conflicts by probability priority (Section 4.2.3); this changes the MDP dynamics and is an approximation inherited from PARCO.

how reviews work

0 comments
Cite this review

Pith. "Pith review of CAMP: Collaborative Attention Model with Profiles for Vehicle Routing Problems." pith.science (2026). https://pith.science/paper/JYHXIHKS

@misc{pith2026250102977,
  author       = {Pith},
  title        = {Pith review of: CAMP: Collaborative Attention Model with Profiles for Vehicle Routing Problems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JYHXIHKS}},
  note         = {Machine review of arXiv:2501.02977}
}
read the original abstract

The profiled vehicle routing problem (PVRP) is a generalization of the heterogeneous capacitated vehicle routing problem (HCVRP) in which the objective is to optimize the routes of vehicles to serve client demands subject to different vehicle profiles, with each having a preference or constraint on a per-client basis. While existing learning methods have shown promise for solving the HCVRP in real-time, no learning method exists to solve the more practical and challenging PVRP. In this paper, we propose a Collaborative Attention Model with Profiles (CAMP), a novel approach that learns efficient solvers for PVRP using multi-agent reinforcement learning. CAMP employs a specialized attention-based encoder architecture to embed profiled client embeddings in parallel for each vehicle profile. We design a communication layer between agents for collaborative decision-making across profiled embeddings at each decoding step and a batched pointer mechanism to attend to the profiled embeddings to evaluate the likelihood of the next actions. We evaluate CAMP on two variants of PVRPs: PVRP with preferences, which explicitly influence the reward function, and PVRP with zone constraints with different numbers of agents and clients, demonstrating that our learned solvers achieve competitive results compared to both classical state-of-the-art neural multi-agent models in terms of solution quality and computational efficiency. We make our code openly available at https://github.com/ai4co/camp.

Figures

Figures reproduced from arXiv: 2501.02977 by the authors.

Figure 1
Figure 1. Practical examples of PVRPs. [Left] PVRP-P has [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Overview of CAMP. context, enabling a richer, more interconnected representation. The bipartite graph structure enables two-directional message passing: • Vehicle-to-Client Update: The vehicle embeddings are propagated to the client nodes they are connected to, ag￾gregating vehicle-specific information to update customer embeddings: ℎ ′𝑐 𝑗 = Φ(ℎ 𝑣 𝑖 , ℎ𝑐 𝑗 , ℎ′ 𝑖𝑗) • Client-to-Vehicle Update: The customer embeddings… view at source ↗
Figure 3
Figure 3. Pareto plot of VRP-P gaps at varying values of [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Visualization of CAMP solutions of PVRP-P with angle and cluster preference distribution. CAMP successfully routes according to the preference distribution. 5.3 Ablation Studies [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

83 extracted references · 45 canonical work pages

  1. [1]

    Satomi AIKO, Phathinan THAITHATKUL, and Yasuo Asakura. 2018. Incorporat- ing user preference into optimal vehicle routing problem of integrated sharing transport system. Asian Transport Studies 5, 1 (2018), 98–116

    2018

  2. [2]

    Irwan Bello, Hieu Pham, Quoc V Le, Mohammad Norouzi, and Samy Bengio

  3. [3]

    Yoshua Bengio, Andrea Lodi, and Antoine Prouvost. 2021. Machine learning for combinatorial optimization: a methodological tour d’horizon. European Journal of Operational Research 290, 2 (2021), 405–421

    2021

  4. [4]

    Federico Berto, Chuanbo Hua, Laurin Luttmann, Jiwoo Son, Junyoung Park, Kyuree Ahn, Changhyun Kwon, Lin Xie, and Jinkyoo Park. 2024. PARCO: Learn- ing Parallel Autoregressive Policies for Efficient Multi-Agent Combinatorial Opti- mization. arXiv preprint arXiv:2409.03811 (2024). https://github.com/ai4co/parco

    arXiv 2024

  5. [5]

    Federico Berto, Chuanbo Hua, Nayeli Gast Zepeda, André Hottung, Niels Wouda, Leon Lan, Kevin Tierney, and Jinkyoo Park. 2024. RouteFinder: Towards Foun- dation Models for Vehicle Routing Problems. In ICML 2024 Workshop on Foun- dation Models in the Wild (Oral) . https://openreview.net/forum?id=hCiaiZ6e4G https://github.com/ai4co/routefinder

    work page 2024

  6. [6]

    Jieyi Bi, Yining Ma, Jianan Zhou, Wen Song, Zhiguang Cao, Yaoxin Wu, and Jie Zhang. 2024. Learning to Handle Complex Constraints for Vehicle Routing Problems. arXiv preprint arXiv:2410.21066 (2024)

    work page Pith review arXiv 2024

  7. [7]

    Aigerim Bogyrbayeva, Taehyun Yoon, Hanbum Ko, Sungbin Lim, Hyokun Yun, and Changhyun Kwon. 2023. A deep reinforcement learning approach for solving the traveling salesman problem with drone. Transportation Research Part C: Emerging Technologies 148 (2023), 103981

    work page 2023

  8. [8]

    Kris Braekers, Katrien Ramaekers, and Inneke Van Nieuwenhuyse. 2016. The vehicle routing problem: State of the art classification and review. Computers & industrial engineering 99 (2016), 300–313

    work page 2016

Show all 83 references
  1. [9]

    Federico Julian Camerota Verdù, Lorenzo Castelli, and Luca Bortolussi. 2025. Scaling Combinatorial Optimization Neural Improvement Heuristics with On- line Search and Adaptation. In Proceedings of the AAAI Conference on Artificial Intelligence

    2025

  2. [10]

    Jinbiao Chen, Zizhen Zhang, Zhiguang Cao, Yaoxin Wu, Yining Ma, Te Ye, and Jiahai Wang. 2024. Neural multi-objective combinatorial optimization with diversity enhancement. Advances in Neural Information Processing Systems 36 (2024)

    2024

  3. [11]

    Elija Deineko and Carina Kehrt. 2024. Learn to Solve Vehicle Routing Problems ASAP: A Neural Optimization Approach for Time-Constrained Vehicle Routing Problems with Finite Vehicle Fleet. arXiv preprint arXiv:2411.04777 (2024)

    2024 arXiv

  4. [12]

    Darko Drakulic, Sofia Michel, and Jean-Marc Andreoli. 2024. GOAL: A Generalist Combinatorial Optimization Agent Learning. arXiv preprint arXiv:2406.15079 (2024)

    2024 arXiv

  5. [13]

    Darko Drakulic, Sofia Michel, Florian Mai, Arnaud Sors, and Jean-Marc An- dreoli. 2024. Bq-nco: Bisimulation quotienting for efficient neural combinatorial optimization. Advances in Neural Information Processing Systems 36 (2024)

    2024

  6. [14]

    Jonas K Falkner and Lars Schmidt-Thieme. 2020. Learning to solve vehicle routing problems with time windows through joint attention. arXiv preprint arXiv:2006.09100 (2020)

    2020 arXiv

  7. [15]

    Ricardo Gama, Daniel Fuertes, Carlos R del Blanco, and Hugo L Fernandes

  8. [16]

    Chengrui Gao, Haopu Shang, Ke Xue, Dong Li, and Chao Qian. 2023. Towards Generalizable Neural Solvers for Vehicle Routing Problems via Ensemble with Transferrable Local Policy. arXiv preprint arXiv:2308.14104 (2023)

    2023 arXiv

  9. [17]

    Bruce Golden, Arjang Assad, Larry Levy, and Filip Gheysens. 1984. The fleet size and mix vehicle routing problem. Computers & Operations Research 11, 1 (1984), 49–66

    1984

  10. [18]

    Nathan Grinsztajn, Daniel Furelos-Blanco, Shikha Surana, Clément Bonnet, and Tom Barrett. 2023. Winner takes it all: Training performant RL populations for combinatorial optimization. Advances in Neural Information Processing Systems 36 (2023), 48485–48509

    2023

  11. [19]

    André Hottung, Yeong-Dae Kwon, and Kevin Tierney. 2021. Efficient active search for combinatorial optimization problems. arXiv preprint arXiv:2106.05126 (2021)

    2021 arXiv

  12. [20]

    André Hottung and Kevin Tierney. 2020. Neural large neighborhood search for the capacitated vehicle routing problem. In ECAI 2020. IOS Press, 443–450

    2020

  13. [21]

    André Hottung, Paula Wong-Chung, and Kevin Tierney. 2025. Neural Decon- struction Search for Vehicle Routing Problems. arXiv preprint arXiv:2501.03715 (2025)

    2025

  14. [22]

    Qingchun Hou, Jingwei Yang, Yiqiang Su, Xiaoqing Wang, and Yuming Deng

  15. [23]

    Stuart Hunter

    J. Stuart Hunter. 1986. The Exponentially Weighted Moving Average. Journal of Quality Technology 18, 4 (1986), 203–210. https://doi.org/10.1080/00224065.1986. 11979014 arXiv:https://doi.org/10.1080/00224065.1986.11979014

    1986

  16. [24]

    Xia Jiang, Yaoxin Wu, Yuan Wang, and Yingqian Zhang. 2024. Unco: Towards unifying neural combinatorial optimization through large language model. arXiv preprint arXiv:2408.12214 (2024)

    2024 arXiv

  17. [25]

    Yuan Jiang, Zhiguang Cao, Yaoxin Wu, Wen Song, and Jie Zhang. 2023. Ensemble- based Deep Reinforcement Learning for Vehicle Routing Problems under Dis- tribution Shift. In Thirty-seventh Conference on Neural Information Processing Systems

    2023

  18. [26]

    Yan Jin, Yuandong Ding, Xuanhao Pan, Kun He, Li Zhao, Tao Qin, Lei Song, and Jiang Bian. 2023. Pointerformer: Deep Reinforced Multi-Pointer Transformer for the Traveling Salesman Problem. arXiv preprint arXiv:2304.09407 (2023)

    2023 arXiv

  19. [27]

    David S Johnson and Lyle A McGeoch. 1997. The traveling salesman problem: a case study. Local search in combinatorial optimization (1997), 215–310

    1997

  20. [28]

    Minsu Kim, Sanghyeok Choi, Jiwoo Son, Hyeonah Kim, Jinkyoo Park, and Yoshua Bengio. 2024. Ant Colony Sampling with GFlowNets for Combinatorial Opti- mization. arXiv preprint arXiv:2403.07041 (2024)

    2024 arXiv

  21. [29]

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

    2022

  22. [30]

    Diederik P Kingma and Jimmy Ba. 2014. Adam: A method for stochastic opti- mization. arXiv preprint arXiv:1412.6980 (2014)

    2014 arXiv

  23. [31]

    Detian Kong, Yining Ma, Zhiguang Cao, Tianshu Yu, and Jianhua Xiao. 2024. Efficient Neural Collaborative Search for Pickup and Delivery Problems. IEEE Transactions on Pattern Analysis and Machine Intelligence (2024)

    2024

  24. [32]

    Wouter Kool, Herke Van Hoof, and Max Welling. 2018. Attention, learn to solve routing problems! arXiv preprint arXiv:1803.08475 (2018)

    2018 arXiv

  25. [33]

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

    2020

  26. [34]

    Han Li, Fei Liu, Zhi Zheng, Yu Zhang, and Zhenkun Wang. 2024. CaDA: Cross- Problem Routing Solver with Constraint-Aware Dual-Attention. arXiv preprint arXiv:2412.00346 (2024)

    2024 arXiv

  27. [35]

    Jingwen Li, Yining Ma, Ruize Gao, Zhiguang Cao, Andrew Lim, Wen Song, and Jie Zhang. 2022. Deep reinforcement learning for solving the heterogeneous capacitated vehicle routing problem. IEEE Transactions on Cybernetics 52, 12 (2022), 13572–13585

    2022

  28. [36]

    Jingwen Li, Liang Xin, Zhiguang Cao, Andrew Lim, Wen Song, and Jie Zhang

  29. [37]

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

    2021

  30. [38]

    Yang Li, Jinpei Guo, Runzhong Wang, and Junchi Yan. 2024. From distribution learning in training to gradient search in testing for combinatorial optimization. Advances in Neural Information Processing Systems 36 (2024)

    2024

  31. [39]

    Yifu Li, Chenhao Zhou, Peixue Yuan, and Thi Tu Anh Ngo. 2023. Experience- based territory planning and driver assignment with predicted demand and driver present condition. Transportation research part E: logistics and transportation review 171 (2023), 103036

    2023

  32. [40]

    Xi Lin, Zhiyuan Yang, and Qingfu Zhang. 2022. Pareto set learning for neu- ral multi-objective combinatorial optimization. arXiv preprint arXiv:2203.15386 (2022)

    2022 arXiv

  33. [41]

    Zhuoyi Lin, Yaoxin Wu, Bangjian Zhou, Zhiguang Cao, Wen Song, Yingqian Zhang, and Senthilnath Jayavelu. 2024. Cross-Problem Learning for Solving Vehicle Routing Problems. IJCAI (2024)

    2024

  34. [42]

    Fei Liu, Xi Lin, Zhenkun Wang, Qingfu Zhang, Tong Xialiang, and Mingxuan Yuan. 2024. 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 . 1898–1908

    2024

  35. [43]

    Fei Liu, Tong Xialiang, Mingxuan Yuan, Xi Lin, Fu Luo, Zhenkun Wang, Zhichao Lu, and Qingfu Zhang. 2024. Evolution of Heuristics: Towards Efficient Auto- matic Algorithm Design Using Large Language Model. In Forty-first International Conference on Machine Learning

    2024

  36. [44]

    Qidong Liu, Chaoyue Liu, Shaoyao Niu, Cheng Long, Jie Zhang, and Mingliang Xu. 2024. 2D-Ptr: 2D Array Pointer Network for Solving the Heterogeneous Capacitated Vehicle Routing Problem. In Proceedings of the 23rd International Conference on Autonomous Agents and Multiagent Syst...

    2024

  37. [45]

    Manuel Lozano, Daniel Molina, and Francisco Herrera. 2011. Editorial scalability of evolutionary algorithms and other metaheuristics for large-scale continuous optimization problems. Soft computing 15 (2011), 2085–2087

    2011

  38. [46]

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

    2023

  39. [47]

    Yining Ma, Zhiguang Cao, and Yeow Meng Chee. 2024. Learning to search feasible and infeasible regions of routing problems with flexible neural k-opt. Advances in Neural Information Processing Systems 36 (2024)

    2024

  40. [48]

    Yining Ma, Jingwen Li, Zhiguang Cao, Wen Song, Le Zhang, Zhenghua Chen, and Jing Tang. 2021. Learning to iteratively solve routing problems with dual-aspect collaborative transformer. Advances in Neural Information Processing Systems 34 (2021), 11096–11107

    2021

  41. [49]

    1998.Combinatorial optimization: algorithms and complexity

    Christos H Papadimitriou and Kenneth Steiglitz. 1998.Combinatorial optimization: algorithms and complexity. Courier Corporation

    1998

  42. [50]

    Junyoung Park, Changhyun Kwon, and Jinkyoo Park. 2023. Learn to Solve the Min-max Multiple Traveling Salesmen Problem with Reinforcement Learning. In Proceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems. 878–886

    2023

  43. [51]

    Laurent Perron and Vincent Furnon. 2023. OR-Tools. Google

    2023

  44. [52]

    Vu Tuan Dat Pham, Long Doan, and Thi Thanh Binh Huynh. 2025. HSEvo: Ele- vating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMs. InProceedings of the AAAI Conference on Artificial Intelligence (AAAI). Association for the Advance...

    2025

  45. [53]

    Wei Qin, Zilong Zhuang, Zizhao Huang, and Haozhe Huang. 2021. A novel reinforcement learning-based hyper-heuristic for heterogeneous vehicle routing problem. Computers & Industrial Engineering 156 (2021), 107252

    2021

  46. [54]

    Jiwoo Son, Minsu Kim, Sanghyeok Choi, Hyeonah Kim, and Jinkyoo Park. 2024. Equity-Transformer: Solving NP-Hard Min-Max Routing Problems as Sequen- tial Generation with Equity Context. In Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 38. 20265–20273

    2024

  47. [55]

    Jiwoo Son, Minsu Kim, Hyeonah Kim, and Jinkyoo Park. 2023. Meta-sage: Scale meta-learning scheduled adaptation with guided exploration for mitigating scale shift on combinatorial optimization. In International Conference on Machine Learning. PMLR, 32194–32210

    2023

  48. [56]

    Zhiqing Sun, Zhuohan Li, Haoqing Wang, Di He, Zi Lin, and Zhihong Deng. 2019. Fast structured decoding for sequence models. Advances in Neural Information Processing Systems 32 (2019)

    2019

  49. [57]

    Zhiqing Sun and Yiming Yang. 2023. Difusco: Graph-based diffusion solvers for combinatorial optimization. In Thirty-seventh Conference on Neural Information Processing Systems

    2023

  50. [58]

    Team Locus. 2020. Zone-Based Routing is the Need of the Hour. https://www. locus.sh/blog/zone-based-routing-is-the-need-of-the-hour. Locus Blog (12 May 2020). https://www.locus.sh/blog/zone-based-routing-is-the-need-of-the-hour Accessed: 2024-10-17

    2020

  51. [59]

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. 2017. Attention is all you need. Advances in neural information processing systems 30 (2017)

    2017

  52. [60]

    José Manuel Vera and Andres G Abad. 2019. Deep reinforcement learning for routing a heterogeneous fleet of vehicles. In 2019 IEEE Latin American Conference on Computational Intelligence (LA-CCI). IEEE, 1–6

    2019

  53. [61]

    Thibaut Vidal. 2022. Hybrid genetic search for the CVRP: Open-source implemen- tation and SWAP* neighborhood. Computers & Operations Research 140 (2022), 105643

    2022

  54. [62]

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

    2015

  55. [63]

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

    1992

  56. [64]

    Niels A Wouda, Leon Lan, and Wouter Kool. 2024. PyVRP: A high-performance VRP solver package. INFORMS Journal on Computing (2024)

    2024

  57. [65]

    Yubin Xiao, Di Wang, Huanhuan Chen, Boyang Li, Wei Pang, Xuan Wu, Hao Li, Dong Xu, Yanchun Liang, and You Zhou. 2023. Reinforcement learning- based non-autoregressive solver for traveling salesman problems. arXiv preprint arXiv:2308.00560 (2023)

    2023 arXiv

  58. [66]

    Zhongxia Yan and Cathy Wu. 2024. Neural Neighborhood Search for Multi-agent Path Finding. In The Twelfth International Conference on Learning Representations

    2024

  59. [67]

    Yunhao Yang and Andrew Whinston. 2023. A survey on reinforcement learn- ing for combinatorial optimization. In 2023 IEEE World Conference on Applied Intelligence and Computing (AIC) . IEEE, 131–136

    2023

  60. [68]

    Haoran Ye, Jiarui Wang, Zhiguang Cao, Federico Berto, Chuanbo Hua, Haeyeon Kim, Jinkyoo Park, and Guojie Song. 2024. ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution. In Advances in Neural Information Processing Systems. https://github.com/ai4co/reevo

    2024

  61. [69]

    Haoran Ye, Jiarui Wang, Zhiguang Cao, Helan Liang, and Yong Li. 2023. DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization. In Advances in Neural Information Processing Systems

    2023

  62. [70]

    Haoran Ye, Jiarui Wang, Helan Liang, Zhiguang Cao, Yong Li, and Fanzhang Li. 2024. 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

  63. [71]

    Ke Zhang, Fang He, Zhengchao Zhang, Xi Lin, and Meng Li. 2020. Multi-vehicle routing problems with soft time windows: A multi-agent reinforcement learning approach. Transportation Research Part C: Emerging Technologies 121 (2020), 102861

    2020

  64. [72]

    Zhi Zheng, Shunyu Yao, Zhenkun Wang, Tong Xialiang, Mingxuan Yuan, and Ke Tang. 2024. DPN: Decoupling Partition and Navigation for Neural Solvers of Min-max Vehicle Routing Problems. In Forty-first International Conference on Machine Learning. https://openreview.net/forum?id=a...

    2024

  65. [73]

    Zhi Zheng, Changliang Zhou, Tong Xialiang, Mingxuan Yuan, and Zhenkun Wang. 2024. UDC: A unified neural divide-and-conquer framework for large-scale combinatorial optimization problems. arXiv preprint arXiv:2407.00312 (2024)

    2024 arXiv

  66. [74]

    Hongsheng Zhong, Randolph W Hall, and Maged Dessouky. 2007. Territory planning and vehicle dispatching with driver learning. Transportation Science 41, 1 (2007), 74–89

    2007

  67. [75]

    Jianan Zhou, Zhiguang Cao, Yaoxin Wu, Wen Song, Yining Ma, Jie Zhang, and Chi Xu. 2024. MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts. arXiv preprint arXiv:2405.01029 (2024)

    2024 arXiv

  68. [76]

    Jianan Zhou, Yaoxin Wu, Zhiguang Cao, Wen Song, Jie Zhang, and Zhenghua Chen. 2023. Learning large neighborhood search for vehicle routing in airport ground handling. IEEE Transactions on Knowledge and Data Engineering (2023)

    2023

  69. [77]

    Jianan Zhou, Yaoxin Wu, Zhiguang Cao, Wen Song, Jie Zhang, and Zhiqi Shen

  70. [78]

    Zefang Zong, Meng Zheng, Yong Li, and Depeng Jin. 2022. Mapdp: Cooperative multi-agent reinforcement learning to solve pickup and delivery problems. In Proceedings of the AAAI Conference on Artificial Intelligence , Vol. 36. 9980–9988

    2022

  71. [82]

    arXiv preprint arXiv:2410.04968 (2024)

    Collaboration! Towards Robust Neural Methods for Routing Problems. arXiv preprint arXiv:2410.04968 (2024)

    2024 arXiv

  72. [2016]

    arXiv preprint arXiv:1611.09940 (2016)

    Neural combinatorial optimization with reinforcement learning. arXiv preprint arXiv:1611.09940 (2016)

    2016 arXiv

  73. [2021]

    IEEE Transactions on Intelligent Transportation Systems 23, 3 (2021), 2306–2315

    Heterogeneous attentions for solving pickup and delivery problem via deep reinforcement learning. IEEE Transactions on Intelligent Transportation Systems 23, 3 (2021), 2306–2315

    2021

  74. [2023]

    In The Eleventh International Conference on Learning Representations

    Generalize learned heuristics to solve large-scale vehicle routing problems in real-time. In The Eleventh International Conference on Learning Representations

  75. [2024]

    arXiv preprint arXiv:2411.14411 (2024)

    Multi-Agent Environments for Vehicle Routing Problems. arXiv preprint arXiv:2411.14411 (2024)

    2024 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.