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REVIEW 4 major objections 5 minor 43 references

DeepMDV: Global Spatial Matching for Multi-depot Vehicle Routing Problems

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read DeepMDV claims a learned multi-depot routing solver that scales to 1,000 customers and beats a strong classical heuristic on large instances.

desk verdict Solid, incremental neural MDVRP solver with a strong but over-scoped HGS comparison; deserves conditional acceptance after code release and fairer baselines. read the letter →

arxiv 2411.17080 v3 pith:MWWKLTFP submitted 2024-11-26 cs.DB cs.AIcs.LG

Saeed Nasehi , Farhana Choudhury , Egemen Tanin , Majid Sarvi This is my paper · ORCID
classification cs.DBcs.AIcs.LG MSC 90C2790B0668T07
keywords SpatialdatamanagementVehicleRoutingProblemDeepreinforcementlearningMulti-depotVRPTransformerdecoderNeuralcombinatorialoptimizationScalabilityGeneralization
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

The paper presents DeepMDV, a deep-reinforcement-learning solver for the Multi-Depot Vehicle Routing Problem (MDVRP), and claims it is the first learning-based method that scales to 1,000 customers while generalizing to depot counts it never saw during training. The central idea is to split the problem into two decoupled tasks: an interdependent partitioner that globally matches customers to depot-tours, and an independent router that sequences visits within each tour with a TSP solver. On synthetic, skewed, and real-world benchmarks, DeepMDV reports better distances than every learning-based baseline, and on 700- to 1,000-customer instances it reports improvements over HGS, a strong classical metaheuristic, while producing each solution in seconds. If these results hold, near-optimal multi-depot delivery planning becomes practical at urban scale without retraining for new depot configurations.

What carries the argument

The load-bearing object is the decoder made of the Tour Selection and Local Context Generation Layer (TSLCGL) paired with the Node Selection Layer (NSL). TSLCGL looks at the $k$ nearest unvisited customers around each active tour's last node, computes a local context by multi-head attention over every active tour's state (depot embedding, last node, remaining capacity), and produces a compatibility score for choosing the next tour; NSL then picks the next customer for that tour using the enriched embeddings. A second load-bearing component is the closed-form estimate of the maximum number of tours, $\lceil \sum_i \delta_i / C \rceil + |D|$, which masks when new tours can start and when active tours can return to the depot. The three-step training procedure, in which the router is first trained on uniform TSP instances, the partitioner is then trained using that router's tour lengths as reward, and the router is finally fine-tuned on the partitioner's tours, is what lets the router cope with the non-uniform spatial distributions found inside large tours.

What would settle it

Build a benchmark instance whose proven optimum needs a single depot to run two partially loaded tours concurrently (for example, two dense clusters near the same depot, total demand just over one vehicle capacity, and the other depots far away), then compare DeepMDV's total distance with HGS or an exact solver. If DeepMDV's objective falls well behind HGS on such instances, the one-active-tour-per-depot restriction is the limiting factor.

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Extended reading notes

Core claim

DeepMDV's claim is that customer-to-depot assignment and tour formation in the MDVRP can be learned as a global spatial matching problem, decoupled from intra-tour sequencing, without sacrificing solution quality. The partitioner is a transformer-based policy that, at each decoding step, first selects the most compatible active tour and then the best unvisited customer for it; a local-context layer evaluates each candidate customer against all active tours instead of only the selected one, so the assignment reflects the whole system state. The independent router then solves a TSP per tour, so any TSP solver can be plugged in, with AM used during training and LKH3 at inference. The paper reports that this architecture outperforms all learning-based baselines across 2 to 4 depots and 100 to 1,000 customers, and that on 1,000-customer instances it improves on HGS by at least 3.25%, with each instance solved in about 5 seconds; it also reports that the same model, trained on two depots, transfers to one, three, or four depots and to single-depot VRP without retraining.

Load-bearing premise

DeepMDV assumes only one active tour per depot at a time, so it cannot represent optimal solutions in which a depot runs two partially filled tours simultaneously.

Editorial extensions

If this is right

  • If the reported results hold, logistics operators can get near-optimal multi-depot routes for 1,000-customer instances in seconds, where classical metaheuristics take hours or run out of memory.
  • A single model trained with two depots transfers to one, three, or four depots with small gaps, so deployments with changing depot counts do not need retraining.
  • Because routing is a separate TSP subproblem, any future improvement in TSP solving translates directly into better DeepMDV solutions without changing the partitioner.
  • DeepMDV retains most of its advantage on skewed customer distributions and real-world instances, where distance-based clustering baselines degrade, suggesting it is suited to heterogeneous urban logistics.
  • A model trained for MDVRP also beats VRP-specific learned solvers on large single-depot instances, so the same method can serve both multi-depot and single-depot routing.

Reading between the lines

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

  • A natural test of the paper's central mechanism is whether the one-active-tour-per-depot restriction ever costs optimality: on instances whose optimum requires a depot to run two partially filled tours simultaneously, DeepMDV cannot represent that solution, and its measured edge over HGS could shrink.
  • The polar-coordinate input encoding, which makes representations invariant to shifts, rotations, and scaling, suggests the model might transfer across different map scales or coordinate systems without fine-tuning, though the paper does not isolate this effect.
  • The tour-count formula $\lceil \sum_i \delta_i / C \rceil + |D|$ generalizes a known VRP bound and could be adapted to time windows or heterogeneous fleets as a cheap feasibility mask for other learned solvers.
  • If the claimed scaling is robust, the partitioner could be stacked with a portfolio of TSP solvers selected by instance geometry, turning DeepMDV into a meta-solver whose quality tracks the best available router.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper proposes DeepMDV, a two-stage deep reinforcement learning framework for the Multi-Depot Vehicle Routing Problem (MDVRP). A transformer-based partitioner assigns customers to depots and tours through a global spatial matching mechanism, and an independent router (AM or LKH3) solves the resulting TSP subproblems. The method uses a three-step training procedure and a proposed formula for an upper bound on the number of tours. Experiments on synthetic uniform, skewed, and real-world datasets report that DeepMDV outperforms learning-based baselines at all scales and, for 1,000-customer instances, surpasses HGS by 3.25% or more, while also generalizing to varying depot counts and to single-depot VRP.

Significance. If the empirical claims hold under fair comparison, this is a strong practical contribution: it is among the first learning-based MDVRP methods to scale to 1,000 customers, runs in seconds per instance, and shows robustness across depot counts and spatial distributions. The paper's strengths include extensive experiments across multiple datasets, a real-world case study with Gurobi as reference, a sensitivity analysis of the key hyperparameter k, and an ablation study isolating the main components. At the same time, the central comparative claims rest on a small number of tables and on the choice of runtime budgets for the metaheuristic baseline; the current presentation overstates the results relative to what the tables actually show. If the HGS comparison is made fair and scoped, the contribution would be solid; as written, the headline superiority claims are not yet fully supported.

major comments (4)
  1. [Section 5.2, Table 1] The headline claim that DeepMDV surpasses HGS by at least 3.25% on MDVRP1K is computed against HGS run for 2 hours total per 100 instances, i.e., about 72 seconds per 1,000-customer instance. HGS/PyVRP is known to improve steeply with additional runtime, yet no time-quality curve is provided, and the text's statement that HGS 'becomes computationally expensive and infeasible for larger problems' is not supported by a 72-second budget. Please report HGS with substantially longer per-instance budgets (e.g., 5–30 minutes) and include time-quality curves, or qualify the 'surpasses HGS' claim as being specific to the stated short budget.
  2. [Section 5.2, Table 1, DeepMDV (LKH3, G, P) variant] The (LKH3, G, P) variant reports, for each instance, the best result obtained over four different values of k (30%, 40%, 50%, and 60% of the customer count) using multiple GPUs, while all other methods are reported as single runs. The 3.25% improvement is therefore a best-of-four-k result, and no mean, standard deviation, or training-seed variance is provided. Please report results for fixed-k variants and include error bars or variance information, and clearly disclose the multiple-trial selection procedure. Without this, the margin that drives the central claim is not a fair single-configuration comparison.
  3. [Section 5.2 and abstract; Table 2] The abstract's claim that 'our method outperforms all baselines across varying problem sizes' is internally contradicted by Table 2, where HGS achieves the best objective in every skewed-distribution setting, and by Table 1, where HGS is the best method for all instances with up to 400 customers. The empirical claims should be scoped to learning-based baselines and to the uniform-distribution, large-instance regime. As written, the abstract's sweeping wording overstates the results and should be corrected.
  4. [Section 3.1 and Section 4.1, Equations (1)-(2) and (10)] The paper asserts that restricting the search to at most one active tour per depot, and the related upper bound l_max = ceil(sum(demands)/C) + |D| with the deactivation threshold T_t, do not exclude optimal solutions. This is not proven. The threshold in Equations (1)-(2) forces tours to be filled beyond T_t before deactivation, which can exclude optimal solutions that contain many underfull tours from the same depot; the HGS wins in the skewed experiments of Table 2 are consistent with this risk. Please either provide a proof of optimality preservation or add an ablation that compares against unconstrained tour counts on small instances where exact solutions are available.
minor comments (5)
  1. [Appendix A, Equation (16)] Equation (16) as written requires every vehicle v to depart from and return to every depot d, which is not the MDVRP; the formulation should select a unique depot for each vehicle.
  2. [Table 7 (Appendix C)] The TAM-AM entry for CVRP7k reports an objective of 10.1 with a 24.9% gap relative to HGS = 212; this is numerically inconsistent and appears to be a typo (the objective should be around 264.7). Please correct it.
  3. [Section 5.3 and Table 2 caption] The text states HGS runtimes were increased to 60 minutes for small and 6 hours for large instances, while the Table 2 caption says 40M, 100M, and 5H for 100, 400, and 1,000 customers, respectively. Please clarify whether these are per-instance or total-for-100-instances budgets and reconcile the two statements.
  4. [References and front matter] Reference [26] is cited as 'Berman et al.' but the bibliography entry is Ombuki-Berman and Hanshar; the ACM Reference Format line contains '2018' while the conference year is 2025; and Figure 3's caption should clarify whether 'Obj' is the normalized Euclidean objective or the raw distance, since the text describes both.
  5. [Section 4.4] The training description says that tours are padded by repeating the depot node, but it is not stated how this padding is masked during loss computation; please clarify to avoid the router being trained on repeated depot tokens.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: DeepMDV's claims are empirical, and its lmax constraint and training pipeline are not derived from the results they support.

full rationale

This paper does not present a derivation whose conclusion is equivalent to its inputs. The load-bearing claims are empirical comparisons reported in Tables 1-3, and the method's behavior is measured against external baselines (HGS, OR-tools, POMO, GLOP, UDC, RouteFinder, MADRL, etc.), so the reported objectives are not true by construction. The 'optimal maximum number of tours' formula lmax = ceil(sum of demands / C) + |D| in Section 4.1 is a heuristic upper bound on the number of tours and is explicitly treated as a constraint that accelerates convergence; it is not a prediction derived from the model, and its contribution is tested by ablation (Table 6, ONT rows). Section 3.1's assumption of only one active tour per depot is an acknowledged modeling restriction, not a hidden encoding of the optimal solution; the paper does not claim this restriction preserves optimality. The three-step training procedure (Section 4.4 and Algorithm 1) couples the router and partitioner, but the coupling is a training pipeline: the router is first trained on TSP instances, the partitioner is trained using AM-generated route lengths as rewards, and the router is then fine-tuned on partitioner-generated tours. Each step optimizes an externally defined objective (tour length), so final performance is not forced by definition. The single author self-citation ([12]) is contextual related work and is not load-bearing. Correctness concerns, such as the unequal HGS runtime budget of about 72 seconds per 1,000-customer instance in Table 1 and the contradiction between the abstract's 'outperforms all baselines' and Table 2's skewed-distribution results where HGS remains best, are empirical fairness issues rather than circularity; they do not reduce any claimed result to its own inputs. No circular step is present.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The contribution is empirical. Its performance depends on three modeling assumptions: the one-active-tour-per-depot restriction, the local-neighbor heuristic for restricting attention to k nodes, and the heuristic upper bound l_max. The only tuned free parameter is k; the depot margin in l_max is ad hoc. No new physical or conceptual entities are introduced.

free parameters (2)
  • k (neighbor count in TSLCGL) = 50 for 100-node instances; 30% to 60% of customers for larger instances, selected per distribution
    Section 5, Inference and Appendix D: k is chosen by sensitivity analysis, and the parallel variant searches over several k values and reports the best, so it is tuned on test instances and directly controls the local context.
  • l_max depot margin = |D|
    Section 4.1 adds the number of depots to the demand-based lower bound to define the "optimal maximum number of tours"; this is an ad hoc allowance rather than a proven bound and constrains the solution space.
assumptions (4)
  • ad hoc to paper Only one active tour per depot is allowed at a time.
    Section 3.1 states this assumption explicitly for training efficiency; it restricts representable solutions and is not justified by optimality.
  • domain assumption Optimal actions in VRP are concentrated among local neighbors, so restricting attention to k nearest nodes is sufficient.
    Section 4.2.2 relies on this heuristic from the literature to build the candidate set zeta; if it fails on skewed instances, assignment quality degrades.
  • domain assumption Polar coordinates relative to the first depot capture the spatial structure of MDVRP.
    Section 4.2.1 transforms coordinates to polar form to gain invariance to shifts, rotations, and scaling; this assumes relative geometry is sufficient for near-optimal partitioning.
  • ad hoc to paper The upper bound l_max = ceil(sum of demands / C) + |D| is valid and does not exclude optimal solutions.
    Section 4.1 defines this bound without proof; the ablation study shows only a small effect, but the bound is an imposed constraint on the search space.

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Cite this review

Pith. "Pith review of DeepMDV: Global Spatial Matching for Multi-depot Vehicle Routing Problems." pith.science (2026). https://pith.science/paper/MWWKLTFP

@misc{pith2026241117080,
  author       = {Pith},
  title        = {Pith review of: DeepMDV: Global Spatial Matching for Multi-depot Vehicle Routing Problems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MWWKLTFP}},
  note         = {Machine review of arXiv:2411.17080}
}
read the original abstract

The rapid growth of online retail and e-commerce has made effective and efficient Vehicle Routing Problem (VRP) solutions essential. To meet rising demand, companies are adding more depots, which changes the VRP problem to a complex optimization task of Multi-Depot VRP (MDVRP) where the routing decisions of vehicles from multiple depots are highly interdependent. The complexities render traditional VRP methods suboptimal and non-scalable for the MDVRP. In this paper, we propose a novel approach to solve MDVRP addressing these interdependencies, hence achieving more effective results. The key idea is, the MDVRP can be broken down into two core spatial tasks: assigning customers to depots and optimizing the sequence of customer visits. We adopt task-decoupling approach and propose a two-stage framework that is scalable: (i) an interdependent partitioning module that embeds spatial and tour context directly into the representation space to globally match customers to depots and assign them to tours; and (ii) an independent routing module that determines the optimal visit sequence within each tour. Extensive experiments on both synthetic and real-world datasets demonstrate that our method outperforms all baselines across varying problem sizes, including the adaptations of learning-based solutions for single-depot VRP. Its adaptability and performance make it a practical and readily deployable solution for real-world logistics challenges.

Figures

Figures reproduced from arXiv: 2411.17080 by the authors.

Figure 1
Figure 1. The DeepMDV uses the embeddings produced by [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. The architecture of decoder focusing on TSLCGL. First, the model selects the top [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. MDVRP in Melbourne with three depots: two lo [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Sensitivity analysis of the influence of [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]

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Works this paper leans on

43 extracted references · 35 canonical work pages

  1. [1]

    Mahdi Alinaghian and Nadia Shokouhi. 2018. Multi-depot multi-compartment vehicle routing problem, solved by a hybrid adaptive large neighborhood search. Omega 76 (2018), 85–99

    work page 2018

  2. [2]

    Ali Arishi and Krishna Krishnan. 2023. A multi-agent deep reinforcement learn- ing approach for solving the multi-depot vehicle routing problem. Journal of Management Analytics 10, 3 (2023), 493–515

    work page 2023

  3. [3]

    Enrique Benavent and Antonio Martínez. 2013. Multi-depot multiple TSP: a polyhedral study and computational results. Annals of Operations Research 207 (2013), 7–25

    work page 2013

  4. [4]

    Federico Berto, Chuanbo Hua, Nayeli Gast Zepeda, André Hottung, Niels Wouda, Leon Lan, Junyoung Park, Kevin Tierney, and Jinkyoo Park. 2025. Routefinder: Towards foundation models for vehicle routing problems. arXiv preprint arXiv:2406.15007 (2025)

    arXiv 2025

  5. [5]

    https://www.manhattanbp.nyc.gov/in-ny-daily-news-manhattan-bp- calls-for-delivery-reforms-as-nyc-residents-businesses-receive-more-than-2- 4-million-packages-per-day

    E-Commerce Blueprint. 2022. In NY Daily News: Manhattan BP calls for delivery reforms as NYC residents, businesses receive more than 2.4 million packages per day. "https://www.manhattanbp.nyc.gov/in-ny-daily-news-manhattan-bp- calls-for-delivery-reforms-as-nyc-residents-businesses-receive-more-than-2- 4-million-packages-per-day"

    work page 2022

  6. [6]

    I-Ming Chao, Bruce L Golden, and Edward Wasil. 1993. A new heuristic for the multi-depot vehicle routing problem that improves upon best-known solutions. American Journal of Mathematical and Management Sciences 13, 3-4 (1993), 371– 406

    work page 1993

  7. [7]

    Nicos Christofides and Samuel Eilon. 1969. An algorithm for the vehicle- dispatching problem. Journal of the Operational Research Society 20, 3 (1969), 309–318

    work page 1969

  8. [8]

    Claudio Contardo and Rafael Martinelli. 2014. A new exact algorithm for the multi-depot vehicle routing problem under capacity and route length constraints. Discrete Optimization 12 (2014), 129–146

    work page 2014

Show all 43 references
  1. [9]

    Jean-François Cordeau, Michel Gendreau, and Gilbert Laporte. 1997. A tabu search heuristic for periodic and multi-depot vehicle routing problems. Networks: An International Journal 30, 2 (1997), 105–119

    1997

  2. [10]

    John Willmer Escobar, Rodrigo Linfati, Paolo Toth, and Maria G Baldoquin. 2014. A hybrid granular tabu search algorithm for the multi-depot vehicle routing problem. Journal of Heuristics 20 (2014), 483–509

    2014

  3. [11]

    Chengrui Gao, Haopu Shang, Ke Xue, Dong Li, and Chao Qian. 2024. 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. 6914–6922

    2024

  4. [12]

    Udesh Gunarathna, Renata Borovica-Gajic, Shanika Karunasekera, and Egemen Tanin. 2022. Dynamic graph combinatorial optimization with multi-attention deep reinforcement learning. In Proceedings of the 30th International Conference on Advances in Geographic Information Systems (...

    2022

  5. [13]

    Gurobi Optimization, LLC. 2008. Gurobi Optimizer. https://www.gurobi.com/. Accessed: 2025-04-21

    2008

  6. [14]

    Keld Helsgaun. 2017. An extension of the Lin-Kernighan-Helsgaun TSP solver for constrained traveling salesman and vehicle routing problems. Roskilde: Roskilde University 12 (2017), 966–980

    2017

  7. [15]

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

  8. [16]

    Beom Sae Kim, Arash Mozhdehi, Yunli Wang, Sun Sun, and Xin Wang. 2024. Clustering-Based Enhanced Ant Colony Optimization for Multi-Trip Vehicle Routing Problem with Heterogeneous Fleet and Time Windows: An Industrial Case Study. InProceedings of the 17th ACM SIGSPATIAL Interna...

    2024

  9. [17]

    Wouter Kool, Herke van Hoof, and Max Welling. 2018. Attention, Learn to Solve Routing Problems!. In International Conference on Learning Representations

    2018

  10. [18]

    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

  11. [19]

    Rahma Lahyani, Anne-Lise Gouguenheim, and Leandro C Coelho. 2019. A hybrid adaptive large neighbourhood search for multi-depot open vehicle routing problems. International Journal of Production Research 57, 22 (2019), 6963–6976

    2019

  12. [20]

    Jinqi Li, Bing Tian Dai, Yunyun Niu, Jianhua Xiao, and Yaoxin Wu. 2024. Multi- type attention for solving multi-depot vehicle routing problems.IEEE Transactions on Intelligent Transportation Systems (2024)

    2024

  13. [21]

    Jingwen Li, Yining Ma, Ruize Gao, Zhiguang Cao, Andrew Lim, Wen Song, and Jie Zhang. 2021. Deep reinforcement learning for solving the heterogeneous capacitated vehicle routing problem. IEEE Transactions on Cybernetics 52, 12 (2021), 13572–13585

    2021

  14. [22]

    Andrew Lim and Fan Wang. 2005. Multi-depot vehicle routing problem: A one- stage approach. IEEE transactions on Automation Science and Engineering 2, 4 (2005), 397–402

    2005

  15. [23]

    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

  16. [24]

    Arash Mozhdehi, Mahdi Mohammadizadeh, Yunli Wang, Sun Sun, and Xin Wang

  17. [25]

    United Stetes Department of Energy. 2024. Average annual Vehicle miles traveled by major vehicle category. https://afdc.energy.gov/data/10309

    2024

  18. [26]

    Beatrice Ombuki-Berman and Franklin T Hanshar. 2009. Using genetic algorithms for multi-depot vehicle routing. In Bio-inspired Algorithms for the Vehicle Routing Problem. 77–99

    2009

  19. [27]

    Arjun Paul, Ravi Shankar Kumar, Chayanika Rout, and Adrijit Goswami. 2021. Designing a multi-depot multi-period vehicle routing problem with time win- dow: hybridization of tabu search and variable neighbourhood search algorithm. S¯adhan¯a 46, 3 (2021), 183

    2021

  20. [28]

    David Pisinger and Stefan Ropke. 2019. Large neighborhood search. Handbook of Metaheuristics (2019), 99–127

    2019

  21. [29]

    Martin L Puterman. 1990. Markov decision processes. Handbooks in operations research and management science 2 (1990), 331–434

    1990

  22. [30]

    Mir Ehsan Hesam Sadati, Bülent Çatay, and Deniz Aksen. 2021. An efficient variable neighborhood search with tabu shaking for a class of multi-depot vehicle routing problems. Computers & Operations Research 133 (2021), 105269

    2021

  23. [31]

    Petr Stodola. 2020. Hybrid ant colony optimization algorithm applied to the multi-depot vehicle routing problem. Natural Computing 19, 2 (2020), 463–475

    2020

  24. [32]

    Paneerselvam Surekha and Sai Sumathi. 2011. Solution to multi-depot vehicle routing problem using genetic algorithms.World Applied Programming1, 3 (2011), 118–131

    2011

  25. [33]

    Paolo Toth and Daniele Vigo. 2002. The vehicle routing problem . SIAM

    2002

  26. [34]

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

    2022

  27. [35]

    Sihan Wang, Wei Sun, and Min Huang. 2024. An adaptive large neighborhood search for the multi-depot dynamic vehicle routing problem with time windows. Computers & Industrial Engineering 191 (2024), 110122

    2024

  28. [36]

    Haomin Wen, Youfang Lin, Fan Wu, Huaiyu Wan, Shengnan Guo, Lixia Wu, Chao Song, and Yinghui Xu. 2021. Package pick-up route prediction via modeling couriers’ spatial-temporal behaviors. In 2021 IEEE 37th International Conference on Data Engineering (ICDE) . IEEE, 2141–2146

    2021

  29. [37]

    Wouda, Leon Lan, and Wouter Kool

    Niels A. Wouda, Leon Lan, and Wouter Kool. 2024. PyVRP: a high-performance VRP solver package. INFORMS Journal on Computing (2024). https://doi.org/10. 1287/ijoc.2023.0055

    2024

  30. [38]

    Liang Xin, Wen Song, Zhiguang Cao, and Jie Zhang. 2021. Multi-decoder atten- tion model with embedding glimpse for solving vehicle routing problems. In Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 35. 12042–12049

    2021

  31. [39]

    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. In Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 38. 20284–20292

    2024

  32. [40]

    Bin Yu, ZZ Yang, and Jing-Xin Xie. 2011. A parallel improved ant colony opti- mization for multi-depot vehicle routing problem. Journal of the Operational Research Society 62, 1 (2011), 183–188

    2011

  33. [41]

    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. Advances in Neural Information Processing Systems 37 (2024), 6081–6125. SIGSPATIAL ’25, No...

    2024

  34. [2022]

    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

  35. [2024]

    In Proceedings of the 32nd ACM International Conference on Advances in Geographic Information Systems (SIGSPATIAL)

    EFECTIW-ROTER: Deep Reinforcement Learning Approach for Solving Heterogeneous Fleet and Demand Vehicle Routing Problem with Time-Window Constraints. In Proceedings of the 32nd ACM International Conference on Advances in Geographic Information Systems (SIGSPATIAL). 17–28

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