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REVIEW 5 major objections 5 minor 46 references

One4Many-StablePacker: An Efficient Deep Reinforcement Learning Framework for the 3D Bin Packing Problem

T0 review · 5 major / 5 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read One deep RL model for 3D bin packing generalizes to unseen bin dimensions and enforces stability constraints, via a weighted loading-rate/height-difference reward and entropy-controlled PPO.

desk verdict A coherent DRL framework for 3D-BPP with stability and cross-dimension generalization, but the empirical comparisons are weaker than claimed because baselines appear to be quoted, not re-run. read the letter →

arxiv 2510.10057 v2 pith:JCJX2GI7 submitted 2025-10-11 cs.LG

Lei Gao , Shihong Huang , Shengjie Wang , Hong Ma , Feng Zhang , Hengda Bao , Qichang Chen , Weihua Zhou This is my paper
classification cs.LG
keywords packingo4m-spconstraintsdimensionspolicyacrossdeepdiverse
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

3D bin packing asks how to place rectangular boxes into a container to use space efficiently. Real packing must respect stability: a box needs enough support underneath, and a heavy box cannot sit on a much lighter one. Most learning-based packers ignore these rules, and each model works only for one container size.

O4M-SP trains a single policy network that reads the container size, the empty spaces, and the remaining items, and chooses which item to place where. The state is a matrix of coordinates, sizes, and weights. A stability checker rejects actions that violate support or weight rules, so the policy only sees feasible placements. The reward combines the usual volume-based loading rate with a new term that penalizes uneven packing heights, encouraging flat layers and avoiding blocked future placements. Training uses a modified PPO that prevents the policy from becoming overconfident too early: it skips gradient updates at high-uncertainty decision steps and adds a penalty at the first placement step.

In tests, O4M-SP outperformed several published DRL baselines on 100 by 100 bins, and it still packed reasonably on completely new bin dimensions. However, the paper does not release code or data, reports no variance for most comparisons, and loses to a Monte-Carlo-tree-search baseline on generalization tests. The stability case study shows the checker works, but only for a simplified one-contact weight rule.

Extended reading notes

Core claim

O4M-SP, the first DRL framework for offline 3D-BPP that simultaneously addresses stability constraints and generalizes across diverse bin dimensions in a single training process. The paper also claims that 'O4M-SP achieves superior packing performance over baseline methods.' If correct, a single trained policy can produce stable, efficient packings across varying bin dimensions, with the weighted reward and entropy-control mechanisms as the key enablers.

Load-bearing premise

The screening heuristic that selects one 'current space' from an EMS stack using XYZ ordering (prioritizing X, then Y, then Z) and pops unstable spaces restricts the action space to the FLB corner of that space. If this heuristic prunes good placements, the policy cannot reach optimal utilization regardless of training. This is stated in Methodology: 'The loading sequence follows an XYZ order ... all available spaces are pushed onto a stack. The stability of the top space on the stack is evaluated, and if stable, it is selected as the current space.' Additionally, the stability checker models physical stability only via support ratio and single-contact weight ratio, ignoring torque and multiple-contact weight distribution, which the conclusion explicitly lists as future work.

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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

5 major / 5 minor

Summary. The paper proposes O4M-SP, a deep reinforcement learning framework for offline 3D bin packing with support and weight stability constraints and the ability to generalize across bin dimensions in a single trained policy. The method uses an EMS-based state representation with a stack-based screening heuristic, an attention-based actor-critic architecture, a weighted reward combining loading rate and a height-difference metric, and a PPO variant with entropy control at selected decision nodes. Experiments compare against six published baselines (Table 2), test generalization to unseen bin dimensions against greedy and MCTS (Table 4), run ablations of the reward and entropy-control components (Table 5), and provide a stability case study (Figure 5). The main claims are: (1) train-once generalize-to-many-bin-dimensions, (2) superior packing performance over existing methods, and (3) effective enforcement of practical stability constraints.

Significance. If the empirical claims were properly substantiated, the paper would make a practically useful contribution: a single policy that handles varied bin dimensions and stability constraints without retraining, with inference fast enough for deployment. The height-difference reward is a plausible mechanism for encoding flatness without dense reward shaping, and the entropy-control adaptation is a sensible transfer of recent insights from LLM reinforcement learning to combinatorial packing. The paper also provides a useful survey table of prior DRL approaches (Table 1) and is explicit about its simplified stability model. However, the experimental evidence as reported is not sufficient to support the headline superiority claim because the baseline comparisons are not controlled on the same test instances and several results are internally inconsistent with the claim of uniform outperformance.

major comments (5)
  1. [Experiments, Table 2] The baseline numbers in Table 2 appear to be quoted from the DMRL paper (Zhao et al., 2024) rather than measured on the same instances used for O4M-SP: the DMRL column is numerically identical to that paper's reported results, and no baseline error bars are given. Because the test instances are newly generated (random bin dimensions and item quantities), differences in loading rate may reflect dataset distribution instead of algorithmic quality. Moreover, O4M-SP is not uniformly better: O4M-SP(M) is 77.71% vs DMRL's 81.10% on 30 items (Table 2), and O4M-SP trained on 10 items is 77.81% vs DMRL's 78.90% on 20 items (Table 3). Please rerun all baselines in the same environment with the same test instances, report variances and significance tests, or explicitly and prominently label baseline columns as quoted from the original papers rather than as comparisons on the same benchmark.
  2. [Experiments, Generalization, Table 4] On the unseen-dimension test sets (B1_30, B2_30, B3_30, BM_M), O4M-SP is on average about 5.2 percentage points worse than MCTS (means 77.6% vs 82.8%; per-set differences range from -3.9 to -7.0 points). The paper's phrasing 'remains effective' and the emphasis on runtime are legitimate, but they do not support the abstract's claim of 'significantly outperforms baseline methods.' The generalization claim should be scoped to 'competitive with heuristic baselines at a fraction of the runtime,' or the method must be improved to close the gap with MCTS. Also, Table 4 reports no variance or significance information for either method, so the observed gaps cannot be assessed statistically.
  3. [Methodology, State and Action] The screening heuristic selects the current space by popping from an EMS stack in XYZ order and discarding unstable spaces, and the action places the chosen item at the FLB corner of that space. This restricts the policy's reachable set: if the true optimal packing requires placing an item at a different corner of an EMS or in a space that the heuristic discards, no training signal can recover it. The paper provides no proof or empirical evidence that the restricted action space contains an optimal packing for the defined stability model. This is load-bearing for both the generalization and superiority claims; please either prove the restriction is lossless for the simplified model, or compare empirically against a less restrictive space-selection baseline (e.g., evaluating all EMS corners) on small instances where strong or optimal solutions are available.
  4. [Problem Statement; Conclusion; Handling Stability Constraints] The stability model checks only (a) total bottom contact area F >= r_s f and (b) for an item with exactly one contact below, G_j <= r_w G_i. As the conclusion acknowledges, the model does not handle torque or weight distribution when an item contacts multiple supporting items. The abstract and introduction nevertheless claim that O4M-SP 'explicitly integrates stability-related constraints to ensure real-world feasibility' and 'effectively addresses packing scenarios with stability constraints.' The case study in Figure 5 verifies only this simplified checker (e.g., Scenarios 2 and 4 report support ratio >=66%, not physical stability under multi-contact loads). Please revise the wording to state clearly that the framework handles single-contact weight constraints and area-based support, and leave broader physical-fidelity claims to future work.
  5. [Methodology, Reward, Eqs. (2)-(4)] The height-difference term r_HD_t is defined as a difference of differences, and the text says the result is normalized so that smaller height differences yield larger rewards, but no normalization formula or range is given. The weights alpha_1 and alpha_2 are introduced in Eq. (2) but their values are never reported in the experimental setup or in the ablation analysis. Since the weighted reward is a central contribution and the ablation (Table 5) removes it entirely, the missing normalization and hyperparameter settings make it impossible to reproduce the training procedure or to interpret the magnitude of the WR effect. Please specify the normalization, give the alpha values, and ideally include a small sensitivity study.
minor comments (5)
  1. [Eq. (2) and Eq. (7)] Eq. (2) has 'α1, α1' where it should read 'α1, α2.' Eq. (7) uses both J_t(θ) and J_p(θ) for the same quantity, and the penalty P_policy is described only in prose; please define all symbols consistently.
  2. [Eq. (4)] Please clarify whether H_t' is the second-largest distinct height among packed items or the second value in the sorted list, and fix the grammar ('denote' should be 'denotes').
  3. [Table 5] The ablation results report only point estimates. Adding standard deviations or confidence intervals across random seeds or bootstrap samples would make the differences between O4M-SP, w/o EC, and w/o WR more interpretable.
  4. [Table 1] The 'Our Work' row lists 'Multi.' under Bin Size, which is ambiguous; consider 'Variable' or 'Multiple' for clarity.
  5. [Abstract and Conclusion] The phrase 'the first DRL framework' for simultaneous stability and cross-dimension generalization should be softened to 'to our knowledge,' since Table 1 shows earlier work with stability elements (e.g., Laterre et al. 2018) and variable-bin-size work (e.g., Zhang et al. 2021); the novelty claim needs a more careful literature comparison.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity (score 1): the weighted reward (Eqs. 2–4) is an explicit shaping heuristic, the entropy identity (Eq. 5) is cited from external work, ablation results are empirical, and the only self-citations are non-load-bearing; quoted baselines in Table 2 are a comparison-validity caveat, not circularity.

full rationale

Derivation-chain review: the paper's central outputs (loading rates on held-out instances, Tables 2–5) are empirical measurements of a trained policy, not quantities derived from the model's inputs by construction. The weighted reward (Eqs. 2–4) is an openly stated shaping heuristic: r_LR^t is the incremental loading rate and r_HD^t is the change in the (max − second-max) height gap; neither is a fitted value renamed as a prediction, and Fig. 1 exhibits a case where the two reward terms select different items, so the height-difference term is not a re-labeling of loading rate. The entropy-control scheme (Eqs. 5–7) rests on an approximate covariance identity cited from Cui et al. (2025) (an external group) and on the paper's own measurement (Fig. 3), and its effect is established by ablation (Table 5), not by assumption. It is true that Eqs. (6)–(7) mechanically block/penalize policy updates at exactly the targeted nodes, so 'entropy is preserved' is partly a designed property of the mechanism rather than a surprising prediction; however, this does not reduce the central claim (packing performance) to the mechanism's definition, since performance is measured independently. Self-citations are present but not load-bearing: Huang et al. (2025) appears only in the related-work survey; Wang et al. (2025b) motivates the 'critical decision nodes' idea, which the paper independently supports with Fig. 3, and Wang et al. is not the source of Eq. (5). No uniqueness theorem or ansatz is imported from the authors' prior work. Two caveats are validity issues rather than circularity: (i) baseline numbers in Table 2 (e.g., DMRL 73.00/77.20/78.90/81.10) appear identical to published values in Zhao et al. (2024), and the paper does not state that baselines were rerun on the same 10,000 test instances, so 'significantly outperforms' is less controlled than claimed (O4M-SP(S) nevertheless exceeds those quoted numbers at all four sizes); (ii) the stability checker simplifies physics (single-contact weight ratio, support-ratio only), a limitation the conclusion itself acknowledges ('Future research could extend the framework to address more complex scenarios, such as irregularly shaped items and weight constraints for items contacting multiple supporting items below'). Neither caveat is a self-referential reduction. No score-relevant circular step found.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central claims rest on: (i) hyperparameters that are not reported (alpha_1, alpha_2, beta, phi), (ii) a space-selection heuristic that constrains the search space, and (iii) a simplified stability model. These are not fitted to the test set but are hand-set and may be tuned on validation.

free parameters (6)
  • alpha_1 (loading-rate reward weight)
    Hyperparameter in Eq. (2); value not reported in paper, chosen by hand or tuned on validation.
  • alpha_2 (height-difference reward weight)
    Hyperparameter in Eq. (2); the paper accidentally writes 'alpha_1, alpha_1 are hyperparameters', so alpha_2 is never specified.
  • beta (policy drifting penalty coefficient)
    Penalty strength in Eq. (7) for first-step nodes; not reported.
  • phi (portion of high-covariance nodes clipped)
    Fraction of high-covariance nodes in Eq. (6); not reported.
  • support ratio r_s = 0.66 (case study)
    Predefined constraint parameter in the environment; set to 0.66 in the stability case study, but is a problem input rather than a fitted model parameter.
  • weight ratio r_w = 3.0 (case study)
    Predefined constraint parameter; case study uses 3.0.
assumptions (4)
  • ad hoc to paper EMS-based space selection with XYZ-order screening and popping unstable spaces does not exclude any optimal packing.
    The MDP action space is restricted to the FLB corner of a single selected 'current space'; if this heuristic prunes good placements, the policy can never reach optimal utilization. See Methodology: Problem Statement and Formulation.
  • domain assumption Physical stability is fully captured by support ratio (F >= r_s f) and single-contact weight ratio (G_j <= r_w G_i).
    The stability checker ignores torque, moments, and weight distribution over multiple contacts; the conclusion explicitly lists 'weight constraints for items contacting multiple supporting items below' as future work, so single-contact model is a stated limitation.
  • domain assumption Bin height is set to the sum of the maximum dimensions of the items, making the problem always feasible.
    This H definition makes the loading-rate objective different from classic fixed-bin 3D-BPP and may affect comparability with baselines. See Dataset section.
  • standard math The entropy-covariance identity (Eq. 5) from Cui et al. (2025) holds for the 3D-BPP policy.
    Used to identify high-covariance critical decision nodes; cited, not re-derived for this problem.

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Pith. "Pith review of One4Many-StablePacker: An Efficient Deep Reinforcement Learning Framework for the 3D Bin Packing Problem." pith.science (2026). https://pith.science/paper/JCJX2GI7

@misc{pith2026251010057,
  author       = {Pith},
  title        = {Pith review of: One4Many-StablePacker: An Efficient Deep Reinforcement Learning Framework for the 3D Bin Packing Problem},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JCJX2GI7}},
  note         = {Machine review of arXiv:2510.10057}
}
read the original abstract

The three-dimensional bin packing problem (3D-BPP) is widely applied in logistics and warehousing. Existing learning-based approaches often neglect practical stability-related constraints and exhibit limitations in generalizing across diverse bin dimensions. To address these limitations, we propose a novel deep reinforcement learning framework, One4Many-StablePacker (O4M-SP). The primary advantage of O4M-SP is its ability to handle various bin dimensions in a single training process while incorporating support and weight constraints common in practice. Our training method introduces two innovative mechanisms. First, it employs a weighted reward function that integrates loading rate and a new height difference metric for packing layouts, promoting improved bin utilization through flatter packing configurations. Second, it combines clipped policy gradient optimization with a tailored policy drifting method to mitigate policy entropy collapse, encouraging exploration at critical decision nodes during packing to avoid suboptimal solutions. Extensive experiments demonstrate that O4M-SP generalizes successfully across diverse bin dimensions and significantly outperforms baseline methods. Furthermore, O4M-SP exhibits strong practical applicability by effectively addressing packing scenarios with stability constraints.

Figures

Figures reproduced from arXiv: 2510.10057 by the authors.

Figure 1
Figure 1. Space selection with different reward functions [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Overview of our method. (a) Space selection: A heuristic for selecting the space for placement. (b) Stability checker: [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Variation of policy entropy with decision steps [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Policy entropy curves Handling Stability Constraints To verify O4M-SP’s ability to handle practical constraints, we conduct a case study with seven item types (see Fig￾ure 5). The bin has a fixed length and width of 100, with its height set to the maximum item height m…

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Works this paper leans on

46 extracted references · 11 linked inside Pith

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address archivePrefix author booktitle chapter edition editor eid eprint howpublished institution isbn journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.a...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

  3. [3]

    V.; Norouzi, M.; and Bengio, S

    Bello, I.; Pham, H.; Le, Q. V.; Norouzi, M.; and Bengio, S. 2016. Neural combinatorial optimization with reinforcement learning. arXiv preprint arXiv:1611.09940

    arXiv 2016

  4. [4]

    Chen, C.-S.; Lee, S.-M.; and Shen, Q. 1995. An analytical model for the container loading problem. European Journal of operational research, 80(1): 68--76

    1995

  5. [5]

    G.; Perboli, G.; and Tadei, R

    Crainic, T. G.; Perboli, G.; and Tadei, R. 2008. Extreme point-based heuristics for three-dimensional bin packing. Informs Journal on computing, 20(3): 368--384

    2008

  6. [6]

    G.; Perboli, G.; and Tadei, R

    Crainic, T. G.; Perboli, G.; and Tadei, R. 2009. TS2PACK: A two-level tabu search for the three-dimensional bin packing problem. European Journal of Operational Research, 195(3): 744--760

    2009

  7. [7]

    Cui, G.; Zhang, Y.; Chen, J.; Yuan, L.; Wang, Z.; Zuo, Y.; Li, H.; Fan, Y.; Chen, H.; Chen, W.; et al. 2025. The entropy mechanism of reinforcement learning for reasoning language models. arXiv preprint arXiv:2505.22617

    arXiv 2025

  8. [8]

    P.; and Sokolov, B

    Dolgui, A.; Ivanov, D.; Sethi, S. P.; and Sokolov, B. 2019. Scheduling in production, supply chain and Industry 4.0 systems by optimal control: fundamentals, state-of-the-art and applications. International journal of production research, 57(2): 411--432

    2019

Show all 46 references
  1. [9]

    Duan, L.; Hu, H.; Qian, Y.; Gong, Y.; Zhang, X.; Xu, Y.; and Wei, J. 2018. A multi-task selected learning approach for solving 3D flexible bin packing problem. arXiv preprint arXiv:1804.06896

    2018 arXiv

  2. [10]

    Feng, S.; and Yang, Y. 2025. Sorrel: Suboptimal-demonstration-guided reinforcement learning for learning to branch. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, 11212--11220

    2025

  3. [11]

    J.; Paterson, M

    Fowler, R. J.; Paterson, M. S.; and Tanimoto, S. L. 1981. Optimal packing and covering in the plane are NP-complete. Information processing letters, 12(3): 133--137

    1981

  4. [12]

    Fu, Z.-H.; Qiu, K.-B.; and Zha, H. 2021. Generalize a small pre-trained model to arbitrarily large tsp instances. In Proceedings of the AAAI conference on artificial intelligence, volume 35, 7474--7482

    2021

  5. [13]

    Goyal, A.; and Deng, J. 2020. Packit: A virtual environment for geometric planning. In International Conference on Machine Learning, 3700--3710. PMLR

    2020

  6. [14]

    Hu, H.; Zhang, X.; Yan, X.; Wang, L.; and Xu, Y. 2017. Solving a new 3d bin packing problem with deep reinforcement learning method. arXiv preprint arXiv:1708.05930

    2017 arXiv

  7. [15]

    Hu, R.; Xu, J.; Chen, B.; Gong, M.; Zhang, H.; and Huang, H. 2020. TAP-Net: transport-and-pack using reinforcement learning. ACM Transactions on Graphics (TOG), 39(6): 1--15

    2020

  8. [16]

    Huang, S.; Zhu, H.; Wang, H.; Liu, K.; Liu, X.; and Zhang, Z.-H. 2025. Balancing the Trade-off between Efficiency and Equity in a Stochastic Emergency Supplies Allocation Problem. Applied Mathematical Modelling, 116242

    2025

  9. [17]

    Jiang, Y.; Cao, Z.; and Zhang, J. 2021 a . Learning to solve 3-D bin packing problem via deep reinforcement learning and constraint programming. IEEE transactions on cybernetics, 53(5): 2864--2875

    2021

  10. [18]

    Jiang, Y.; Cao, Z.; and Zhang, J. 2021 b . Solving 3D bin packing problem via multimodal deep reinforcement learning

    2021

  11. [19]

    Khalil, E.; Dai, H.; Zhang, Y.; Dilkina, B.; and Song, L. 2017. Learning combinatorial optimization algorithms over graphs. Advances in neural information processing systems, 30

    2017

  12. [20]

    Kocsis, L.; and Szepesv \'a ri, C. 2006. Bandit based monte-carlo planning. In European conference on machine learning, 282--293. Springer

    2006

  13. [21]

    K.; Cohen, A.-S.; Kas, D.; Hajjar, K.; Dahl, T

    Laterre, A.; Fu, Y.; Jabri, M. K.; Cohen, A.-S.; Kas, D.; Hajjar, K.; Dahl, T. S.; Kerkeni, A.; and Beguir, K. 2018. Ranked reward: Enabling self-play reinforcement learning for combinatorial optimization. arXiv preprint arXiv:1807.01672

    2018 arXiv

  14. [22]

    Li, D.; Gu, Z.; Wang, Y.; Ren, C.; and Lau, F. C. 2022. One model packs thousands of items with recurrent conditional query learning. Knowledge-Based Systems, 235: 107683

    2022

  15. [23]

    Li, D.; Ren, C.; Gu, Z.; Wang, Y.; and Lau, F. 2020. Solving packing problems by conditional query learning

    2020

  16. [24]

    Li, Y.; Wang, S.; Sun, H.; and Zhou, S. 2025. Collaborative vessel--unmanned aerial vehicle routing for time-window-constrained offshore parcel delivery. Transportation Research Part C: Emerging Technologies, 178: 105189

    2025

  17. [25]

    Li, Y.; Wang, S.; Zhou, S.; and Wang, Z. 2024. A mathematical formulation and a tabu search heuristic for the joint vessel-UAV routing problem. Computers & Operations Research, 169: 106723

    2024

  18. [26]

    Liu, Z.; Meng, F.; Du, L.; Zhou, Z.; Yu, C.; Shao, W.; and Zhang, Q. 2025. CPGD: Toward Stable Rule-based Reinforcement Learning for Language Models. arXiv preprint arXiv:2505.12504

    2025 arXiv

  19. [27]

    Loshchilov, I.; and Hutter, F. 2017. Decoupled weight decay regularization. arXiv preprint arXiv:1711.05101

    2017 arXiv

  20. [28]

    Luo, F.; Lin, X.; Liu, F.; Zhang, Q.; and Wang, Z. 2023. Neural combinatorial optimization with heavy decoder: Toward large scale generalization. Advances in Neural Information Processing Systems, 36: 8845--8864

    2023

  21. [29]

    Martello, S.; Pisinger, D.; and Vigo, D. 2000 a . The three-dimensional bin packing problem. Operations research, 48(2): 256--267

    2000

  22. [30]

    Martello, S.; Pisinger, D.; and Vigo, D. 2000 b . The three-dimensional bin packing problem. Operations research, 48(2): 256--267

    2000

  23. [31]

    Schrijver, A. 2002. Combinatorial Optimization: Theory and Algorithms

    2002

  24. [32]

    Sutton, R. S. 1988. Learning to predict by the methods of temporal differences. Machine learning, 3(1): 9--44

    1988

  25. [33]

    Veres, M.; and Moussa, M. 2019. Deep learning for intelligent transportation systems: A survey of emerging trends. IEEE Transactions on Intelligent transportation systems, 21(8): 3152--3168

    2019

  26. [34]

    Wang, B.; Lin, Z.; Kong, W.; and Dong, H. 2025 a . Bin packing optimization via deep reinforcement learning. IEEE Robotics and Automation Letters

    2025

  27. [35]

    Wang, S.; Yu, L.; Gao, C.; Zheng, C.; Liu, S.; Lu, R.; Dang, K.; Chen, X.; Yang, J.; Zhang, Z.; et al. 2025 b . Beyond the 80/20 rule: High-entropy minority tokens drive effective reinforcement learning for llm reasoning. arXiv preprint arXiv:2506.01939

    2025 arXiv

  28. [36]

    Wu, W.; Fan, C.; Huang, J.; Liu, Z.; and Yan, J. 2023. Machine learning for the multi-dimensional bin packing problem: Literature review and empirical evaluation. arXiv preprint arXiv:2312.08103

    2023 arXiv

  29. [37]

    L.; and Zhou, Y

    Wu, X.; Wang, D.; Wen, L.; Xiao, Y.; Wu, C.; Wu, Y.; Yu, C.; Maskell, D. L.; and Zhou, Y. 2024. Neural combinatorial optimization algorithms for solving vehicle routing problems: A comprehensive survey with perspectives. arXiv preprint arXiv:2406.00415

    2024 arXiv

  30. [38]

    Wu, Y.; Li, W.; Goh, M.; and De Souza, R. 2010. Three-dimensional bin packing problem with variable bin height. European journal of operational research, 202(2): 347--355

    2010

  31. [39]

    Xiong, H.; Guo, C.; Peng, J.; Ding, K.; Chen, W.; Qiu, X.; Bai, L.; and Xu, J. 2024. GOPT: Generalizable online 3D bin packing via transformer-based deep reinforcement learning. IEEE Robotics and Automation Letters

    2024

  32. [40]

    Yang, S.; Song, S.; Chu, S.; Song, R.; Cheng, J.; Li, Y.; and Zhang, W. 2023. Heuristics integrated deep reinforcement learning for online 3d bin packing. IEEE Transactions on Automation Science and Engineering, 21(1): 939--950

    2023

  33. [41]

    Zhang, J.; and Shuai, T. 2024. Online Three-Dimensional Bin Packing: A DRL Algorithm with the Buffer Zone. Found. Comput. Decis. Sci, 49: 63--74

    2024

  34. [42]

    Zhang, J.; Zi, B.; and Ge, X. 2021. Attend2pack: Bin packing through deep reinforcement learning with attention. arXiv preprint arXiv:2107.04333

    2021 arXiv

  35. [43]

    Zhao, A.; Li, T.; and Lin, L. 2024. A dynamic multi-modal deep reinforcement learning framework for 3D bin packing problem. Knowledge-Based Systems, 299: 111990

    2024

  36. [44]

    Zhao, H.; She, Q.; Zhu, C.; Yang, Y.; and Xu, K. 2021. Online 3D bin packing with constrained deep reinforcement learning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, 741--749

    2021

  37. [45]

    Zhao, H.; Yu, Y.; and Xu, K. 2021. Learning efficient online 3D bin packing on packing configuration trees. In International conference on learning representations

    2021

  38. [46]

    Zhou, P.; Gao, Z.; Li, C.; and Chong, N. Y. 2024. An Efficient Deep Reinforcement Learning Model for Online 3D Bin Packing Combining Object Rearrangement and Stable Placement. In 2024 24th International Conference on Control, Automation and Systems (ICCAS), 964--969. IEEE

    2024

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