Pith. sign in

REVIEW 4 major objections 4 minor 73 references

FORGE: Foundational Optimization Representations from Graph Embeddings

T0 review · 4 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read FORGE claims that one unsupervised vector-quantized graph autoencoder yields MIP embeddings that transfer across domains, sizes, and downstream solver tasks.

desk verdict A genuinely useful unsupervised MIP embedding paper, but the solver gains need control arms before the headline claim holds. read the letter →

arxiv 2508.20330 v5 pith:V7UDU7IK submitted 2025-08-28 cs.LG

Zohair Shafi , Serdar Kadioglu This is my paper · ORCID
classification cs.LG
keywords mixed-integerprogramminggraphneuralnetworksvectorquantizationunsupervisedrepresentationlearningcombinatorialoptimizationintegralitygapsearchguidancefoundationmodels
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 argues that a single unsupervised pre-trained model can serve as a foundational representation for mixed-integer programs (MIPs), replacing the common practice of training a dedicated model for each problem distribution and downstream task. It claims that vector quantization over a graph autoencoder captures global structure that plain graph-neural-network embeddings lose, so the resulting code histograms cluster unseen instances by problem type and transfer to new tasks and sizes with little labeled data. If true, this would remove a major bottleneck of learning-based optimization: the expensive, solver-dependent collection of optimal or near-optimal labels for every new problem family. A commercially relevant consequence is that one pre-trained model can be fine-tuned to generate pseudo-cuts or search hints that make a commercial solver find better solutions faster.

What carries the argument

The central object is the vector-quantized graph autoencoder (VQ-GAE) over the bipartite variable-constraint graph of a MIP. The GNN encoder uses two GraphSAGE layers with 1,024 dimensions; a 5,000-code book quantizes node embeddings into discrete codewords; a linear decoder reconstructs the original node features and adjacency. The instance embedding is the frequency histogram of the codes, which is what carries global structure across instances and enables the downstream prediction heads.

What would settle it

Take two problem families whose bipartite graphs have identical distributions of the ten static node features but different constraint structure, and check whether FORGE's instance embeddings separate them above chance; if they do not, the reported transfer is carried by dataset statistics rather than by the learned codebook representation.

Watch

Extended reading notes

Core claim

FORGE is a vector-quantized graph autoencoder trained without labels or solver calls on 2,850 MIP instances sampled from public benchmark libraries. It encodes the bipartite variable-constraint graph of an instance with two GraphSAGE layers, assigns every node a discrete code from a 5,000-entry codebook, and reconstructs node features and edges from the codewords; the instance-level embedding is the histogram of code assignments. The paper's central claim is that this discrete vocabulary preserves global structure that ordinary GNN readouts lose, so a single pre-trained model can separate unseen instances by problem domain (NMI 0.843 versus 0.790 and 0.087 for the ablations) and, after light fine-tuning, improve a commercial solver's primal gap by up to 85% for pseudo-cut generation and up to 48% for search guidance, including on a problem class never seen during fine-tuning.

Load-bearing premise

The load-bearing premise is that the ten static node features—variable type, bounds, objective coefficient, constraint sense, and right-hand side—are enough for the autoencoder to learn structures that transfer to fully unseen problem classes such as MVC without additional pre-training.

Editorial extensions

If this is right

  • The same pre-trained autoencoder can serve both instance-level tasks (integrality gap prediction and pseudo-cut generation) and node-level tasks (variable hints for search guidance) without re-pre-training.
  • A new problem family needs only a small fine-tuning set, around 50 to 100 instances per class, rather than a large solver-labeled corpus.
  • Because labels come from time-limited solves rather than optimal solutions, labeling cost scales with the time budget, not with the difficulty of proving optimality.
  • When the learned hints are integrated into a commercial solver, primal gaps fall consistently across Combinatorial Auction, Set Cover, Generalized Independent Set, and Minimum Vertex Cover, with the last of these absent from fine-tuning.

Reading between the lines

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

  • A testable extension is to treat the codebook as a tokenizer for MIPs and check whether instances sharing code distributions can share fine-tuned prediction heads across domains, which the paper does not test.
  • The vector-arithmetic observations (for example, Vertex Cover minus Set Cover plus Bin Packing moving toward Independent Set) suggest embedding directions carry interpretable structure semantics; if so, they could be used to generate synthetic training instances or to steer instance generation.
  • Because only ten formulation-level features are used, the transfer may weaken when the same underlying problem is reformulated with redundant constraints or rescaled coefficients; perturbing formulations while keeping the problem fixed would test this.
  • The clusters show an easy-to-hard ordering within domains, so the embeddings could plausibly serve as a cheap difficulty predictor for curriculum learning, an application the paper leaves unexplored.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper introduces FORGE, an unsupervised vector-quantized graph autoencoder that learns MIP representations from bipartite variable-constraint graphs without solver solutions. Instance-level embeddings are formed from codebook frequency histograms, and variable/constraint-level codewords serve as local embeddings. The authors pre-train FORGE on MIPLIB and D-MIPLIB instances, evaluate clustering of unseen instances, and then fine-tune the same pre-trained model on two downstream tasks: integrality-gap prediction for pseudo-cut generation and variable prediction for search guidance. They report consistent primal-gap improvements over Gurobi on CA, SC, GIS, and MVC instances, as well as improvements over the SOTA methods of Li et al. (2025) and PS-Gurobi (Han et al., 2023), and they release code, pre-trained weights, and embeddings.

Significance. If the claims hold, FORGE would be a genuinely useful step toward general-purpose MIP representations: it is unsupervised, does not require solving instances for pre-training, produces both instance- and node-level embeddings, and is evaluated on two very different downstream tasks with a single shared backbone. The paper is commendable for open-sourcing training code, pre-trained weights, and embeddings, and for including a random-vector control for the PS-Gurobi augmentation. The clustering results in Section 4 and Appendix A.3 are suggestive, and the vector-arithmetic experiments, while qualitative, are a creative sanity check. The central limitation is that the solver-integration experiments do not yet causally separate the contribution of FORGE's learned representations from the mechanisms that use them, and the downstream evaluation as written appears to overlap with the pre-training corpus.

major comments (4)
  1. [§5 (Training the Foundational FORGE Model; §5.1, §5.2 Test Instances)] The downstream test instances appear to have been part of the pre-training corpus. The foundational model is trained on 1,800 MIPLIB instances plus the 1,050 D-MIPLIB instances, while the Task I and Task II test sets are described as '50 very-hard instances each of CA, SC, GIS, and MVC' and '50 medium instances' of the same D-MIPLIB problem families; the text only states that MVC is unseen in fine-tuning, not that the test instances were excluded from pre-training. Since a central contribution claim is that a single pre-trained model transfers to unseen domains and sizes, the paper must either demonstrate disjointness between pre-training and test instances or re-run the experiments on genuinely held-out instances.
  2. [§5.1, Figure 4] The Gurobi versus Gurobi+FORGE pseudo-cut comparison lacks the control arms needed to attribute the reported gains to FORGE's learned embeddings. A control using a constant predicted gap (for example, the median or mean of the fine-tuning distribution) or permuted FORGE predictions is necessary, because the pseudo-cut mechanism itself may tighten the LP bound whenever the prediction is conservatively underestimating; without such controls, the 29-85% primal-gap gains cannot be uniquely attributed to the learned representation. The figure also reports single averages over 50 instances with no confidence intervals or paired statistical tests, so the word 'consistently' overstates the current evidence.
  3. [§5.2, Figure 5 and Appendix A.8] The search-guidance experiment compares Gurobi with and without FORGE hints, but it does not include a control that uses the 1-second feasible solution alone or random top/bottom-decile hints. The random-vector control in Appendix A.8 covers only the PS-Gurobi augmentation, not the direct Gurobi integration, so the confound between the hint mechanism and the learned variable scores remains. As in Task I, the 50-instance averages are shown without error bars or paired significance tests, and the claimed 'up to 35% speed-ups' is not visible in the reported primal-gap plots.
  4. [§4 and Appendix A.4] The codebook size k=5,000 is selected by measuring NMI on the same 1,050 D-MIPLIB instances used to report the clustering result, so the reported NMI of 0.843 is not a fully out-of-sample evaluation. Although the ablation in Table 1 suggests the NMI is insensitive to the codebook size, the selection procedure should be based on a held-out validation split or the authors should explicitly note the selection-on-test caveat before presenting the clustering accuracy as evidence of unsupervised generalization.
minor comments (4)
  1. [Abstract and Section 7] The phrase 'trained on ∼2.8 instances' appears to be a typo; it should read 'trained on ∼2,850 instances.'
  2. [Figures 4 and 5] The captions in the full text contain duplicated subplot labels, with both lowercase '(a)-(d)' and uppercase '(A)-(D)' versions listed; one set should be removed.
  3. [§5.2] The claim that FORGE 'converges to optimal solutions significantly faster (up to 35% speed-ups)' is not supported by Figure 5, which only plots primal gap; please add a time-to-optimality metric or a separate figure.
  4. [§3-F, Equation (2)] The notation uses \hat X both for the reconstructed feature matrix and in the edge-reconstruction term \hat X \hat X^T, which makes the loss definition hard to parse; please introduce separate symbols for the reconstructed node-feature matrix and the edge-score matrix.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: FORGE's unsupervised reconstruction objective is independent of the downstream labels it predicts; remaining concerns are experimental controls and data leakage, not circular derivation.

full rationale

FORGE's pre-training objective is reconstruction of static bipartite node features and edges (Eq. 2), with no dependence on solver solutions or downstream targets, so the instance, variable, and constraint embeddings are not defined from the quantities they later predict. Downstream fine-tuning uses separately collected cheap labels (120-second timeout solutions for gap prediction; five feasible solutions for variable hints), and the predicted gap or hint scores are not algebraic rearrangements of those labels. The pseudo-cut and search-guidance experiments compare Gurobi with and without FORGE on D-MIPLIB instances, but the comparison is empirical rather than definitional. The more serious methodological concerns are missing control arms and the fact that the Section 5 pre-training corpus includes the D-MIPLIB instances later used for evaluation, which is data leakage rather than circularity. The codebook-size ablation in Table 1 is hyperparameter selection on the clustering evaluation set, not a fitted parameter renamed as a prediction. The vector-arithmetic appendix is an explicitly flagged "stretch analogy" computed post hoc on the same embeddings and is not load-bearing. No quoted equation equates a downstream target with FORGE's inputs by construction, and no load-bearing claim rests on a self-citation. Therefore the paper's derivation chain is not circular.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The framework relies on a standard set of model hyperparameters (codebook size, embedding dimension, loss weights) and domain assumptions about MIP feature sufficiency and label quality. No new physical or mathematical entities are introduced.

free parameters (5)
  • Codebook size k = 5000
    Selected by maximizing NMI on the clustering test set (D-MIPLIB) in the ablation study of Appendix A.4; this is a hyperparameter tuned on the evaluation data.
  • Embedding dimension d = 1024
    Set without ablation; the dimensionality of GNN hidden layers and codewords (Section 3-B).
  • Commitment loss weight alpha = not reported
    Appears in the commitment loss (Eq. 4) but no value is provided, leaving a free hyperparameter in the pre-training objective.
  • Triplet loss margin = 2
    Set in Appendix A.7 for the search guidance fine-tuning.
  • Search guidance radius = 0.1
    Fixed radius for neighbor selection in search guidance, reported in Appendix A.6.
assumptions (4)
  • domain assumption The bipartite graph representation with the chosen 10-dimensional node features captures enough structure for unsupervised reconstruction to induce transferable MIP embeddings.
    Introduced in Section 3-A; the entire pre-training and downstream transfer depend on this feature sufficiency.
  • domain assumption A pseudo-cut based on a conservatively estimated integrality gap does not degrade solver performance when the estimate is incorrect.
    Assumed in Section 5.1 for the pseudo-cut generation; the paper argues the timeout labeling strategy ensures conservative estimates.
  • domain assumption Pooling five feasible solutions within five minutes provides meaningful positive and negative variable signals for search guidance.
    Used in Section 5.2 for labeling; optimality is not required, so the labels are noisy but assumed useful.
  • standard math Graph neural network message passing and vector quantization produce discrete codes that preserve global instance structure.
    Background assumption from GNN and VQ literature, used throughout the architecture.

how reviews work

0 comments
Cite this review

Pith. "Pith review of FORGE: Foundational Optimization Representations from Graph Embeddings." pith.science (2026). https://pith.science/paper/V7UDU7IK

@misc{pith2026250820330,
  author       = {Pith},
  title        = {Pith review of: FORGE: Foundational Optimization Representations from Graph Embeddings},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V7UDU7IK}},
  note         = {Machine review of arXiv:2508.20330}
}
read the original abstract

Combinatorial optimization problems are ubiquitous in science and engineering. Still, learning-based approaches to accelerate combinatorial optimization often require solving a large number of difficult instances to collect training data, incurring significant computational cost. Existing learning-based methods require training dedicated models for each problem distribution, for each downstream task, severely limiting their scalability and generalization. We introduce Forge: Foundational Optimization Representations from Graph Embeddings, a framework that pre-trains a vector-quantized graph autoencoder on a large, diverse collection of mixed-integer programming (MIP) instances in an unsupervised manner, without relying on optimization solvers or optimal solutions. Vector quantization produces discrete code assignments that serve as a vocabulary for representing optimization instances. We evaluate Forge in both unsupervised and supervised settings. In the unsupervised setting, Forge embeddings effectively cluster unseen instances across problem domains and sizes. In the supervised setting, we fine-tune Forge embeddings and show that a single pre-trained model helps predicting both the integrality gap for cut-generation and variable hints for search guidance across multiple problem and size distributions. In both tasks, we improve the performance of a commercial optimization solver and outperform state-of-the-art learning-based methods. Finally, we open-source our training code, pre-trained Forge weights, and embeddings for multiple MIP distributions to foster further research in representation learning for optimization problems https://skadio.github.io/forge/

Figures

Figures reproduced from arXiv: 2508.20330 by the authors.

Figure 1
Figure 1. FORGE: Our approach for learning MIP embeddings without supervision. Starting with the bipartite representation and its GNN embedding (A-B), FORGE uses a vector quantized graph autoencoder (C-D) to reconstruct node features and edges (E). It is pretrained across a diverse set of problems and sizes to learn generic MIP representations without dependency on optimal solutions. 2 BACKGROUND: MIXED-INTEGER PROGRAMMING Le… view at source ↗
Figure 2
Figure 2. Visualization of MIP embeddings and NMIs from (a) the mean readout in F [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. (A) Supervised fine-tuning flow for FORGE. (B) Distribution of integrality gap across problem types. (C) Triplet generation for search guidance by grouping positive/negative variables. We therefore study two fundamentally different downstream tasks: predicting the integrality gap of a given MIP instance, as also studied in (Li et al., 2025), and predicting variables for search guidance, as also studied in (Han et al… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Gurobi vs. Gurobi + FORGE Pseudo-Cuts. Each subplot shows the primal gap (the lower, the better) averaged across 50 very-hard instances in each problem. relaxation. As mentioned, overestimating the integrality gap (for minimization problems) can lead to suboptimal solu…
Figure 5
Figure 5. Figure 5: Gurobi vs. Gurobi + FORGE Search Guidance. Each subplot shows the primal gap (the lower, the better) averaged across 50 medium instances in each problem. Supervised Fine-Tuning: Given five feasible solutions, variables that never appear in any solution is marked as ‘ne…
Figure 6
Figure 6. Figure 6: PS-Gurobi vs. PS-Gurobi + FORGE Search Guid￾ance. Each subplot shows primal gap (the lower, the better) averaged across 50 medium instances in each problem. We evalaute on the common subset of problems, CA and GIS, used in PS-Gurobi experiments. As shown in [PITH_FULL…
Figure 7
Figure 7. Figure 7: (A) Each node in the bipartite graph representation of the MIP instance is assigned a [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: Visualization of MIP embeddings from strIPlib. F [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]
Figure 9
Figure 9. Figure 9: A (stretch) analogy of King−Men+W oman ≈ Queen for Combinatorial Optimization: V ertex Cover − Set Cover + Bin P acking ≈ Independent Set. The updated Vertex Cover instances are shown in black which move closer to the Maximal Independent Set instances. Observation: In …
Figure 10
Figure 10. Figure 10: A (stretch) analogy of King − M an + W oman ≈ Queen for Combinatorial Optimiza￾tion: Set Cover − V ertex Cover + Independent Set ≈ Bin P acking. The updated Set Cover instances are shown in black that move closer to the Bin Packing instances. Similarly, we further exa…
Figure 11
Figure 11. Figure 11: A (stretch) analogy of King − Men + W oman ≈ Queen for Combinatorial Optimiza￾tion: Independent Set−Bin P acking+Set Cover ≈ V ertex Cover. The updated Independent Set instances are shown in black that move closer to the Minimum Vertex Cover instances. A.6 DETAILS OF …
Figure 12
Figure 12. Figure 12: PS-Gurobi vs. PS-Gurobi + FORGE vs. PS-Gurobi + Random Search Guidance. Each subplot shows primal gap (the lower, the better) averaged across 50 medium instances in each prob￾lem. A.7 DETAILS OF THE TRIPLET LOSS Recall that FORGE generates embedding vectors per instan…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

73 extracted references · 53 canonical work pages

  1. [1]

    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 format.date year duplicate empty "emp...

  2. [2]

    strIPlib: Structured Integer Programming Library

    Michael Bastubbe, Alexander Helber, Lukas Kirchhart, Marco L \"u bbecke, Niklas Rieken, and Jonas Witt. strIPlib: Structured Integer Programming Library . Unpublished, 2025. URL https://striplib.or.rwth-aachen.de

    work page 2025

  3. [3]

    Machine learning for combinatorial optimization: A methodological tour d’horizon

    Yoshua Bengio, Andrea Lodi, and Antoine Prouvost. Machine learning for combinatorial optimization: A methodological tour d’horizon. European Journal of Operational Research, 290 0 (2): 0 405--421, 2021 a . ISSN 0377-2217. doi:https://doi.org/10.1016/j.ejor.2020.07.063. URL https://www.sciencedirect.com/science/article/pii/S0377221720306895

    doi:10.1016/j.ejor.2020.07.063 2021

  4. [4]

    Machine learning for combinatorial optimization: a methodological tour d’horizon

    Yoshua Bengio, Andrea Lodi, and Antoine Prouvost. Machine learning for combinatorial optimization: a methodological tour d’horizon. European Journal of Operational Research, 290 0 (2): 0 405--421, 2021 b

    work page 2021

  5. [5]

    Routefinder: Towards foundation models for vehicle routing problems

    Federico Berto, Chuanbo Hua, Nayeli Gast Zepeda, Andr \'e Hottung, Niels Wouda, Leon Lan, Kevin Tierney, and Jinkyoo Park. Routefinder: Towards foundation models for vehicle routing problems. In ICML 2024 Workshop on Foundation Models in the Wild, 2024

    work page 2024

  6. [6]

    Routefinder: Towards foundation models for vehicle routing problems, 2025

    Federico Berto, Chuanbo Hua, Nayeli Gast Zepeda, André Hottung, Niels Wouda, Leon Lan, Junyoung Park, Kevin Tierney, and Jinkyoo Park. Routefinder: Towards foundation models for vehicle routing problems, 2025. URL https://arxiv.org/abs/2406.15007

    arXiv 2025

  7. [7]

    Towards a generic representation of combinatorial problems for learning-based approaches

    L \'e o Boisvert, H \'e l \`e ne Verhaeghe, and Quentin Cappart. Towards a generic representation of combinatorial problems for learning-based approaches. In International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research, pp.\ 99--108, 2024

    work page 2024

  8. [8]

    Tackling prevalent conditions in unsupervised combinatorial optimization: Cardinality, minimum, covering, and more

    Fanchen Bu, Hyeonsoo Jo, Soo Yong Lee, Sungsoo Ahn, and Kijung Shin. Tackling prevalent conditions in unsupervised combinatorial optimization: Cardinality, minimum, covering, and more. In International Conference on Machine Learning, pp.\ 4696--4729, 2024

    work page 2024

Show all 73 references
  1. [9]

    Learning backdoors for mixed integer linear programs with contrastive learning

    Junyang Cai, Taoan Huang, and Bistra Dilkina. Learning backdoors for mixed integer linear programs with contrastive learning. In European Conference on Artificial Intelligence, volume 392, pp.\ 2418--2425, 2024 a

    2024

  2. [10]

    Balans: Multi-armed bandits-based adaptive large neighborhood search for mixed-integer programming problem

    Junyang Cai, Serdar Kadioglu, and Bistra Dilkina. Balans: Multi-armed bandits-based adaptive large neighborhood search for mixed-integer programming problem. arXiv preprint arXiv:2412.14382, 2024 b

    2024 arXiv

  3. [11]

    Multi-task representation learning for mixed integer linear programming

    Junyang Cai, Taoan Huang, and Bistra Dilkina. Multi-task representation learning for mixed integer linear programming. In Guido Tack (ed.), Integration of Constraint Programming, Artificial Intelligence, and Operations Research, pp.\ 134--151, Cham, 2025 a . Springer Nature Sw...

    2025

  4. [12]

    Balans: Multi-armed bandits-based adaptive large neighborhood search for mixed-integer programming problem

    Junyang Cai, Serdar Kadioglu, and Bistra Dilkina. Balans: Multi-armed bandits-based adaptive large neighborhood search for mixed-integer programming problem. In Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence, IJCAI-25 . International ...

    2025

  5. [13]

    u rk, Taha Varol, Reyhan Aydo g an, and Okan \

    Furkan Cant \"u rk, Taha Varol, Reyhan Aydo g an, and Okan \"O rsan \"O zener. Scalable primal heuristics using graph neural networks for combinatorial optimization. Journal of Artificial Intelligence Research, 80: 0 327--376, 2024

    2024

  6. [14]

    On representing linear programs by graph neural networks

    Ziang Chen, Jialin Liu, Xinshang Wang, and Wotao Yin. On representing linear programs by graph neural networks. In International Conference on Learning Representations, 2023

    2023

  7. [15]

    Rethinking the capacity of graph neural networks for branching strategy

    Ziang Chen, Jialin Liu, Xiaohan Chen, Wang Wang, and Wotao Yin. Rethinking the capacity of graph neural networks for branching strategy. Neural Information Processing Systems, 37: 0 123991--124024, 2024

    2024

  8. [17]

    Augment with care: Contrastive learning for combinatorial problems

    Haonan Duan, Pashootan Vaezipoor, Max B Paulus, Yangjun Ruan, and Chris Maddison. Augment with care: Contrastive learning for combinatorial problems. In International Conference on Machine Learning, pp.\ 5627--5642, 2022

    2022

  9. [18]

    Towards understanding linear word analogies

    Kawin Ethayarajh, David Duvenaud, and Graeme Hirst. Towards understanding linear word analogies. arXiv preprint arXiv:1810.04882, 2018

    2018 arXiv

  10. [19]

    A comprehensive evaluation of contemporary ml-based solvers for combinatorial optimization

    Shengyu Feng, Weiwei Sun, Shanda Li, Ameet Talwalkar, and Yiming Yang. A comprehensive evaluation of contemporary ml-based solvers for combinatorial optimization. arXiv preprint arXiv:2505.16952, 2025

    2025

  11. [20]

    Ferber, Jialin Song, Bistra Dilkina, and Yisong Yue

    Aaron M. Ferber, Jialin Song, Bistra Dilkina, and Yisong Yue. Learning pseudo-backdoors for mixed integer programs. In Integration of Constraint Programming, Artificial Intelligence, and Operations Research, volume 13292, pp.\ 91--102, 2022

    2022

  12. [21]

    Network Design with Applications to Transportation and Logistics

    Teodor Gabriel Crainic, Michel Gendreau, and Bernard Gendron. Network Design with Applications to Transportation and Logistics. Springer, 2021

    2021

  13. [22]

    Exact combinatorial optimization with graph convolutional neural networks

    Maxime Gasse, Didier Ch \'e telat, Nicola Ferroni, Laurent Charlin, and Andrea Lodi. Exact combinatorial optimization with graph convolutional neural networks. Neural Information Processing Systems, 32: 0 15554--15566, 2019

    2019

  14. [23]

    Deep learning in search heuristics

    Nayeli Gast Zepeda, Andr \'e Hottung, and Kevin Tierney. Deep learning in search heuristics. In Handbook of Heuristics, pp.\ 1--18. Springer, 2025

    2025

  15. [24]

    Christophel, Kati Jarck, Thorsten Koch, Jeff Linderoth, Marco L\"ubbecke, Hans D

    Ambros Gleixner, Gregor Hendel, Gerald Gamrath, Tobias Achterberg, Michael Bastubbe, Timo Berthold, Philipp M. Christophel, Kati Jarck, Thorsten Koch, Jeff Linderoth, Marco L\"ubbecke, Hans D. Mittelmann, Derya Ozyurt, Ted K. Ralphs, Domenico Salvagnin, and Yuji Shinano. MIPLI...

    2017

  16. [25]

    Gurobi Optimizer Reference Manual , 2024

    Gurobi Optimization, LLC . Gurobi Optimizer Reference Manual , 2024. URL https://www.gurobi.com

    2024

  17. [26]

    Hamilton, Zhitao Ying, and Jure Leskovec

    William L. Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs. In Neural Information Processing Systems, pp.\ 1024--1034, 2017

    2017

  18. [27]

    A gnn-guided predict-and-search framework for mixed-integer linear programming

    Qingyu Han, Linxin Yang, Qian Chen, Xiang Zhou, Dong Zhang, Akang Wang, Ruoyu Sun, and Xiaodong Luo. A gnn-guided predict-and-search framework for mixed-integer linear programming. In International Conference on Learning Representations, 2023

    2023

  19. [28]

    Learning to search in branch and bound algorithms

    He He, Hal Daume III, and Jason M Eisner. Learning to search in branch and bound algorithms. In Z. Ghahramani, M. Welling, C. Cortes, N. Lawrence, and K.Q. Weinberger (eds.), Advances in Neural Information Processing Systems, volume 27. Curran Associates, Inc., 2014 a . URL ht...

    2014

  20. [29]

    Learning to search in branch and bound algorithms

    He He, Hal Daume III, and Jason M Eisner. Learning to search in branch and bound algorithms. Advances in neural information processing systems, 27, 2014 b

    2014

  21. [30]

    Automatic milp solver configuration by learning problem similarities

    Abdelrahman Hosny and Sherief Reda. Automatic milp solver configuration by learning problem similarities. Annals of Operations Research, 339 0 (1): 0 909--936, 2024

    2024

  22. [31]

    Neural large neighborhood search for routing problems

    Andr \'e Hottung and Kevin Tierney. Neural large neighborhood search for routing problems. Artificial Intelligence, 313: 0 103786, 2022

    2022

  23. [32]

    Ferber, Yuandong Tian, Bistra Dilkina, and Benoit Steiner

    Taoan Huang, Aaron M. Ferber, Yuandong Tian, Bistra Dilkina, and Benoit Steiner. Searching large neighborhoods for integer linear programs with contrastive learning. In International Conference on Machine Learning, volume 202, pp.\ 13869--13890, 2023

    2023

  24. [33]

    Distributional miplib: a multi-domain library for advancing ml-guided milp methods

    Weimin Huang, Taoan Huang, Aaron M Ferber, and Bistra Dilkina. Distributional miplib: a multi-domain library for advancing ml-guided milp methods. arXiv preprint arXiv:2406.06954, 2024

    2024 arXiv

  25. [34]

    ISAC - instance-specific algorithm configuration

    Serdar Kadioglu, Yuri Malitsky, Meinolf Sellmann, and Kevin Tierney. ISAC - instance-specific algorithm configuration. In Helder Coelho, Rudi Studer, and Michael J. Wooldridge (eds.), ECAI 2010 - 19th European Conference on Artificial Intelligence, Lisbon, Portugal, August 16-...

    2010 doi

  26. [35]

    Algorithm selection and scheduling

    Serdar Kadioglu, Yuri Malitsky, Ashish Sabharwal, Horst Samulowitz, and Meinolf Sellmann. Algorithm selection and scheduling. In Jimmy Ho - Man Lee (ed.), Principles and Practice of Constraint Programming - CP 2011 - 17th International Conference, CP 2011, Perugia, Italy, Sept...

    2011 doi

  27. [36]

    Incorporating variance in impact-based search

    Serdar Kadioglu, Eoin O’Mahony, Philippe Refalo, and Meinolf Sellmann. Incorporating variance in impact-based search. In International Conference on Principles and Practice of Constraint Programming, pp.\ 470--477. Springer, 2011 b

    2011

  28. [37]

    Non-model-based search guidance for set partitioning problems

    Serdar Kadioglu, Yuri Malitsky, and Meinolf Sellmann. Non-model-based search guidance for set partitioning problems. In J \" o rg Hoffmann and Bart Selman (eds.), Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence, July 22-26, 2012, Toronto, Ontario, Ca...

    2012

  29. [38]

    Learning a reactive restart strategy to improve stochastic search

    Serdar Kadioglu, Meinolf Sellmann, and Markus Wagner. Learning a reactive restart strategy to improve stochastic search. In International conference on learning and intelligent optimization, pp.\ 109--123. Springer, 2017

    2017

  30. [39]

    Integrating optimized item selection with active learning for continuous exploration in recommender systems

    Serdar Kad o g lu, Bernard Kleynhans, and Xin Wang. Integrating optimized item selection with active learning for continuous exploration in recommender systems. Annals of Mathematics and Artificial Intelligence, 92 0 (6): 0 1585--1607, 2024

    2024

  31. [40]

    Erdos goes neural: an unsupervised learning framework for combinatorial optimization on graphs

    Nikolaos Karalias and Andreas Loukas. Erdos goes neural: an unsupervised learning framework for combinatorial optimization on graphs. Neural Information Processing Systems, 33: 0 6659--6672, 2020

    2020

  32. [41]

    Configuring mixed-integer programming solvers for large-scale instances

    Robin Kemminer, Jannick Lange, Jens Peter Kempkes, Kevin Tierney, and Dimitri Wei . Configuring mixed-integer programming solvers for large-scale instances. In Operations Research Forum, volume 5 Issue 2, pp.\ 48. Springer, 2024

    2024

  33. [42]

    Learning to branch in mixed integer programming

    Elias Khalil, Pierre Le Bodic, Le Song, George Nemhauser, and Bistra Dilkina. Learning to branch in mixed integer programming. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 30 Issue 1, 2016

    2016

  34. [43]

    Khalil, Bistra Dilkina, George L

    Elias B. Khalil, Bistra Dilkina, George L. Nemhauser, Shabbir Ahmed, and Yufen Shao. Learning to run heuristics in tree search. In International Joint Conference on Artificial Intelligence, pp.\ 659--666, 2017

    2017

  35. [44]

    Autoregressive image generation using residual quantization

    Doyup Lee, Chiheon Kim, Saehoon Kim, Minsu Cho, and Wook-Shin Han. Autoregressive image generation using residual quantization. In Conference on Computer Vision and Pattern Recognition, pp.\ 11513--11522, 2022

    2022

  36. [45]

    Towards foundation models for mixed integer linear programming

    Sirui Li, Janardhan Kulkarni, Ishai Menache, Cathy Wu, and Beibin Li. Towards foundation models for mixed integer linear programming. In International Conference on Learning Representations, 2025

    2025

  37. [46]

    Di Liberto, Serdar Kadioglu, Kevin Leo, and Yuri Malitsky

    Giovanni M. Di Liberto, Serdar Kadioglu, Kevin Leo, and Yuri Malitsky. DASH: dynamic approach for switching heuristics. Eur. J. Oper. Res., 248 0 (3): 0 943--953, 2016. doi:10.1016/j.ejor.2015.08.018. URL https://doi.org/10.1016/j.ejor.2015.08.018

    2016 doi

  38. [47]

    On learning and branching: a survey

    Andrea Lodi and Giulia Zarpellon. On learning and branching: a survey. Top, 25 0 (2): 0 207--236, 2017

    2017

  39. [48]

    Attacking shortest paths by cutting edges

    Benjamin A Miller, Zohair Shafi, Wheeler Ruml, Yevgeniy Vorobeychik, Tina Eliassi-Rad, and Scott Alfeld. Attacking shortest paths by cutting edges. ACM Transactions on Knowledge Discovery from Data, 18 0 (2): 0 1--42, 2023

    2023

  40. [49]

    Solving mixed integer programs using neural networks

    Vinod Nair, Sergey Bartunov, Felix Gimeno, Ingrid Von Glehn, Pawel Lichocki, Ivan Lobov, Brendan O'Donoghue, Nicolas Sonnerat, Christian Tjandraatmadja, Pengming Wang, et al. Solving mixed integer programs using neural networks. arXiv preprint arXiv:2012.13349, 2020

    2012 arXiv

  41. [50]

    Learning to cut by looking ahead: Cutting plane selection via imitation learning

    Max B Paulus, Giulia Zarpellon, Andreas Krause, Laurent Charlin, and Chris Maddison. Learning to cut by looking ahead: Cutting plane selection via imitation learning. In International conference on machine learning, pp.\ 17584--17600. PMLR, 2022

    2022

  42. [51]

    A diffusion model framework for unsupervised neural combinatorial optimization

    Sebastian Sanokowski, Sepp Hochreiter, and Sebastian Lehner. A diffusion model framework for unsupervised neural combinatorial optimization. In International Conference on Machine Learning, pp.\ 43346--43367, 2024

    2024

  43. [52]

    Deep reinforcement learning for instance-specific algorithm configuration

    Elias Schede, Moritz Seiler, Kevin Tierney, and Heike Trautmann. Deep reinforcement learning for instance-specific algorithm configuration. In Proceedings of the Genetic and Evolutionary Computation Conference, pp.\ 1190--1198, 2025

    2025

  44. [53]

    Facenet: A unified embedding for face recognition and clustering

    Florian Schroff, Dmitry Kalenichenko, and James Philbin. Facenet: A unified embedding for face recognition and clustering. In IEEE Conference on Computer Vision and Pattern Recognition, pp.\ 815--823, 2015

    2015

  45. [54]

    Accelerated discovery of set cover solutions via graph neural networks

    Zohair Shafi, Benjamin A Miller, Tina Eliassi-Rad, and Rajmonda S Caceres. Accelerated discovery of set cover solutions via graph neural networks. In International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research, pp.\ 1...

    2025

  46. [55]

    A general large neighborhood search framework for solving integer linear programs

    Jialin Song, Yisong Yue, Bistra Dilkina, et al. A general large neighborhood search framework for solving integer linear programs. Neural Information Processing Systems, 33: 0 20012--20023, 2020

    2020

  47. [56]

    Mabwiser: A parallelizable contextual multi-armed bandit library for python

    Emily Strong, Bernard Kleynhans, and Serdar Kadioglu. Mabwiser: A parallelizable contextual multi-armed bandit library for python. In 31st IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2019, Portland, OR, USA, November 4-6, 2019 , pp.\ 909--914. IE...

    2019

  48. [57]

    MABWiser: parallelizable contextual multi-armed bandits

    Emily Strong, Bernard Kleynhans, and Serdar Kadioglu. MABWiser: parallelizable contextual multi-armed bandits. Int. J. Artif. Intell. Tools, 30 0 (4): 0 2150021:1--2150021:19, 2021. doi:10.1142/S0218213021500214. URL https://doi.org/10.1142/S0218213021500214

    2021 doi

  49. [58]

    Reinforcement learning for integer programming: Learning to cut

    Yunhao Tang, Shipra Agrawal, and Yuri Faenza. Reinforcement learning for integer programming: Learning to cut. In International conference on machine learning, pp.\ 9367--9376. PMLR, 2020

    2020

  50. [59]

    One model, any CSP: graph neural networks as fast global search heuristics for constraint satisfaction

    Jan T \" o nshoff, Berke Kisin, Jakob Lindner, and Martin Grohe. One model, any CSP: graph neural networks as fast global search heuristics for constraint satisfaction. In International Joint Conference on Artificial Intelligence, pp.\ 4280--4288, 2023

    2023

  51. [60]

    Neural discrete representation learning

    Aaron Van Den Oord, Oriol Vinyals, et al. Neural discrete representation learning. Advances in neural information processing systems, 30, 2017

    2017

  52. [61]

    Understanding how dimension reduction tools work: an empirical approach to deciphering t-sne, umap, trimap, and pacmap for data visualization

    Yingfan Wang, Haiyang Huang, Cynthia Rudin, and Yaron Shaposhnik. Understanding how dimension reduction tools work: an empirical approach to deciphering t-sne, umap, trimap, and pacmap for data visualization. Journal of Machine Learning Research, 22 0 (201): 0 1--73, 2021

    2021

  53. [62]

    Learning large neighborhood search policy for integer programming

    Yaoxin Wu, Wen Song, Zhiguang Cao, and Jie Zhang. Learning large neighborhood search policy for integer programming. Neural Information Processing Systems, 34: 0 30075--30087, 2021

    2021

  54. [63]

    Hoos, and Kevin Leyton-Brown

    Lin Xu, Frank Hutter, Holger H. Hoos, and Kevin Leyton-Brown. Satzilla: Portfolio-based algorithm selection for sat. Journal of Artificial Intelligence Research, 32: 0 565--606, 2008

    2008

  55. [64]

    Vqgraph: Rethinking graph representation space for bridging gnns and mlps

    Ling Yang, Ye Tian, Minkai Xu, Zhongyi Liu, Shenda Hong, Wei Qu, Wentao Zhang, Bin Cui, Muhan Zhang, and Jure Leskovec. Vqgraph: Rethinking graph representation space for bridging gnns and mlps. In International Conference on Learning Representations, 2024

    2024

  56. [65]

    Are graph neural networks optimal approximation algorithms? Neural Information Processing Systems, 37: 0 73124--73181, 2024

    Morris Yau, Nikolaos Karalias, Eric Lu, Jessica Xu, and Stefanie Jegelka. Are graph neural networks optimal approximation algorithms? Neural Information Processing Systems, 37: 0 73124--73181, 2024

    2024

  57. [66]

    Parbalans: Parallel multi-armed bandits-based adaptive large neighborhood search

    Alican Yilmaz, Junyang Cai, Serdar Kadioglu, and Bistra Dilkina. Parbalans: Parallel multi-armed bandits-based adaptive large neighborhood search. arXiv preprint arXiv:2508.06736, 2025

    2025 arXiv

  58. [67]

    Vector-quantized image modeling with improved vqgan

    Jiahui Yu, Xin Li, Jing Yu Koh, Han Zhang, Ruoming Pang, James Qin, Alexander Ku, Yuanzhong Xu, Jason Baldridge, and Yonghui Wu. Vector-quantized image modeling with improved vqgan. In International Conference on Learning Representations, 2022

    2022

  59. [68]

    Soundstream: An end-to-end neural audio codec

    Neil Zeghidour, Alejandro Luebs, Ahmed Omran, Jan Skoglund, and Marco Tagliasacchi. Soundstream: An end-to-end neural audio codec. IEEE/ACM Transactions on Audio, Speech, and Language Processing, 30: 0 495--507, 2021

    2021

  60. [69]

    A survey for solving mixed integer programming via machine learning

    Jiayi Zhang, Chang Liu, Xijun Li, Hui-Ling Zhen, Mingxuan Yuan, Yawen Li, and Junchi Yan. A survey for solving mixed integer programming via machine learning. Neurocomputing, 519: 0 205--217, 2023

    2023

  61. [70]

    Towards omni-generalizable neural methods for vehicle routing problems

    Jianan Zhou, Yaoxin Wu, Wen Song, Zhiguang Cao, and Jie Zhang. Towards omni-generalizable neural methods for vehicle routing problems. In International Conference on Machine Learning, pp.\ 42769--42789, 2023

    2023

  62. [71]

    Learning from labeled and unlabeled data with label propagation

    Xiaojin Zhu and Zoubin Ghahramani. Learning from labeled and unlabeled data with label propagation. ProQuest number: information to all users, 2002

    2002

  63. [72]

    @esa (Ref

    \@ifxundefined[1] #1\@undefined \@firstoftwo \@secondoftwo \@ifnum[1] #1 \@firstoftwo \@secondoftwo \@ifx[1] #1 \@firstoftwo \@secondoftwo [2] @ #1 \@temptokena #2 #1 @ \@temptokena \@ifclassloaded agu2001 natbib The agu2001 class already includes natbib coding, so you should ...

  64. [73]

    \@lbibitem[] @bibitem@first@sw\@secondoftwo \@lbibitem[#1]#2 \@extra@b@citeb \@ifundefined br@#2\@extra@b@citeb \@namedef br@#2 \@nameuse br@#2\@extra@b@citeb \@ifundefined b@#2\@extra@b@citeb @num @parse #2 @tmp #1 NAT@b@open@#2 NAT@b@shut@#2 \@ifnum @merge>\@ne @bibitem@firs...

  65. [74]

    https://www.gurobi.com

    @open @close @open @close and [1] URL: #1 \@ifundefined chapter * \@mkboth \@ifxundefined @sectionbib * \@mkboth * \@mkboth\@gobbletwo \@ifclassloaded amsart * \@ifclassloaded amsbook * \@ifxundefined @heading @heading NAT@ctr thebibliography [1] @ \@biblabel @NAT@ctr \@bibset...

    2024 arXiv

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.