Title: Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learning
Venue: NeurIPS 2025
Accepted: yes
Keywords: Neural Combinatorial Optimiztion

Large Language Model

Vehicle Routing Problem
Abstract: Neural Combinatorial Optimization (NCO) has emerged as a promising learning-based paradigm for addressing Vehicle Routing Problems (VRPs) by minimizing the need for extensive manual engineering. While existing NCO methods, trained on small-scale instances (e.g., 100 nodes), have demonstrated considerable success on problems of similar scale, their performance significantly degrades when applied to large-scale scenarios. This degradation arises from the distributional shift between training and testing data, rendering policies learned on small instances ineffective for larger problems. To overcome this limitation, we introduce a novel learning framework driven by Large Language Models (LLMs). This framework learns a projection between the training and testing distributions, which is then deployed to enhance the scalability of the NCO model. Notably, unlike prevailing techniques that necessitate joint training with the neural network, our approach operates exclusively during the inference phase, obviating the need for model retraining. Extensive experiments demonstrate that our method enables a backbone model (trained on 100-node instances) to achieve superior performance on large-scale Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) of up to 100K nodes from diverse distributions. The source code can be found in https://github.com/CIAM-Group/TTPL.


Peer reviews:
comments: SUMMARY:
This paper proposes a projection learning framework TTPL based on Large Language Model (LLM). By optimizing the projection strategy and multi-view decision fusion (MVDF) technology, the generalization ability of the neural combinatorial optimization model in large-scale vehicle routing problems (VRP) is significantly improved.

STRENGTHS AND WEAKNESSES:
Strengths:
1.After conducting sufficient ablation experiments and general experiments, I believe the MVDF you proposed has independent significance.
2.The algorithm in this paper successfully solves the problems of TSP-100K and CVRP-100K in an extremely short time, which shows the potential of LLM.
Weaknesses:
1.Although many comparative experiments have been conducted, as far as I know, this is not the first work to apply LLM to the solution of TSP problems. Perhaps, you should compare the results of your model with theirs. For example, the citation [46] in your article. Meanwhile, in the "Related Work" section, if possible, some introductions to the LLM-based generalization method should also be added.
2.You only used GPT-4o-mini and did not use other LLMS. The generalization of the method might be insufficient.
3.I don't know whether the LLM also uses your training data as the pre-training corpus. This will raise a question: Is the excellent performance of your model due to the good performance of the LLM itself or the effectiveness of the solution you proposed? This will greatly affect the assessment of innovation.

QUESTIONS:
Mainly see weaknesses.
Small issues:
1.What is the full name of AHD? Please give its full name when first appeared in the text.

LIMITATIONS:
Yes.
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 2
DATE: 2025-06-12

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses the significant challenge of generalization in Neural Combinatorial Optimization (NCO) for Vehicle Routing Problems (VRPs). While NCO models perform well on problem instances of similar scale to their training data (typically small instances like 100 nodes), their performance degrades significantly when applied to larger-scale problems due to a distributional shift between training and testing data.\n\nTo overcome this limitation, the paper introduces a novel learning framework called Test-Time Projection Learning (TTPL). This framework is designed to learn a projection between the training and testing data distributions, which is then used to enhance the scalability and generalization of existing NCO models.\n\nThe key contributions of this work are:\n\nA novel learning framework driven by Large Language Models (LLMs): This framework learns a projection that bridges the distributional gap between small-scale training data and large-scale test data.\n\nInference-only approach: Unlike many existing techniques that require joint training with the neural network, TTPL operates exclusively during the inference phase. This means it can be applied to pre-trained NCO models without needing to retrain them, making it highly flexible and practical.\n\nEnhanced scalability for NCO models: Extensive experiments demonstrate that TTPL significantly improves the performance of backbone NCO models (trained on 100-node instances) when applied to larger-scale Traveling Salesman Problems (TSP) and Capacitated Vehicle Routing Problems (CVRP) up to 1000 nodes,\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nQuality: The paper presents a novel and well-motivated approach to address a crucial problem in NCO: generalization to larger problem scales. The proposed Test-Time Projection Learning (TTPL) framework is innovative, particularly its inference-only nature. The experimental evaluation is comprehensive, testing TTPL on both TSP and CVRP benchmarks across various scales (from 100-node training to 1000-node testing). The results clearly demonstrate the effectiveness of TTPL in improving the generalization ability of backbone NCO models, outperforming strong baselines.\n\nClarity: The paper is well-written and easy to understand. The problem of distributional shift and generalization in NCO is clearly articulated. The TTPL framework, including the role of LLMs and the projection learning mechanism, is explained logically. Figures (e.g., Figure 1 illustrating the framework) are helpful in conveying complex ideas. The experimental setup, including baseline models and evaluation metrics, is clearly described.\n\nSignificance: The problem of generalization across different scales is a major hurdle for the practical deployment of NCO models. By proposing an effective inference-only solution, this paper makes a highly significant contribution. TTPL's ability to enhance pre-trained models without retraining is a practical advantage that can save significant computational resources and make NCO more accessible for real-world large-scale problems. The use of LLMs to drive this projection learning is also significant, exploring a novel application area for LLMs in optimization.\n\nOriginality: The core idea of \"test-time projection learning\" to address generalization in NCO is highly original. The framework's unique characteristic of operating solely during inference to bridge the distributional gap, and the novel integration of LLMs to learn this projection, are innovative contributions that distinguish this work from previous efforts in NCO generalization (which often involve data augmentation or architectural changes during training).\n\nWeaknesses:\n\nLLM Role and Transparency: While the paper states LLMs are used to drive the learning of projection strategies, the exact mechanism and specific LLM (or family of LLMs) used for this \"projection learning\" could be more transparently detailed. The justification for LLM usage in the declaration section (\"designing projection strategies\") is somewhat vague. More specifics on the LLM's architecture within the framework, its training (if any specific to TTPL), and how it concretely learns and applies the projection would strengthen this aspect.\n\nTheoretical Guarantees/Insights: The paper primarily focuses on empirical results. While impressive, a deeper theoretical analysis into why TTPL works, or under what conditions the projection learning is guaranteed to succeed, would significantly strengthen the foundational understanding. For instance, what properties of the LLM or the projection mechanism enable it to effectively bridge distributional shifts?\n\nComputational Overhead of LLM/TTPL: While TTPL avoids NCO model retraining, the inference-time projection learning itself might introduce a computational overhead. A more detailed analysis of the time and resource costs associated with the LLM-driven projection learning component during inference, especially for very large instances, would be beneficial for practical considerations.\n\nGeneralization to Other Combinatorial Problems: The method is evaluated on TSP and CVRP. While these are fundamental VRPs, discussing how TTPL might extend to other combinatorial optimization problems (e.g., Orienteering Problem, Prize Collecting TSP, other routing problems with complex constraints) would broaden its perceived applicability.\n\nQUESTIONS:\nQuestion: The paper states that LLMs drive the learning of projection strategies. Could the authors provide a more in-depth explanation of how the LLM specifically learns this projection? What kind of prompts are used? What is the input/output format for the LLM during this process? Is the LLM fine-tuned, or is it used as a zero-shot/few-shot learner? What is the architecture of this \"projection learning\" component?\nA clear and comprehensive explanation of the LLM's internal mechanism for projection learning would significantly improve the Quality and Clarity ratings.\n\nQuestion: While TTPL avoids retraining the NCO backbone, it introduces an additional \"test-time projection learning\" step. Could the authors provide a more detailed breakdown of the computational overhead (inference time and memory) introduced by the TTPL framework itself, distinct from the backbone NCO model's inference? This is particularly relevant for large-scale instances (e.g., N=1000).\nSuggestion: Include a table or graph comparing the inference time of the backbone model alone versus the backbone + TTPL, perhaps also breaking down the TTPL component's time. This would offer a more complete picture of the practical efficiency trade-offs.\n\nQuestion: The method shows strong generalization on TSP and CVRP to larger scales. How do the authors anticipate TTPL performing on other, more complex Combinatorial Optimization Problems (COPs) or more constrained VRP variants (e.g., VRP with time windows, multiple depots, pick-up and delivery, heterogeneous fleets)?\nSuggestion: Discuss the potential applicability and limitations of TTPL for a broader range of COPs. A brief qualitative discussion on how the framework might need to be adapted (e.g., new feature representations, different projection strategies) for problems with more complex constraints would be valuable.\n\nQuestion: Are there specific parameters or hyper-parameters within the projection learning component (e.g., related to the LLM's usage, projection dimension, or learning rate for the projection) that significantly influence TTPL's performance? How robust is TTPL to variations in these parameters?\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes Test-Time Projection Learning (TTPL), an LLM-driven evolutionary framework that automatically designs geometric projection functions to reconcile the distribution gap between small-scale training instances (≈100 nodes) and large-scale inference instances (up to 100K nodes) in Vehicle Routing Problems (VRPs). A complementary Multi-View Decision Fusion (MVDF) module ensembles multiple transformed views of each K-nearest-neighbour sub-graph to further stabilise node selection. According to the manuscript, the combined TTPL-MVDF system reduces optimality gaps on large-scale Traveling Salesman Problem (TSP) and Capacitated VRP (CVRP) benchmarks by 60~88% relative to the best competing constructive methods.\n\nSTRENGTHS AND WEAKNESSES:\nStrength:\n1. (Quality) The manuscript includes abundant experimental workloads. It evaluates extensive synthetic and real-world data across five instance sizes per problem. And the ablations isolate the benefit of TTPL and MVDF individually.\n2. (Significance) The introduction of TTPL is a strong advancement in neural combinatorial optimization, improving model generalization on large-scale VRPs without requiring retraining, making it practical for real-world applications.\n3. (Originality) The application of LLMs to design the projection strategies during the inference phase is a novel and promising approach, which is a unique contribution to the field.\n\nWeaknesses:\n1. (Quality) Lack of Theoretical Insights/Interpretability: The paper focuses primarily on experimental results and does not provide any deep theoretical analysis of why the projection strategy works or how it guarantees better performance.\n2. (Quality) Lack of Statistical Significance: The paper does not provide error bars or other statistical measures to indicate the variability or reliability of the results, which would be crucial for validating the robustness of the method.\n3. (Clarity) Some key information is missed: Some critical loss functions and evaluation metrics should be further discussed in the main text. \n4. (Quality) Although results are promising, the paper does not fully address the computational cost, especially in terms of the time required for the LLM optimization process.\n5. (Significance) The paper mentions the slow convergence of the LLM optimization phase, which is a significant practical limitation for deploying this method in real-time applications.\n6. (Clarity) Several typos (e.g., “MVFD” spelled “MVDF”).\n\nQUESTIONS:\n1. It is recommended to provide a more detailed theoretical explanation or interpretability experiment of why the proposed projection strategy improves model generalization in large-scale VRPs.\n2. It is suggested to report mean ±σ over multiple random seeds or instance batches, and add paired-t confidence intervals for key gaps.\n3. The loss functions and the evaluation metrics (e.g., RWD) used in this work needs to be discussed in detail in the main text.\n4. It could be helpful if the author(s) explore ways to speed up the convergence of the LLM optimization phase to improve the practical applicability of TTPL in time-sensitive settings.\n5. Can the authors elaborate on how their LLM-driven method compares to other projection methods (e.g., INViT, LEHD) in terms of computational efficiency, especially for real-time large-scale problems?\n6. Given that TTPL relies on prompt-based LLM outputs, have the authors evaluated the consistency of generated strategies across different LLMs, prompts, or random seeds? Understanding this would help assess the method’s reproducibility and reliability.\n7. Could the authors explain whether the framework could be generalized to other domains beyond VRPs, such as other NP-hard problems?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

comments: SUMMARY:
The paper proposes a framework to use LLMs to generate projection  strategies  that enhance model generalization for solving optimization problems.

STRENGTHS AND WEAKNESSES:
**Strengths:**

The proposed framework is interesting and seems to work well in practice.

**Weaknesses:**

1. The study lacks substantive novelty, with the core value of the methodology appearing to be primarily attributable to EoH [1].
2. The idea of mimicking evolutionary computation via LLMs is not new. In fact, most (all?) crossover and mutation operators are from EoH.
3. It remains unclear what specifically constitutes the NCO model in fitness evaluation and whether the selection thereof significantly impacts the results.
4. The geometric transformations in Multi-View Decision Fusion are not clearly described.
5. The adoption of LEHD [2] as the base model, while employing POMO and other NCO methods as baselines, appears somewhat inappropriate in the experimental design.

[1] Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model, ICML 2024.

[2] Neural combinatorial optimization with heavy decoder: Toward large scale generalization, NeurIPS 2023.

QUESTIONS:
1. What are geometric transformations in Multi-View Decision Fusion?
2. Is the projection strategy a normalization operation?

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 2
IMPACT: 2
ORIGINALITY: 2
DATE: 2025-07-02