Title: MTL-KD: Multi-Task Learning Via Knowledge Distillation for Generalizable Neural Vehicle Routing Solver
Venue: NeurIPS 2025
Accepted: yes
Keywords: Neural Combinatorial Optimization

Vehicle Routing Problem

Multi-Task Learning
Abstract: Multi-Task Learning (MTL) in Neural Combinatorial Optimization (NCO) is a promising approach for training a unified model capable of solving multiple Vehicle Routing Problem (VRP) variants. 
However, existing Reinforcement Learning (RL)-based multi-task methods can only train light decoder models on small-scale problems, exhibiting limited generalization ability when solving large-scale problems. 
To overcome this limitation, this work introduces a novel multi-task learning method driven by knowledge distillation (MTL-KD), which enables efficient training of heavy decoder models with strong generalization ability. 
The proposed MTL-KD method transfers policy knowledge from multiple distinct RL-based single-task models to a single heavy decoder model, facilitating label-free training and effectively improving the model's generalization ability across diverse tasks. 
In addition, we introduce a flexible inference strategy termed Random Reordering Re-Construction (R3C), which is specifically adapted for diverse VRP tasks and further boosts the performance of the multi-task model. 
Experimental results on 6 seen and 10 unseen VRP variants with up to 1,000 nodes indicate that our proposed method consistently achieves superior performance on both uniform and real-world benchmarks, demonstrating robust generalization abilities. The code is available at [https://github.com/CIAM-Group/MTLKD](https://github.com/CIAM-Group/MTLKD).


Peer reviews:
comments: SUMMARY:
The paper presents an extension of Neural Combinatorial Optimization (NCO).

The proposed approach considers smaller instances and multiple smaller and easier models trained on the smaller problems.

The smaller models are trained first (pre-trained models).

Then the final model is trained in a way similar to multi-task learning, where the largest model has an extended loss function that includes all the instances and the associated small pre-trained models, at the same time.

STRENGTHS AND WEAKNESSES:
Strengths :
1. From the experimental session, it is possible to see that the method produces better solutions
2. The paper describes the protocol for training that is relatively intuitive
3. relatively extensive experiments and comparison with other baselines

Weaknesses
1. The method uses many known results (MTL, NCO, knowledge distillation), and does not appear to be very innovative

QUESTIONS:
The smaller models represent different types of problems; for example, VRP with or without Time windows. 

Why should the method take advantage of the instances of other types of problems?

LIMITATIONS:
The approach does not seem to have any criticality, so there does not seem to be a necessity for a limitation session.  

The authors describe the limitations of the work in the last session.
TITLE: Official Review
CLARITY: 2
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-06-30

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a knowledge distillation-based multi-task VRP solver (MTL-KD) aimed at addressing the generalization limitations of existing methods when handling large-scale VRP problems. MTL-KD employs a lightweight encoder–heavy decoder (LEHD) architecture to train multiple teacher models and transfers their knowledge to a decoder model through knowledge distillation, enabling efficient label-free training and improved generalization. In addition, the paper introduces a Random Reordering Reconstruction (R3C) strategy to further enhance model performance.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n•\tQuality: The paper is technically sound and addresses an interesting and practical problem. It introduces a knowledge distillation-based approach to tackle the challenges of training models under multi-variant conditions and limited data availability. Experimental results demonstrate that the proposed MTL-KD model achieves strong performance on training tasks, unseen tasks, and real-world datasets, validating its effectiveness and practicality. Moreover, the authors conduct extensive comparative and ablation studies to verify the model's design.\n•\tClarity: The paper is well-structured, and the writing is fluent. The experimental results and conclusions are clearly articulated. Detailed descriptions of the model architecture and experimental setup help readers understand the main contributions. In addition, the use of well-designed diagrams enhances the clarity of the proposed architecture and the applied optimizations.\n•\tSignificance: The findings of this study are significant for both the VRP and Neural Combinatorial Optimization (NCO) communities. The proposed MTL-KD model demonstrates advantages in both performance and generalization, offering a novel approach to solving large-scale VRP problems.\n•\tOriginality: The paper applies knowledge distillation techniques to the VRP domain and introduces a novel Random Reordering Reconstruction (R3C) strategy, showcasing a degree of innovation.\nWeaknesses\n•\tThe encoder architecture used in the current model appears relatively simplistic for capturing the intricate relational structures present in large-scale VRP problems. This might hinder the model’s overall representational capacity and performance.\n•\tThe description of the training process for the student model is somewhat unclear, which may lead to confusion regarding its training effectiveness. Additionally, the text in the ablation study figures is too small and difficult to read.\nSuggestions\n•\tConsider exploring more powerful encoder designs, such as graph neural network-based encoders, to improve scalability and performance.\n•\tImprove the clarity of the figures, particularly in the ablation study section, and provide a clearer explanation of the student model training process.\nOverall, this paper demonstrates notable strengths in terms of quality, clarity, significance, and originality. However, there are still some areas that require improvement.\n\nQUESTIONS:\n1.\tThe training process of the student model, particularly how it distills and incorporates knowledge from the teacher models, is not clearly described. The current explanation may leave readers uncertain about the effectiveness and implementation details of the knowledge distillation mechanism. Try to make the training procedure of the student model more explicit in both the textual description and the framework figure.\n2.\tThe encoder used in the current model may not fully capture the complex spatial and relational structures present in large-scale VRP instances. This may limit the model’s expressiveness and scalability. Have the authors considered employing graph-based encoder architectures (e.g., GNNs) to better model the underlying structure of the problem? A discussion or experiment in this direction could enhance the technical depth and applicability of the approach.\n3.\tSome figures, especially in the ablation study section, contain text that is too small to read clearly. This affects the readability and interpretability of the experimental results. Improve the visual clarity of these figures would make the paper more accessible and reader-friendly.\n\nLIMITATIONS:\nThe paper does not explicitly discuss the computational overhead introduced by simultaneously training multiple teacher models alongside the student model. This process is likely to incur significant training costs, which may limit the practicality of the approach in resource-constrained settings. It would be helpful for the authors to provide a discussion on whether this overhead is acceptable. Including such analysis would improve the transparency and practical relevance of the method.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nIn their work, the authors attempt to mitigate the issue of poor generalization in multi-task learning for vehicle routing problems. They propose the use of knowledge distillation to train a heavy decoder model using the outputs of individual single-task models, each trained for a VRP variant, and then applying a loss on the difference in the outputted probability distributions. Additionally, to escape local optimas they propose the use of Random Reordering Re-Construction (R3C), which divides routes into smaller sub-routes and shuffles the internal order while respecting the problem constraints. They then study the generalization ability of the model on unseen VRP variants and unseen problem scales.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nThe knowledge distillation approach does seem to greatly improve generalization ability in most scenarios with good ablation experiments. Additionally, the R3C method is relatively novel and well founded in avoiding the local optimization minimas.\n\nWeaknesses:\n\nI do have a few concerns with the paper namely:\n* The authors argue that this is a label free method, however this is not entirely correct since the teachers need to be trained on \"labeled\" data. It is more of a labeled training delegation.\n* Some key baselines are omitted from the results. Namely [1, 2] are referenced in the paper but never compared against, despite being state-of-the-art multi-task VRP neural solvers and reporting better results (I could not find any in-text citation for [1] in the main paper either, only its reference in the bibliography).\n* The novelty of knowledge distillation for VRP solvers is questionable since previous papers such as [3], which the author references, have previously shown the effectiveness of this approach in enhancing model generalization abilities. There was no actual discussion or comparison to it from a methodological perspective. \n* There are some issues with formatting, but this is minor, specifically in table 1 for VRPL MT POMO, the number is unintelligible.\n\n[1] Han Li, Fei Liu, Zhi Zheng, Yu Zhang, and Zhenkun Wang. Cada: Cross-problem routing297 solver with constraint-aware dual-attention. arXiv preprint arXiv:2412.00346, 2024.\n[2] Federico Berto, Chuanbo Hua, Nayeli Gast Zepeda, André Hottung, Niels Wouda, Leon Lan,249 Junyoung Park, Kevin Tierney, and Jinkyoo Park. Routefinder: Towards foundation models for250 vehicle routing problems. arXiv preprint arXiv:2406.15007, 2024.\n[3] Jieyi Bi, Yining Ma, Jiahai Wang, Zhiguang Cao, Jinbiao Chen, Yuan Sun, and Yeow Meng252 Chee. Learning generalizable models for vehicle routing problems via knowledge distillation.253 Advances in Neural Information Processing Systems, 35:31226–31238, 2022.\n\nQUESTIONS:\n1. What seperates your method from a direct application of [3] to MT Solvers?\n2. Although not necessary for this paper, have you tried seeing if the method generalizes to the dynamic constraint problems as well?\n3. Have you tried different sized subsets for R3C?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a multi-task learning method called MTL-KD that enables efficient training of heavy decoder models with strong generalization ability for solving diverse Vehicle Routing Problem (VRP) variants. The main works include 1)  label-free training of heavy decoder models through knowledge distillation from multiple RL-based single-task teacher models; 2) a Random Reordering Reconstruction (R3C) strategy to further enhance the performance of the multi-task model; Experimental results show superior performance of the MTL-KD model on both seen and unseen VRP tasks, as well as real-world datasets, exhibiting good scale generalization ability and outperforming existing multi-task VRP models.\n\nSTRENGTHS AND WEAKNESSES:\nStrength: \nThe paper is well written and relatively easy to follow. The idea of a generic solver for several of VRP variants is well motivated. The use of knowledge distillation for training the proposed model makes good sense. \n\nWeakness: \n1) the introduction fails to explain why the neural solvers are preferred compared to the traditional VRP solvers. As was shown in the paper and the results by the current SOTA neural VRP solvers, the gap of these results to the best heuristic/OR methods is still quite large (sometime as high as 5% or higher). Even for large scale instances, the metaheuristics have proven to be very effective. What are the clear benefits of neural VRP solvers? It is not clearly stated in the paper. \n\n2) the proposed method uses a Random Reordering Reconstruction (R3C) strategy to further improve the performance. However, this would make the proposed method similar to an iterative improvement method widely used in metaheuristics. Therefore, a comparison with the state of the art metaheuristic for VRP should be necessary.\n\nQUESTIONS:\nWhat are the clear benefits of neural VRP solvers in comparison with traditional VRP methods from OR community (e.g. branch-and-price-and-cut methods) and metaheuristics (e.g. genetic algorithm, VLNS, etc.)? \n\nWhy is the Random Reordering Reconstruction (R3C) strategy used? Does this imply weak performance by the proposed neural solver?\n\nLIMITATIONS:\nThe motivation of using neural solver for VRP could be better explained and the use of iterative procedure of R3C needs further justification  and the fairness of comparisons with other methods is questionable as many other methods do not use local search style improvement procedure.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-04"}