A Reinforcement Learning Framework for Scalable Partitioning and Optimization of Large-Scale Capacitated Vehicle Routing Problems

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper proposes a SPORL Scalable Partitioning and Optimization via Reinforcement Learning framework designed specifically for large-scale CVRP. It decomposes the original instance into subproblems using a reinforcement learning-based partitioner, followed by parallel solving with either learned or classical solvers. Experimental results on benchmark datasets show that SPORL performs well. The paper has a complete structure, clear logic, and clear description, making it a good paper.  The paper can improve its quality in the following aspects：

1. The abstract section can be further refined, and it is recommended to revise and improve it;
2. Please clearly state the main contributions of this paper in the introduction section;
3. Tables 1-4 provide a comparison of the calculation results of different methods. The algorithm proposed in this paper does not always perform the best. It is recommended to provide a detailed discussion and analysis of the reasons behind this table.
4. Can you provide more explanation and analysis on the computation time and workload in Table 5? This is not sufficient in the now paper, and it is also a crucial issue in the CVRP;
5. In section 7, the discussion has not been fully developed, and more points can be discussed. The analysis of the computational complexity and computation time of the algorithm after incorporating reinforcement learning strategies, as well as the key points affecting large-scale problems, and how to further improve them, are not detailed in the analysis of the actual problem computation results provided. I suggest further improving this part, as the quality of the paper will be higher.
6. The performance characteristics of the algorithm are not consistent on different datasets. It is recommended that the author provide time-sharing or annotations to obtain more convincing conclusions.

Comments on the Quality of English Language

The language is generally good, and some content can be further refined and improved.

Author Response

We sincerely thank the reviewer for their thoughtful and constructive feedback. We are encouraged by their overall positive assessment and have carefully addressed each point to improve the manuscript's quality. Our detailed responses and revisions are outlined below.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The authors present a very interesting article related to the partitioning and optimization of capacitated vehicle routing problems. This is an important topic, and considering the content of the article, the topic is well-formulated and well-chosen.
In the introduction, the authors clearly demonstrate their reasons for pursuing this topic, referencing carefully selected literature sources at this stage. They indicate in the introduction what exactly they have demonstrated through their research and experiments.
The next chapter is "Related Works." Although it is not quite comprehensive, and I would suggest expanding it, the sources cited there are well-chosen.
The authors present the problem in detail and effectively, using appropriate mathematical formulas. The mathematical formulas presented clearly illustrate the analytical part of the problem and facilitate the understanding and verification of the information provided by the authors later.
In particular, I am referring to the key chapter 4: Reinforcement Learning for the Partitioning Problem. The authors provide a detailed overview of the learning and optimization process, including the general solution assumptions.
The most interesting information can be found in the Results chapter, where the authors' results are presented. Documentation with tables and Russian facilitates their understanding and verification.
It's worth noting that the authors created a separate chapter where they delve into the results and present discussions. This is, unfortunately, not uncommon among authors of scientific publications.
In my opinion, this article is worthy of publication in the Journal.

Author Response

We are deeply grateful to the reviewer for their exceptionally positive and thoughtful assessment of our work. We are delighted that they found the topic well-chosen, the problem effectively presented, and the results chapter particularly interesting and clear.

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1. Some references are quite old. The paper should be empowered by more references of the last 3-5 years.
2. The experimental setup process should be better presented. You should describe with more detail all the process to improve readability and quality.
3. "The training process was conducted on a single NVIDIA RTX 3090 GPU using synthetically
   generated datasets to ensure robustness across varying problem sizes": could you please explain and clarify this point? 
4. How did you select the "CVRPLIB benchmark datasets" compared potentially to other related datasets? Please provide some information.
5. Figure 3 should be explained in a more comprehensive way. 
6. The Discussion section should include more information about the superiority of the proposed solution compared to other state-of-art models. 

Comments on the Quality of English Language

-

Author Response

We thank the reviewers for their insightful and constructive comments, which have helped us significantly improve the quality of our manuscript. We have carefully addressed all the points raised.

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Here are some comments that will help you improve your paper:

1. Please state clearly paper's contribution at the end of Introduction.
2. Address your motivation more clearly.
3. How many nodes is an average for real world applications? Which firm could benefit of the proposed?
4. You implemented greedy method in the proposed algorithm, but there are not explained reasons. Furthermore, greedy methods are not mentioned in the Abstract and/or title.
5. What is the point of repeating data from [34]. It is just more pages of already published. Consider deleting Tables 1- 4. When you delete these tables, there is almost empty section of Results. Try to add or present more details of the results for this manuscript. 
6. The key problem that should be addressed here is the novelty. It should be easy to understand to reader. 
7. Error: "5. Results 6. Experiments" (empty section)
8. Some of paragraphs are not in designated margins. 

Kind regards

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 5 Report

Comments and Suggestions for Authors

SPORL tackles an important problem, that scales CVRP solutions to 1000+ nodes through hierarchical decomposition. The core concept has merit, but the paper needs significant work before it’s ready for publication in a journal. The theoretical foundations are thin, key experiments are missing, and several technical claims don’t hold up under scrutiny.

 

1. Where’s the math backing this up? You jump straight into coding details without explaining why your MDP formulation makes sense. What guarantees can you offer about partition quality? How much do we lose by breaking the problem apart?
2. The paper claims averaging node embeddings captures “structural properties”but never explain what that actually means. Sure, Table 5 shows it helps, but why does it help? What specific features does this capture that other approaches miss?
3. Not comparing with Hou et al. [28] is a major red flag since they tackle the exact same problem. “Code wasn’t available”won’t fly, either implement their approach or at least discuss their reported numbers.
4. AM and POMO getting 200%+ gaps? That screams implementation error, not method failure. These are established techniques that shouldn’t fail this badly.
5. You talk about handling large instances but never analyze computational complexity. What’s the actual runtime scaling? Memory usage?
6. Just minimizing distance ignores crucial factors like balanced partitions and vehicle utilization. This probably explains why performance tanks on larger instances (that 31% gap on X-n1001-k43 isn’t great). The author should consider a multi-objective reward that actually captures partition quality.
7. How exactly do you enforce fleet constraints during partitioning? What if a partition violates capacity? You mention masking but never explain the mechanism.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have successfully addressed the reviewer comments.

Author Response

Thank you for your confirming that our revisions have addressed the reviewers' comments satisfactorily. We appreciate the positive feedback.

Reviewer 4 Report

Comments and Suggestions for Authors

Please enhance you manuscript with following details:

1. It is not clear what is actually the proposed method. Is it SPRL - LKH3, AM or POMO? It cannot be all, because it is not focused and unique algorithm. This should be improved. 
2. Tables 1-4 should be rearranged to emphasize the proposed method over others. The comparative methods should be cited in their columns, not in the table caption, because it can confuse readers.
3. Response to Comment 3 should be integrated in the manuscript, at lease with one sentences and examples of companies that could use it.
4. Figure 3 is too small to observe details. It should be magnified.

Kind regards

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 5 Report

Comments and Suggestions for Authors

This paper can be accepted

Author Response

Thank you very much for your positive decision to accept our manuscript for publication. We are delighted with this news.

We appreciate the opportunity to publish our work and look forward to the next steps.

Sincerely,